diff options
| author | marha <marha@users.sourceforge.net> | 2012-04-10 11:41:26 +0200 |
|---|---|---|
| committer | marha <marha@users.sourceforge.net> | 2012-04-10 11:41:26 +0200 |
| commit | 67326634496ef21b4acbf4cef2f05040d34aef9b (patch) | |
| tree | f19fba7c7b691e44cd97482644e383e09ab98c49 /openssl/crypto/ec | |
| parent | c6f80401dc533b04341afe8d596960d1bc25efce (diff) | |
| download | vcxsrv-67326634496ef21b4acbf4cef2f05040d34aef9b.tar.gz vcxsrv-67326634496ef21b4acbf4cef2f05040d34aef9b.tar.bz2 vcxsrv-67326634496ef21b4acbf4cef2f05040d34aef9b.zip | |
Update to openssl-1.0.1
Diffstat (limited to 'openssl/crypto/ec')
25 files changed, 7834 insertions, 974 deletions
diff --git a/openssl/crypto/ec/Makefile b/openssl/crypto/ec/Makefile index db380ed16..f85fc845c 100644 --- a/openssl/crypto/ec/Makefile +++ b/openssl/crypto/ec/Makefile @@ -19,11 +19,15 @@ APPS= LIB=$(TOP)/libcrypto.a LIBSRC= ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c\ ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c\ - ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c + ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c \ + ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c \ + ecp_oct.c ec2_oct.c ec_oct.c LIBOBJ= ec_lib.o ecp_smpl.o ecp_mont.o ecp_nist.o ec_cvt.o ec_mult.o\ ec_err.o ec_curve.o ec_check.o ec_print.o ec_asn1.o ec_key.o\ - ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o + ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o \ + ecp_nistp224.o ecp_nistp256.o ecp_nistp521.o ecp_nistputil.o \ + ecp_oct.o ec2_oct.o ec_oct.o SRC= $(LIBSRC) @@ -87,6 +91,14 @@ ec2_mult.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec2_mult.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec2_mult.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ec2_mult.o: ../../include/openssl/symhacks.h ec2_mult.c ec_lcl.h +ec2_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ec2_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ec2_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ec2_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ec2_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ec2_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec2_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ec2_oct.o: ../../include/openssl/symhacks.h ec2_oct.c ec_lcl.h ec2_smpl.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ec2_smpl.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ec2_smpl.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h @@ -174,6 +186,14 @@ ec_mult.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec_mult.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec_mult.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ec_mult.o: ../../include/openssl/symhacks.h ec_lcl.h ec_mult.c +ec_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ec_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ec_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ec_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ec_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ec_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ec_oct.o: ../../include/openssl/symhacks.h ec_lcl.h ec_oct.c ec_pmeth.o: ../../e_os.h ../../include/openssl/asn1.h ec_pmeth.o: ../../include/openssl/asn1t.h ../../include/openssl/bio.h ec_pmeth.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h @@ -221,6 +241,18 @@ ecp_nist.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ecp_nist.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ecp_nist.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ecp_nist.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_nist.c +ecp_nistp224.o: ../../include/openssl/opensslconf.h ecp_nistp224.c +ecp_nistp256.o: ../../include/openssl/opensslconf.h ecp_nistp256.c +ecp_nistp521.o: ../../include/openssl/opensslconf.h ecp_nistp521.c +ecp_nistputil.o: ../../include/openssl/opensslconf.h ecp_nistputil.c +ecp_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ecp_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ecp_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ecp_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ecp_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ecp_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ecp_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ecp_oct.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_oct.c ecp_smpl.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ecp_smpl.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ecp_smpl.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h diff --git a/openssl/crypto/ec/ec.h b/openssl/crypto/ec/ec.h index ee7078130..9d01325af 100644 --- a/openssl/crypto/ec/ec.h +++ b/openssl/crypto/ec/ec.h @@ -151,7 +151,24 @@ const EC_METHOD *EC_GFp_mont_method(void); */ const EC_METHOD *EC_GFp_nist_method(void); +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 +/** Returns 64-bit optimized methods for nistp224 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp224_method(void); + +/** Returns 64-bit optimized methods for nistp256 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp256_method(void); + +/** Returns 64-bit optimized methods for nistp521 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp521_method(void); +#endif +#ifndef OPENSSL_NO_EC2M /********************************************************************/ /* EC_METHOD for curves over GF(2^m) */ /********************************************************************/ @@ -161,6 +178,8 @@ const EC_METHOD *EC_GFp_nist_method(void); */ const EC_METHOD *EC_GF2m_simple_method(void); +#endif + /********************************************************************/ /* EC_GROUP functions */ @@ -282,6 +301,7 @@ int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, co */ int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); +#ifndef OPENSSL_NO_EC2M /** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b * \param group EC_GROUP object * \param p BIGNUM with the polynomial defining the underlying field @@ -301,7 +321,7 @@ int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, c * \return 1 on success and 0 if an error occured */ int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); - +#endif /** Returns the number of bits needed to represent a field element * \param group EC_GROUP object * \return number of bits needed to represent a field element @@ -342,7 +362,7 @@ int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx); * \return newly created EC_GROUP object with the specified parameters */ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); - +#ifndef OPENSSL_NO_EC2M /** Creates a new EC_GROUP object with the specified parameters defined * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b) * \param p BIGNUM with the polynomial defining the underlying field @@ -352,7 +372,7 @@ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM * \return newly created EC_GROUP object with the specified parameters */ EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); - +#endif /** Creates a EC_GROUP object with a curve specified by a NID * \param nid NID of the OID of the curve name * \return newly created EC_GROUP object with specified curve or NULL @@ -481,7 +501,7 @@ int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, */ int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, const BIGNUM *x, int y_bit, BN_CTX *ctx); - +#ifndef OPENSSL_NO_EC2M /** Sets the affine coordinates of a EC_POINT over GF2m * \param group underlying EC_GROUP object * \param p EC_POINT object @@ -514,7 +534,7 @@ int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, */ int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, const BIGNUM *x, int y_bit, BN_CTX *ctx); - +#endif /** Encodes a EC_POINT object to a octet string * \param group underlying EC_GROUP object * \param p EC_POINT object @@ -653,9 +673,11 @@ int EC_GROUP_have_precompute_mult(const EC_GROUP *group); /* EC_GROUP_get_basis_type() returns the NID of the basis type * used to represent the field elements */ int EC_GROUP_get_basis_type(const EC_GROUP *); +#ifndef OPENSSL_NO_EC2M int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k); int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, unsigned int *k2, unsigned int *k3); +#endif #define OPENSSL_EC_NAMED_CURVE 0x001 @@ -689,11 +711,21 @@ typedef struct ec_key_st EC_KEY; #define EC_PKEY_NO_PARAMETERS 0x001 #define EC_PKEY_NO_PUBKEY 0x002 +/* some values for the flags field */ +#define EC_FLAG_NON_FIPS_ALLOW 0x1 +#define EC_FLAG_FIPS_CHECKED 0x2 + /** Creates a new EC_KEY object. * \return EC_KEY object or NULL if an error occurred. */ EC_KEY *EC_KEY_new(void); +int EC_KEY_get_flags(const EC_KEY *key); + +void EC_KEY_set_flags(EC_KEY *key, int flags); + +void EC_KEY_clear_flags(EC_KEY *key, int flags); + /** Creates a new EC_KEY object using a named curve as underlying * EC_GROUP object. * \param nid NID of the named curve. @@ -799,6 +831,15 @@ int EC_KEY_generate_key(EC_KEY *key); */ int EC_KEY_check_key(const EC_KEY *key); +/** Sets a public key from affine coordindates performing + * neccessary NIST PKV tests. + * \param key the EC_KEY object + * \param x public key x coordinate + * \param y public key y coordinate + * \return 1 on success and 0 otherwise. + */ +int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y); + /********************************************************************/ /* de- and encoding functions for SEC1 ECPrivateKey */ @@ -926,6 +967,7 @@ void ERR_load_EC_strings(void); /* Error codes for the EC functions. */ /* Function codes. */ +#define EC_F_BN_TO_FELEM 224 #define EC_F_COMPUTE_WNAF 143 #define EC_F_D2I_ECPARAMETERS 144 #define EC_F_D2I_ECPKPARAMETERS 145 @@ -968,6 +1010,15 @@ void ERR_load_EC_strings(void); #define EC_F_EC_GFP_MONT_FIELD_SQR 132 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135 +#define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225 +#define EC_F_EC_GFP_NISTP224_POINTS_MUL 228 +#define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226 +#define EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE 230 +#define EC_F_EC_GFP_NISTP256_POINTS_MUL 231 +#define EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES 232 +#define EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE 233 +#define EC_F_EC_GFP_NISTP521_POINTS_MUL 234 +#define EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES 235 #define EC_F_EC_GFP_NIST_FIELD_MUL 200 #define EC_F_EC_GFP_NIST_FIELD_SQR 201 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202 @@ -1010,6 +1061,7 @@ void ERR_load_EC_strings(void); #define EC_F_EC_KEY_NEW 182 #define EC_F_EC_KEY_PRINT 180 #define EC_F_EC_KEY_PRINT_FP 181 +#define EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES 229 #define EC_F_EC_POINTS_MAKE_AFFINE 136 #define EC_F_EC_POINT_ADD 112 #define EC_F_EC_POINT_CMP 113 @@ -1040,6 +1092,9 @@ void ERR_load_EC_strings(void); #define EC_F_I2D_ECPKPARAMETERS 191 #define EC_F_I2D_ECPRIVATEKEY 192 #define EC_F_I2O_ECPUBLICKEY 151 +#define EC_F_NISTP224_PRE_COMP_NEW 227 +#define EC_F_NISTP256_PRE_COMP_NEW 236 +#define EC_F_NISTP521_PRE_COMP_NEW 237 #define EC_F_O2I_ECPUBLICKEY 152 #define EC_F_OLD_EC_PRIV_DECODE 222 #define EC_F_PKEY_EC_CTRL 197 @@ -1052,12 +1107,15 @@ void ERR_load_EC_strings(void); /* Reason codes. */ #define EC_R_ASN1_ERROR 115 #define EC_R_ASN1_UNKNOWN_FIELD 116 +#define EC_R_BIGNUM_OUT_OF_RANGE 144 #define EC_R_BUFFER_TOO_SMALL 100 +#define EC_R_COORDINATES_OUT_OF_RANGE 146 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117 #define EC_R_DECODE_ERROR 142 #define EC_R_DISCRIMINANT_IS_ZERO 118 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119 #define EC_R_FIELD_TOO_LARGE 143 +#define EC_R_GF2M_NOT_SUPPORTED 147 #define EC_R_GROUP2PKPARAMETERS_FAILURE 120 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 121 #define EC_R_INCOMPATIBLE_OBJECTS 101 @@ -1092,6 +1150,7 @@ void ERR_load_EC_strings(void); #define EC_R_UNKNOWN_GROUP 129 #define EC_R_UNKNOWN_ORDER 114 #define EC_R_UNSUPPORTED_FIELD 131 +#define EC_R_WRONG_CURVE_PARAMETERS 145 #define EC_R_WRONG_ORDER 130 #ifdef __cplusplus diff --git a/openssl/crypto/ec/ec2_mult.c b/openssl/crypto/ec/ec2_mult.c index e12b9b284..26f4a783f 100644 --- a/openssl/crypto/ec/ec2_mult.c +++ b/openssl/crypto/ec/ec2_mult.c @@ -71,6 +71,8 @@ #include "ec_lcl.h" +#ifndef OPENSSL_NO_EC2M + /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective * coordinates. @@ -384,3 +386,5 @@ int ec_GF2m_have_precompute_mult(const EC_GROUP *group) { return ec_wNAF_have_precompute_mult(group); } + +#endif diff --git a/openssl/crypto/ec/ec2_oct.c b/openssl/crypto/ec/ec2_oct.c new file mode 100644 index 000000000..f1d75e5dd --- /dev/null +++ b/openssl/crypto/ec/ec2_oct.c @@ -0,0 +1,407 @@ +/* crypto/ec/ec2_oct.c */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The software is originally written by Sheueling Chang Shantz and + * Douglas Stebila of Sun Microsystems Laboratories. + * + */ +/* ==================================================================== + * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ + +#include <openssl/err.h> + +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_EC2M + +/* Calculates and sets the affine coordinates of an EC_POINT from the given + * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. + * Note that the simple implementation only uses affine coordinates. + * + * The method is from the following publication: + * + * Harper, Menezes, Vanstone: + * "Public-Key Cryptosystems with Very Small Key Lengths", + * EUROCRYPT '92, Springer-Verlag LNCS 658, + * published February 1993 + * + * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe + * the same method, but claim no priority date earlier than July 29, 1994 + * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). + */ +int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) + { + BN_CTX *new_ctx = NULL; + BIGNUM *tmp, *x, *y, *z; + int ret = 0, z0; + + /* clear error queue */ + ERR_clear_error(); + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0) ? 1 : 0; + + BN_CTX_start(ctx); + tmp = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + z = BN_CTX_get(ctx); + if (z == NULL) goto err; + + if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; + if (BN_is_zero(x)) + { + if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; + } + else + { + if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; + if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; + if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; + if (!BN_GF2m_add(tmp, x, tmp)) goto err; + if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) + { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) + { + ERR_clear_error(); + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + } + else + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); + goto err; + } + z0 = (BN_is_odd(z)) ? 1 : 0; + if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; + if (z0 != y_bit) + { + if (!BN_GF2m_add(y, y, x)) goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +/* Converts an EC_POINT to an octet string. + * If buf is NULL, the encoded length will be returned. + * If the length len of buf is smaller than required an error will be returned. + */ +size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y, *yxi; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) + { + /* encodes to a single 0 octet */ + if (buf != NULL) + { + if (len < 1) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + + /* ret := required output buffer length */ + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) + { + if (len < ret) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + + buf[0] = form; + if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) + { + if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; + if (BN_is_odd(yxi)) buf[0]++; + } + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) + { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return 0; + } + + +/* Converts an octet string representation to an EC_POINT. + * Note that the simple implementation only uses affine coordinates. + */ +int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *yxi; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) + { + if (len != 1) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + if (len != enc_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) goto err; + if (BN_ucmp(x, &group->field) >= 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) + { + if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; + } + else + { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; + if (BN_ucmp(y, &group->field) >= 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) + { + if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; + if (y_bit != BN_is_odd(yxi)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } +#endif diff --git a/openssl/crypto/ec/ec2_smpl.c b/openssl/crypto/ec/ec2_smpl.c index 03deae667..e0e59c7d8 100644 --- a/openssl/crypto/ec/ec2_smpl.c +++ b/openssl/crypto/ec/ec2_smpl.c @@ -71,10 +71,20 @@ #include "ec_lcl.h" +#ifndef OPENSSL_NO_EC2M + +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + const EC_METHOD *EC_GF2m_simple_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gf2m_simple_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_characteristic_two_field, ec_GF2m_simple_group_init, ec_GF2m_simple_group_finish, @@ -93,9 +103,7 @@ const EC_METHOD *EC_GF2m_simple_method(void) 0 /* get_Jprojective_coordinates_GFp */, ec_GF2m_simple_point_set_affine_coordinates, ec_GF2m_simple_point_get_affine_coordinates, - ec_GF2m_simple_set_compressed_coordinates, - ec_GF2m_simple_point2oct, - ec_GF2m_simple_oct2point, + 0,0,0, ec_GF2m_simple_add, ec_GF2m_simple_dbl, ec_GF2m_simple_invert, @@ -118,6 +126,7 @@ const EC_METHOD *EC_GF2m_simple_method(void) 0 /* field_set_to_one */ }; return &ret; +#endif } @@ -405,340 +414,6 @@ int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_ return ret; } - -/* Calculates and sets the affine coordinates of an EC_POINT from the given - * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. - * Note that the simple implementation only uses affine coordinates. - * - * The method is from the following publication: - * - * Harper, Menezes, Vanstone: - * "Public-Key Cryptosystems with Very Small Key Lengths", - * EUROCRYPT '92, Springer-Verlag LNCS 658, - * published February 1993 - * - * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe - * the same method, but claim no priority date earlier than July 29, 1994 - * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). - */ -int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { - BN_CTX *new_ctx = NULL; - BIGNUM *tmp, *x, *y, *z; - int ret = 0, z0; - - /* clear error queue */ - ERR_clear_error(); - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - y_bit = (y_bit != 0) ? 1 : 0; - - BN_CTX_start(ctx); - tmp = BN_CTX_get(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - z = BN_CTX_get(ctx); - if (z == NULL) goto err; - - if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; - if (BN_is_zero(x)) - { - if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; - } - else - { - if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; - if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; - if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; - if (!BN_GF2m_add(tmp, x, tmp)) goto err; - if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) - { - unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) - { - ERR_clear_error(); - ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else - ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); - goto err; - } - z0 = (BN_is_odd(z)) ? 1 : 0; - if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; - if (z0 != y_bit) - { - if (!BN_GF2m_add(y, y, x)) goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - -/* Converts an EC_POINT to an octet string. - * If buf is NULL, the encoded length will be returned. - * If the length len of buf is smaller than required an error will be returned. - */ -size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - size_t ret; - BN_CTX *new_ctx = NULL; - int used_ctx = 0; - BIGNUM *x, *y, *yxi; - size_t field_len, i, skip; - - if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); - goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { - /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - buf[0] = 0; - } - return 1; - } - - - /* ret := required output buffer length */ - field_len = (EC_GROUP_get_degree(group) + 7) / 8; - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - goto err; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - used_ctx = 1; - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - - buf[0] = form; - if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (BN_is_odd(yxi)) buf[0]++; - } - - i = 1; - - skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(x, buf + i); - i += skip; - if (i != 1 + field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { - skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(y, buf + i); - i += skip; - } - - if (i != ret) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - - err: - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return 0; - } - - -/* Converts an octet string representation to an EC_POINT. - * Note that the simple implementation only uses affine coordinates. - */ -int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - point_conversion_form_t form; - int y_bit; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y, *yxi; - size_t field_len, enc_len; - int ret = 0; - - if (len == 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - form = buf[0]; - y_bit = form & 1; - form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (form == 0) - { - if (len != 1) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - return EC_POINT_set_to_infinity(group, point); - } - - field_len = (EC_GROUP_get_degree(group) + 7) / 8; - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - if (len != enc_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; - - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (y_bit != BN_is_odd(yxi)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); - goto err; - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - /* Computes a + b and stores the result in r. r could be a or b, a could be b. * Uses algorithm A.10.2 of IEEE P1363. */ @@ -1040,3 +715,5 @@ int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, { return BN_GF2m_mod_div(r, a, b, &group->field, ctx); } + +#endif diff --git a/openssl/crypto/ec/ec_ameth.c b/openssl/crypto/ec/ec_ameth.c index c00f7d746..83909c185 100644 --- a/openssl/crypto/ec/ec_ameth.c +++ b/openssl/crypto/ec/ec_ameth.c @@ -651,6 +651,7 @@ const EVP_PKEY_ASN1_METHOD eckey_asn1_meth = ec_copy_parameters, ec_cmp_parameters, eckey_param_print, + 0, int_ec_free, ec_pkey_ctrl, diff --git a/openssl/crypto/ec/ec_asn1.c b/openssl/crypto/ec/ec_asn1.c index ae5553985..175eec534 100644 --- a/openssl/crypto/ec/ec_asn1.c +++ b/openssl/crypto/ec/ec_asn1.c @@ -83,7 +83,7 @@ int EC_GROUP_get_basis_type(const EC_GROUP *group) /* everything else is currently not supported */ return 0; } - +#ifndef OPENSSL_NO_EC2M int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) { if (group == NULL) @@ -101,7 +101,6 @@ int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) return 1; } - int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, unsigned int *k2, unsigned int *k3) { @@ -124,7 +123,7 @@ int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, return 1; } - +#endif /* some structures needed for the asn1 encoding */ @@ -340,6 +339,12 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) } } else /* nid == NID_X9_62_characteristic_two_field */ +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else { int field_type; X9_62_CHARACTERISTIC_TWO *char_two; @@ -419,6 +424,7 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) } } } +#endif ok = 1; @@ -456,6 +462,7 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) goto err; } } +#ifndef OPENSSL_NO_EC2M else /* nid == NID_X9_62_characteristic_two_field */ { if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) @@ -464,7 +471,7 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) goto err; } } - +#endif len_1 = (size_t)BN_num_bytes(tmp_1); len_2 = (size_t)BN_num_bytes(tmp_2); @@ -775,8 +782,13 @@ static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) /* get the field parameters */ tmp = OBJ_obj2nid(params->fieldID->fieldType); - if (tmp == NID_X9_62_characteristic_two_field) +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else { X9_62_CHARACTERISTIC_TWO *char_two; @@ -862,6 +874,7 @@ static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GF2m(p, a, b, NULL); } +#endif else if (tmp == NID_X9_62_prime_field) { /* we have a curve over a prime field */ @@ -1065,6 +1078,7 @@ EC_GROUP *d2i_ECPKParameters(EC_GROUP **a, const unsigned char **in, long len) if ((group = ec_asn1_pkparameters2group(params)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_PKPARAMETERS2GROUP_FAILURE); + ECPKPARAMETERS_free(params); return NULL; } diff --git a/openssl/crypto/ec/ec_curve.c b/openssl/crypto/ec/ec_curve.c index 23274e403..c72fb2697 100644 --- a/openssl/crypto/ec/ec_curve.c +++ b/openssl/crypto/ec/ec_curve.c @@ -3,7 +3,7 @@ * Written by Nils Larsch for the OpenSSL project. */ /* ==================================================================== - * Copyright (c) 1998-2004 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -72,6 +72,7 @@ #include "ec_lcl.h" #include <openssl/err.h> #include <openssl/obj_mac.h> +#include <openssl/opensslconf.h> typedef struct { int field_type, /* either NID_X9_62_prime_field or @@ -703,6 +704,8 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } }; +#ifndef OPENSSL_NO_EC2M + /* characteristic two curves */ static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } _EC_SECG_CHAR2_113R1 = { @@ -1300,7 +1303,7 @@ static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } { 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, /* seed */ 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD, - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, 0x07, 0x01,0x08,0xB3,0x9E,0x77,0xC4,0xB1,0x08,0xBE,0xD9, /* a */ @@ -1817,103 +1820,128 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } 0xBA,0xFC,0xA7,0x5E } }; +#endif + typedef struct _ec_list_element_st { int nid; const EC_CURVE_DATA *data; + const EC_METHOD *(*meth)(void); const char *comment; } ec_list_element; static const ec_list_element curve_list[] = { - /* prime field curves */ + /* prime field curves */ /* secg curves */ - { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, "SECG/WTLS curve over a 112 bit prime field"}, - { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, "SECG curve over a 112 bit prime field"}, - { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, "SECG curve over a 128 bit prime field"}, - { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, "SECG curve over a 128 bit prime field"}, - { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, "SECG curve over a 160 bit prime field"}, - { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, "SECG curve over a 160 bit prime field"}, - { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, "SECG/WTLS curve over a 160 bit prime field"}, + { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field" }, + { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ - { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, "SECG curve over a 192 bit prime field"}, - { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, "SECG curve over a 224 bit prime field"}, - { NID_secp224r1, &_EC_NIST_PRIME_224.h, "NIST/SECG curve over a 224 bit prime field"}, - { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, "SECG curve over a 256 bit prime field"}, + { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, + { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" }, +#else + { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, +#endif + { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ - { NID_secp384r1, &_EC_NIST_PRIME_384.h, "NIST/SECG curve over a 384 bit prime field"}, - { NID_secp521r1, &_EC_NIST_PRIME_521.h, "NIST/SECG curve over a 521 bit prime field"}, + { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" }, +#else + { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, +#endif /* X9.62 curves */ - { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, "NIST/X9.62/SECG curve over a 192 bit prime field"}, - { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, "X9.62 curve over a 192 bit prime field"}, - { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, "X9.62 curve over a 192 bit prime field"}, - { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, "X9.62/SECG curve over a 256 bit prime field"}, + { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, + { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" }, +#else + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, +#endif +#ifndef OPENSSL_NO_EC2M /* characteristic two field curves */ /* NIST/SECG curves */ - { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, "SECG curve over a 113 bit binary field"}, - { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, "SECG curve over a 113 bit binary field"}, - { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, "SECG/WTLS curve over a 131 bit binary field"}, - { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, "SECG curve over a 131 bit binary field"}, - { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, "SECG curve over a 163 bit binary field"}, - { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, "NIST/SECG curve over a 163 bit binary field" }, - { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, "SECG curve over a 193 bit binary field"}, - { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, "SECG curve over a 193 bit binary field"}, - { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, "SECG curve over a 239 bit binary field"}, - { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, "NIST/SECG curve over a 571 bit binary field" }, - { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, "NIST/SECG curve over a 571 bit binary field" }, + { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field" }, + { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field" }, + { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field" }, + { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field" }, + { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field" }, + { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field" }, + { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field" }, /* X9.62 curves */ - { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, "X9.62 curve over a 176 bit binary field"}, - { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, "X9.62 curve over a 208 bit binary field"}, - { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, "X9.62 curve over a 272 bit binary field"}, - { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, "X9.62 curve over a 304 bit binary field"}, - { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, "X9.62 curve over a 359 bit binary field"}, - { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, "X9.62 curve over a 368 bit binary field"}, - { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, "X9.62 curve over a 431 bit binary field"}, + { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field" }, + { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field" }, + { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field" }, + { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field" }, + { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field" }, + { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field" }, + { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field" }, /* the WAP/WTLS curves * [unlike SECG, spec has its own OIDs for curves from X9.62] */ - { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, "WTLS curve over a 113 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, "NIST/SECG/WTLS curve over a 163 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, "SECG curve over a 113 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, "X9.62 curve over a 163 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, "SECG/WTLS curve over a 112 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, "SECG/WTLS curve over a 160 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, "WTLS curve over a 112 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, "WTLS curve over a 160 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, "NIST/SECG/WTLS curve over a 233 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, "NIST/SECG/WTLS curve over a 233 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, "WTLS curvs over a 224 bit prime field"}, + { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, +#endif + { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field" }, +#ifndef OPENSSL_NO_EC2M + { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, +#endif + { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curvs over a 224 bit prime field" }, +#ifndef OPENSSL_NO_EC2M /* IPSec curves */ - { NID_ipsec3, &_EC_IPSEC_155_ID3.h, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n""\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, - { NID_ipsec4, &_EC_IPSEC_185_ID4.h, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n""\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, + { NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, + { NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, +#endif }; #define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element)) -static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) +static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) { EC_GROUP *group=NULL; EC_POINT *P=NULL; BN_CTX *ctx=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; + BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; int ok=0; int seed_len,param_len; + const EC_METHOD *meth; + const EC_CURVE_DATA *data; const unsigned char *params; if ((ctx = BN_CTX_new()) == NULL) @@ -1922,10 +1950,11 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } + data = curve.data; seed_len = data->seed_len; param_len = data->param_len; - params = (const unsigned char *)(data+1); /* skip header */ - params += seed_len; /* skip seed */ + params = (const unsigned char *)(data+1); /* skip header */ + params += seed_len; /* skip seed */ if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL)) || !(a = BN_bin2bn(params+1*param_len, param_len, NULL)) @@ -1935,7 +1964,17 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } - if (data->field_type == NID_X9_62_prime_field) + if (curve.meth != 0) + { + meth = curve.meth(); + if (((group = EC_GROUP_new(meth)) == NULL) || + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) + { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } + else if (data->field_type == NID_X9_62_prime_field) { if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { @@ -1943,6 +1982,7 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } } +#ifndef OPENSSL_NO_EC2M else /* field_type == NID_X9_62_characteristic_two_field */ { if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) @@ -1951,20 +1991,21 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } } +#endif if ((P = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } - + if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL)) || !(y = BN_bin2bn(params+4*param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; } - if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) + if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; @@ -2025,7 +2066,7 @@ EC_GROUP *EC_GROUP_new_by_curve_name(int nid) for (i=0; i<curve_list_length; i++) if (curve_list[i].nid == nid) { - ret = ec_group_new_from_data(curve_list[i].data); + ret = ec_group_new_from_data(curve_list[i]); break; } diff --git a/openssl/crypto/ec/ec_cvt.c b/openssl/crypto/ec/ec_cvt.c index d45640bab..bfcbab35f 100644 --- a/openssl/crypto/ec/ec_cvt.c +++ b/openssl/crypto/ec/ec_cvt.c @@ -78,7 +78,32 @@ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM const EC_METHOD *meth; EC_GROUP *ret; +#if defined(OPENSSL_BN_ASM_MONT) + /* + * This might appear controversial, but the fact is that generic + * prime method was observed to deliver better performance even + * for NIST primes on a range of platforms, e.g.: 60%-15% + * improvement on IA-64, ~25% on ARM, 30%-90% on P4, 20%-25% + * in 32-bit build and 35%--12% in 64-bit build on Core2... + * Coefficients are relative to optimized bn_nist.c for most + * intensive ECDSA verify and ECDH operations for 192- and 521- + * bit keys respectively. Choice of these boundary values is + * arguable, because the dependency of improvement coefficient + * from key length is not a "monotone" curve. For example while + * 571-bit result is 23% on ARM, 384-bit one is -1%. But it's + * generally faster, sometimes "respectfully" faster, sometimes + * "tolerably" slower... What effectively happens is that loop + * with bn_mul_add_words is put against bn_mul_mont, and the + * latter "wins" on short vectors. Correct solution should be + * implementing dedicated NxN multiplication subroutines for + * small N. But till it materializes, let's stick to generic + * prime method... + * <appro> + */ + meth = EC_GFp_mont_method(); +#else meth = EC_GFp_nist_method(); +#endif ret = EC_GROUP_new(meth); if (ret == NULL) @@ -122,7 +147,7 @@ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM return ret; } - +#ifndef OPENSSL_NO_EC2M EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { const EC_METHOD *meth; @@ -142,3 +167,4 @@ EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM return ret; } +#endif diff --git a/openssl/crypto/ec/ec_err.c b/openssl/crypto/ec/ec_err.c index 84b483337..0d1939873 100644 --- a/openssl/crypto/ec/ec_err.c +++ b/openssl/crypto/ec/ec_err.c @@ -1,6 +1,6 @@ /* crypto/ec/ec_err.c */ /* ==================================================================== - * Copyright (c) 1999-2007 The OpenSSL Project. All rights reserved. + * Copyright (c) 1999-2011 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -70,6 +70,7 @@ static ERR_STRING_DATA EC_str_functs[]= { +{ERR_FUNC(EC_F_BN_TO_FELEM), "BN_TO_FELEM"}, {ERR_FUNC(EC_F_COMPUTE_WNAF), "COMPUTE_WNAF"}, {ERR_FUNC(EC_F_D2I_ECPARAMETERS), "d2i_ECParameters"}, {ERR_FUNC(EC_F_D2I_ECPKPARAMETERS), "d2i_ECPKParameters"}, @@ -112,6 +113,15 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_SQR), "ec_GFp_mont_field_sqr"}, {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE), "ec_GFp_mont_group_set_curve"}, {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP), "EC_GFP_MONT_GROUP_SET_CURVE_GFP"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE), "ec_GFp_nistp224_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL), "ec_GFp_nistp224_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp224_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE), "ec_GFp_nistp256_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINTS_MUL), "ec_GFp_nistp256_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp256_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE), "ec_GFp_nistp521_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINTS_MUL), "ec_GFp_nistp521_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp521_point_get_affine_coordinates"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"}, {ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE), "ec_GFp_nist_group_set_curve"}, @@ -154,6 +164,7 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_EC_KEY_NEW), "EC_KEY_new"}, {ERR_FUNC(EC_F_EC_KEY_PRINT), "EC_KEY_print"}, {ERR_FUNC(EC_F_EC_KEY_PRINT_FP), "EC_KEY_print_fp"}, +{ERR_FUNC(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES), "EC_KEY_set_public_key_affine_coordinates"}, {ERR_FUNC(EC_F_EC_POINTS_MAKE_AFFINE), "EC_POINTs_make_affine"}, {ERR_FUNC(EC_F_EC_POINT_ADD), "EC_POINT_add"}, {ERR_FUNC(EC_F_EC_POINT_CMP), "EC_POINT_cmp"}, @@ -184,6 +195,9 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_I2D_ECPKPARAMETERS), "i2d_ECPKParameters"}, {ERR_FUNC(EC_F_I2D_ECPRIVATEKEY), "i2d_ECPrivateKey"}, {ERR_FUNC(EC_F_I2O_ECPUBLICKEY), "i2o_ECPublicKey"}, +{ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "NISTP224_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP256_PRE_COMP_NEW), "NISTP256_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP521_PRE_COMP_NEW), "NISTP521_PRE_COMP_NEW"}, {ERR_FUNC(EC_F_O2I_ECPUBLICKEY), "o2i_ECPublicKey"}, {ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE), "OLD_EC_PRIV_DECODE"}, {ERR_FUNC(EC_F_PKEY_EC_CTRL), "PKEY_EC_CTRL"}, @@ -199,12 +213,15 @@ static ERR_STRING_DATA EC_str_reasons[]= { {ERR_REASON(EC_R_ASN1_ERROR) ,"asn1 error"}, {ERR_REASON(EC_R_ASN1_UNKNOWN_FIELD) ,"asn1 unknown field"}, +{ERR_REASON(EC_R_BIGNUM_OUT_OF_RANGE) ,"bignum out of range"}, {ERR_REASON(EC_R_BUFFER_TOO_SMALL) ,"buffer too small"}, +{ERR_REASON(EC_R_COORDINATES_OUT_OF_RANGE),"coordinates out of range"}, {ERR_REASON(EC_R_D2I_ECPKPARAMETERS_FAILURE),"d2i ecpkparameters failure"}, {ERR_REASON(EC_R_DECODE_ERROR) ,"decode error"}, {ERR_REASON(EC_R_DISCRIMINANT_IS_ZERO) ,"discriminant is zero"}, {ERR_REASON(EC_R_EC_GROUP_NEW_BY_NAME_FAILURE),"ec group new by name failure"}, {ERR_REASON(EC_R_FIELD_TOO_LARGE) ,"field too large"}, +{ERR_REASON(EC_R_GF2M_NOT_SUPPORTED) ,"gf2m not supported"}, {ERR_REASON(EC_R_GROUP2PKPARAMETERS_FAILURE),"group2pkparameters failure"}, {ERR_REASON(EC_R_I2D_ECPKPARAMETERS_FAILURE),"i2d ecpkparameters failure"}, {ERR_REASON(EC_R_INCOMPATIBLE_OBJECTS) ,"incompatible objects"}, @@ -239,6 +256,7 @@ static ERR_STRING_DATA EC_str_reasons[]= {ERR_REASON(EC_R_UNKNOWN_GROUP) ,"unknown group"}, {ERR_REASON(EC_R_UNKNOWN_ORDER) ,"unknown order"}, {ERR_REASON(EC_R_UNSUPPORTED_FIELD) ,"unsupported field"}, +{ERR_REASON(EC_R_WRONG_CURVE_PARAMETERS) ,"wrong curve parameters"}, {ERR_REASON(EC_R_WRONG_ORDER) ,"wrong order"}, {0,NULL} }; diff --git a/openssl/crypto/ec/ec_key.c b/openssl/crypto/ec/ec_key.c index 522802c07..bf9fd2dc2 100644 --- a/openssl/crypto/ec/ec_key.c +++ b/openssl/crypto/ec/ec_key.c @@ -64,7 +64,9 @@ #include <string.h> #include "ec_lcl.h" #include <openssl/err.h> -#include <string.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif EC_KEY *EC_KEY_new(void) { @@ -78,6 +80,7 @@ EC_KEY *EC_KEY_new(void) } ret->version = 1; + ret->flags = 0; ret->group = NULL; ret->pub_key = NULL; ret->priv_key= NULL; @@ -197,6 +200,7 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) dest->enc_flag = src->enc_flag; dest->conv_form = src->conv_form; dest->version = src->version; + dest->flags = src->flags; return dest; } @@ -237,6 +241,11 @@ int EC_KEY_generate_key(EC_KEY *eckey) BIGNUM *priv_key = NULL, *order = NULL; EC_POINT *pub_key = NULL; +#ifdef OPENSSL_FIPS + if (FIPS_mode()) + return FIPS_ec_key_generate_key(eckey); +#endif + if (!eckey || !eckey->group) { ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER); @@ -371,6 +380,82 @@ err: return(ok); } +int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) + { + BN_CTX *ctx = NULL; + BIGNUM *tx, *ty; + EC_POINT *point = NULL; + int ok = 0, tmp_nid, is_char_two = 0; + + if (!key || !key->group || !x || !y) + { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + ctx = BN_CTX_new(); + if (!ctx) + goto err; + + point = EC_POINT_new(key->group); + + if (!point) + goto err; + + tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(key->group)); + + if (tmp_nid == NID_X9_62_characteristic_two_field) + is_char_two = 1; + + tx = BN_CTX_get(ctx); + ty = BN_CTX_get(ctx); +#ifndef OPENSSL_NO_EC2M + if (is_char_two) + { + if (!EC_POINT_set_affine_coordinates_GF2m(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(key->group, point, + tx, ty, ctx)) + goto err; + } + else +#endif + { + if (!EC_POINT_set_affine_coordinates_GFp(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GFp(key->group, point, + tx, ty, ctx)) + goto err; + } + /* Check if retrieved coordinates match originals: if not values + * are out of range. + */ + if (BN_cmp(x, tx) || BN_cmp(y, ty)) + { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + if (!EC_KEY_set_public_key(key, point)) + goto err; + + if (EC_KEY_check_key(key) == 0) + goto err; + + ok = 1; + + err: + if (ctx) + BN_CTX_free(ctx); + if (point) + EC_POINT_free(point); + return ok; + + } + const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key) { return key->group; @@ -461,3 +546,18 @@ int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx) return 0; return EC_GROUP_precompute_mult(key->group, ctx); } + +int EC_KEY_get_flags(const EC_KEY *key) + { + return key->flags; + } + +void EC_KEY_set_flags(EC_KEY *key, int flags) + { + key->flags |= flags; + } + +void EC_KEY_clear_flags(EC_KEY *key, int flags) + { + key->flags &= ~flags; + } diff --git a/openssl/crypto/ec/ec_lcl.h b/openssl/crypto/ec/ec_lcl.h index 3e2c34b0b..da7967df3 100644 --- a/openssl/crypto/ec/ec_lcl.h +++ b/openssl/crypto/ec/ec_lcl.h @@ -3,7 +3,7 @@ * Originally written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== - * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -82,10 +82,15 @@ # endif #endif +/* Use default functions for poin2oct, oct2point and compressed coordinates */ +#define EC_FLAGS_DEFAULT_OCT 0x1 + /* Structure details are not part of the exported interface, * so all this may change in future versions. */ struct ec_method_st { + /* Various method flags */ + int flags; /* used by EC_METHOD_get_field_type: */ int field_type; /* a NID */ @@ -244,6 +249,7 @@ struct ec_key_st { point_conversion_form_t conv_form; int references; + int flags; EC_EXTRA_DATA *method_data; } /* EC_KEY */; @@ -391,3 +397,50 @@ int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ec2_mult.c */ +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + +#ifndef OPENSSL_EC_NISTP_64_GCC_128 +/* method functions in ecp_nistp224.c */ +int ec_GFp_nistp224_group_init(EC_GROUP *group); +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp256.c */ +int ec_GFp_nistp256_group_init(EC_GROUP *group); +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp521.c */ +int ec_GFp_nistp521_group_init(EC_GROUP *group); +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); + +/* utility functions in ecp_nistputil.c */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)); +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in); +#endif diff --git a/openssl/crypto/ec/ec_lib.c b/openssl/crypto/ec/ec_lib.c index dd7da0fcf..25247b580 100644 --- a/openssl/crypto/ec/ec_lib.c +++ b/openssl/crypto/ec/ec_lib.c @@ -425,7 +425,7 @@ int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM * return group->meth->group_get_curve(group, p, a, b, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { if (group->meth->group_set_curve == 0) @@ -446,7 +446,7 @@ int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM } return group->meth->group_get_curve(group, p, a, b, ctx); } - +#endif int EC_GROUP_get_degree(const EC_GROUP *group) { @@ -856,7 +856,7 @@ int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { @@ -872,7 +872,7 @@ int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, } return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } - +#endif int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) @@ -890,7 +890,7 @@ int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *p return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { @@ -906,75 +906,7 @@ int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT * } return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } - - -int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { - if (group->meth->point_set_compressed_coordinates == 0) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); - } - - -int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { - if (group->meth->point_set_compressed_coordinates == 0) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); - } - - -size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->point2oct == 0) - { - ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point2oct(group, point, form, buf, len, ctx); - } - - -int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->oct2point == 0) - { - ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->oct2point(group, point, buf, len, ctx); - } - +#endif int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { diff --git a/openssl/crypto/ec/ec_oct.c b/openssl/crypto/ec/ec_oct.c new file mode 100644 index 000000000..fd9db0798 --- /dev/null +++ b/openssl/crypto/ec/ec_oct.c @@ -0,0 +1,199 @@ +/* crypto/ec/ec_lib.c */ +/* + * Originally written by Bodo Moeller for the OpenSSL project. + */ +/* ==================================================================== + * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Binary polynomial ECC support in OpenSSL originally developed by + * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. + */ + +#include <string.h> + +#include <openssl/err.h> +#include <openssl/opensslv.h> + +#include "ec_lcl.h" + +int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, int y_bit, BN_CTX *ctx) + { + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); +#endif + } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + } + +#ifndef OPENSSL_NO_EC2M +int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, int y_bit, BN_CTX *ctx) + { + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + else + return ec_GF2m_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + } +#endif + +size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + if (group->meth->point2oct == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_point2oct(group, point, + form, buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_point2oct(group, point, + form, buf, len, ctx); +#endif + } + + return group->meth->point2oct(group, point, form, buf, len, ctx); + } + + +int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + if (group->meth->oct2point == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_oct2point(group, point, + buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_oct2point(group, point, + buf, len, ctx); +#endif + } + return group->meth->oct2point(group, point, buf, len, ctx); + } + diff --git a/openssl/crypto/ec/ec_pmeth.c b/openssl/crypto/ec/ec_pmeth.c index f433076ca..d1ed66c37 100644 --- a/openssl/crypto/ec/ec_pmeth.c +++ b/openssl/crypto/ec/ec_pmeth.c @@ -221,6 +221,7 @@ static int pkey_ec_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) case EVP_PKEY_CTRL_MD: if (EVP_MD_type((const EVP_MD *)p2) != NID_sha1 && + EVP_MD_type((const EVP_MD *)p2) != NID_ecdsa_with_SHA1 && EVP_MD_type((const EVP_MD *)p2) != NID_sha224 && EVP_MD_type((const EVP_MD *)p2) != NID_sha256 && EVP_MD_type((const EVP_MD *)p2) != NID_sha384 && diff --git a/openssl/crypto/ec/eck_prn.c b/openssl/crypto/ec/eck_prn.c index 7d3e175ae..06de8f395 100644 --- a/openssl/crypto/ec/eck_prn.c +++ b/openssl/crypto/ec/eck_prn.c @@ -207,7 +207,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) reason = ERR_R_MALLOC_FAILURE; goto err; } - +#ifndef OPENSSL_NO_EC2M if (is_char_two) { if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) @@ -217,6 +217,7 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) } } else /* prime field */ +#endif { if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) { diff --git a/openssl/crypto/ec/ecp_mont.c b/openssl/crypto/ec/ecp_mont.c index 9fc4a466a..079e47431 100644 --- a/openssl/crypto/ec/ecp_mont.c +++ b/openssl/crypto/ec/ecp_mont.c @@ -63,12 +63,20 @@ #include <openssl/err.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + #include "ec_lcl.h" const EC_METHOD *EC_GFp_mont_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_mont_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_mont_group_init, ec_GFp_mont_group_finish, @@ -87,9 +95,7 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -108,7 +114,9 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_mont_field_decode, ec_GFp_mont_field_set_to_one }; + return &ret; +#endif } diff --git a/openssl/crypto/ec/ecp_nist.c b/openssl/crypto/ec/ecp_nist.c index 2a5682ea4..aad2d5f44 100644 --- a/openssl/crypto/ec/ecp_nist.c +++ b/openssl/crypto/ec/ecp_nist.c @@ -67,9 +67,17 @@ #include <openssl/obj_mac.h> #include "ec_lcl.h" +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + const EC_METHOD *EC_GFp_nist_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_nist_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_simple_group_init, ec_GFp_simple_group_finish, @@ -88,9 +96,7 @@ const EC_METHOD *EC_GFp_nist_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -110,6 +116,7 @@ const EC_METHOD *EC_GFp_nist_method(void) 0 /* field_set_to_one */ }; return &ret; +#endif } int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src) diff --git a/openssl/crypto/ec/ecp_nistp224.c b/openssl/crypto/ec/ecp_nistp224.c new file mode 100644 index 000000000..b5ff56c25 --- /dev/null +++ b/openssl/crypto/ec/ecp_nistp224.c @@ -0,0 +1,1658 @@ +/* crypto/ec/ecp_nistp224.c */ +/* + * Written by Emilia Kasper (Google) for the OpenSSL project. + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication + * + * Inspired by Daniel J. Bernstein's public domain nistp224 implementation + * and Adam Langley's public domain 64-bit C implementation of curve25519 + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint64_t u64; +typedef int64_t s64; + + +/******************************************************************************/ +/* INTERNAL REPRESENTATION OF FIELD ELEMENTS + * + * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 + * using 64-bit coefficients called 'limbs', + * and sometimes (for multiplication results) as + * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 + * using 128-bit coefficients called 'widelimbs'. + * A 4-limb representation is an 'felem'; + * a 7-widelimb representation is a 'widefelem'. + * Even within felems, bits of adjacent limbs overlap, and we don't always + * reduce the representations: we ensure that inputs to each felem + * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, + * and fit into a 128-bit word without overflow. The coefficients are then + * again partially reduced to obtain an felem satisfying a_i < 2^57. + * We only reduce to the unique minimal representation at the end of the + * computation. + */ + +typedef uint64_t limb; +typedef uint128_t widelimb; + +typedef limb felem[4]; +typedef widelimb widefelem[7]; + +/* Field element represented as a byte arrary. + * 28*8 = 224 bits is also the group order size for the elliptic curve, + * and we also use this type for scalars for point multiplication. + */ +typedef u8 felem_bytearray[28]; + +static const felem_bytearray nistp224_curve_params[5] = { + {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, + {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, + {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ + 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, + 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, + {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ + 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, + 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, + {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ + 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, + 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} +}; + +/* Precomputed multiples of the standard generator + * Points are given in coordinates (X, Y, Z) where Z normally is 1 + * (0 for the point at infinity). + * For each field element, slice a_0 is word 0, etc. + * + * The table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^56G + * 3 | 0 0 1 1 | (2^56 + 1)G + * 4 | 0 1 0 0 | 2^112G + * 5 | 0 1 0 1 | (2^112 + 1)G + * 6 | 0 1 1 0 | (2^112 + 2^56)G + * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G + * 8 | 1 0 0 0 | 2^168G + * 9 | 1 0 0 1 | (2^168 + 1)G + * 10 | 1 0 1 0 | (2^168 + 2^56)G + * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G + * 12 | 1 1 0 0 | (2^168 + 2^112)G + * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G + * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G + * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G + * followed by a copy of this with each element multiplied by 2^28. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + */ +static const felem gmul[2][16][3] = +{{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}}}; + +/* Precomputation for the group generator. */ +typedef struct { + felem g_pre_comp[2][16][3]; + int references; +} NISTP224_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp224_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + +/* Helper functions to convert field elements to/from internal representation */ +static void bin28_to_felem(felem out, const u8 in[28]) + { + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; + } + +static void felem_to_bin28(u8 out[28], const felem in) + { + unsigned i; + for (i = 0; i < 7; ++i) + { + out[i] = in[0]>>(8*i); + out[i+7] = in[1]>>(8*i); + out[i+14] = in[2]>>(8*i); + out[i+21] = in[3]>>(8*i); + } + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* From OpenSSL BIGNUM to internal representation */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; + } + +/* From internal representation to OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) + { + felem_bytearray b_in, b_out; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + +/******************************************************************************/ +/* FIELD OPERATIONS + * + * Field operations, using the internal representation of field elements. + * NB! These operations are specific to our point multiplication and cannot be + * expected to be correct in general - e.g., multiplication with a large scalar + * will cause an overflow. + * + */ + +static void felem_one(felem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* Sum two field elements: out += in */ +static void felem_sum(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* Get negative value: out = -in */ +/* Assumes in[i] < 2^57 */ +static void felem_neg(felem out, const felem in) + { + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; + } + +/* Subtract field elements: out -= in */ +/* Assumes in[i] < 2^57 */ +static void felem_diff(felem out, const felem in) + { + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Subtract in unreduced 128-bit mode: out -= in */ +/* Assumes in[i] < 2^119 */ +static void widefelem_diff(widefelem out, const widefelem in) + { + static const widelimb two120 = ((widelimb) 1) << 120; + static const widelimb two120m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 64); + static const widelimb two120m104m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + } + +/* Subtract in mixed mode: out128 -= in64 */ +/* in[i] < 2^63 */ +static void felem_diff_128_64(widefelem out, const felem in) + { + static const widelimb two64p8 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 8); + static const widelimb two64m48m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Multiply a field element by a scalar: out = out * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void felem_scalar(felem out, const limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + } + +/* Multiply an unreduced field element by a scalar: out = out * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void widefelem_scalar(widefelem out, const widelimb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + } + +/* Square a field element: out = in^2 */ +static void felem_square(widefelem out, const felem in) + { + limb tmp0, tmp1, tmp2; + tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; + out[0] = ((widelimb) in[0]) * in[0]; + out[1] = ((widelimb) in[0]) * tmp1; + out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; + out[3] = ((widelimb) in[3]) * tmp0 + + ((widelimb) in[1]) * tmp2; + out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; + out[5] = ((widelimb) in[3]) * tmp2; + out[6] = ((widelimb) in[3]) * in[3]; + } + +/* Multiply two field elements: out = in1 * in2 */ +static void felem_mul(widefelem out, const felem in1, const felem in2) + { + out[0] = ((widelimb) in1[0]) * in2[0]; + out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; + out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + + ((widelimb) in1[2]) * in2[0]; + out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + + ((widelimb) in1[3]) * in2[1]; + out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; + out[6] = ((widelimb) in1[3]) * in2[3]; + } + +/* Reduce seven 128-bit coefficients to four 64-bit coefficients. + * Requires in[i] < 2^126, + * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ +static void felem_reduce(felem out, const widefelem in) + { + static const widelimb two127p15 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 15); + static const widelimb two127m71 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71); + static const widelimb two127m71m55 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + widelimb output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6] & 0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5] & 0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] = output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + /* output[2] < 2^56 + 2^56 = 2^57 */ + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + /* output[2] < 2^57 + 2^72 */ + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + /* output[3] <= 2^56 + 2^16 */ + out[2] = output[2] & 0x00ffffffffffffff; + + /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] <= 2^56 + 2^16 (due to final carry), + * so out < 2*p */ + out[3] = output[3]; + } + +static void felem_square_reduce(felem out, const felem in) + { + widefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); + } + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) + { + widefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); + } + +/* Reduce to unique minimal representation. + * Requires 0 <= in < 2*p (always call felem_reduce first) */ +static void felem_contract(felem out, const felem in) + { + static const int64_t two56 = ((limb) 1) << 56; + /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ + /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = in[0]; + tmp[1] = in[1]; + tmp[2] = in[2]; + tmp[3] = in[3]; + /* Case 1: a = 1 iff in >= 2^224 */ + a = (in[3] >> 56); + tmp[0] -= a; + tmp[1] += a << 40; + tmp[3] &= 0x00ffffffffffffff; + /* Case 2: a = 0 iff p <= in < 2^224, i.e., + * the high 128 bits are all 1 and the lower part is non-zero */ + a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | + (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + a &= 0x00ffffffffffffff; + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = (a - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one*/ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + + /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must + * be non-zero, so we only need one step */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= out < p */ + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; + } + +/* Zero-check: returns 1 if input is 0, and 0 otherwise. + * We know that field elements are reduced to in < 2^225, + * so we only need to check three cases: 0, 2^224 - 2^96 + 1, + * and 2^225 - 2^97 + 2 */ +static limb felem_is_zero(const felem in) + { + limb zero, two224m96p1, two225m97p2; + + zero = in[0] | in[1] | in[2] | in[3]; + zero = (((int64_t)(zero) - 1) >> 63) & 1; + two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; + two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); + } + +static limb felem_is_zero_int(const felem in) + { + return (int) (felem_is_zero(in) & ((limb)1)); + } + +/* Invert a field element */ +/* Computation chain copied from djb's code */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2, ftmp3, ftmp4; + widefelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ + { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ + } + +/* Copy in constant time: + * if icopy == 1, copy in to out, + * if icopy == 0, copy out to itself. */ +static void +copy_conditional(felem out, const felem in, limb icopy) + { + unsigned i; + /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ + const limb copy = -icopy; + for (i = 0; i < 4; ++i) + { + const limb tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/******************************************************************************/ +/* ELLIPTIC CURVE POINT OPERATIONS + * + * Points are represented in Jacobian projective coordinates: + * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), + * or to the point at infinity if Z == 0. + * + */ + +/* Double an elliptic curve point: + * (X', Y', Z') = 2 * (X, Y, Z), where + * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 + * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 + * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + widefelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + widefelem_diff(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); + } + +/* Add two elliptic curve points: + * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where + * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - + * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 + * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - + * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 + * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) + * + * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. + */ + +/* This function is not entirely constant-time: + * it includes a branch for checking whether the two input points are equal, + * (while not equal to the point at infinity). + * This case never happens during single point multiplication, + * so there is no timing leak for ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb z1_is_zero, z2_is_zero, x_equal, y_equal; + + if (!mixed) + { + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp2 = z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* ftmp4 = z2^3*y1 */ + felem_assign(ftmp4, y1); + + /* ftmp2 = z2^2*x1 */ + felem_assign(ftmp2, x1); + } + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* tmp = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* tmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* the formulae are incorrect if the points are equal + * so we check for this and do doubling if this happens */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + if (!mixed) + { + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + } + else + { + /* special case z2 = 0 is handled later */ + felem_assign(ftmp5, z1); + } + + /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z_out, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp2); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x_out, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ + felem_diff(ftmp2, x_out); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - + z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + widefelem_diff(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp2); + + /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is + * the point at infinity, so we need to check for this separately */ + + /* if point 1 is at infinity, copy point 2 to output, and vice versa */ + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) + { + unsigned i, j; + limb *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(felem)); + + for (i = 0; i < size; i++) + { + const limb *inlimbs = &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < 4 * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, unsigned i) + { + if (i >= 224) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) + { + int i, skip; + unsigned num; + unsigned gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (two in each of the last 28 rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 27)) + { + /* first, look 28 bits upwards */ + bits = get_bit(g_scalar, i + 196) << 3; + bits |= get_bit(g_scalar, i + 140) << 2; + bits |= get_bit(g_scalar, i + 84) << 1; + bits |= get_bit(g_scalar, i + 28); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 168) << 3; + bits |= get_bit(g_scalar, i + 112) << 2; + bits |= get_bit(g_scalar, i + 56) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_conditional(tmp[1], tmp[3], sign); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP224_PRE_COMP *nistp224_pre_comp_new() + { + NISTP224_PRE_COMP *ret = NULL; + ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) + { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp224_pre_comp_dup(void *src_) + { + NISTP224_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp224_pre_comp_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp224_pre_comp_clear_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp224_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *)) felem_one, + (int (*)(const void *)) felem_is_zero_int, + (void (*)(void *, const void *)) felem_assign, + (void (*)(void *, const void *)) felem_square_reduce, + (void (*)(void *, const void *, const void *)) felem_mul_reduce, + (void (*)(void *, const void *)) felem_inv, + (void (*)(void *, const void *)) felem_contract); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + unsigned i; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP224_PRE_COMP *pre = NULL; + const felem (*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp224_pre_comp_dup, nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[0][1][0]) || + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points = num_points + 1; + } + + if (num_points > 0) + { + if (num_points >= 3) + { + /* unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); + if (mixed) + tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + felem_assign(pre_comp[i][1][0], x_out); + felem_assign(pre_comp[i][1][1], y_out); + felem_assign(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof g_secret); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const felem (*)[17][3]) pre_comp, + g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_felems != NULL) + OPENSSL_free(tmp_felems); + return ret; + } + +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[32]; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) + goto err; + /* compute 2^56*G, 2^112*G, 2^168*G for the first table, + * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) + { + point_double( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) + { + point_double( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) + { + point_double( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); + } + } + for (i = 0; i < 2; i++) + { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ + point_add( + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) + { + /* odd multiples: add G resp. 2^28*G */ + point_add( + pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], + pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], + pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], + 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp224_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } + +#else +static void *dummy=&dummy; +#endif diff --git a/openssl/crypto/ec/ecp_nistp256.c b/openssl/crypto/ec/ecp_nistp256.c new file mode 100644 index 000000000..4bc0f5dce --- /dev/null +++ b/openssl/crypto/ec/ecp_nistp256.c @@ -0,0 +1,2171 @@ +/* crypto/ec/ecp_nistp256.c */ +/* + * Written by Adam Langley (Google) for the OpenSSL project + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ + typedef __int128_t int128_t; +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint32_t u32; +typedef uint64_t u64; +typedef int64_t s64; + +/* The underlying field. + * + * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element + * of this field into 32 bytes. We call this an felem_bytearray. */ + +typedef u8 felem_bytearray[32]; + +/* These are the parameters of P256, taken from FIPS 186-3, page 86. These + * values are big-endian. */ +static const felem_bytearray nistp256_curve_params[5] = { + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ + {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, + 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, + 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, + 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, + {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ + 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, + 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, + 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, + {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ + 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, + 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, + 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} +}; + +/* The representation of field elements. + * ------------------------------------ + * + * We represent field elements with either four 128-bit values, eight 128-bit + * values, or four 64-bit values. The field element represented is: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p) + * or: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p) + * + * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits + * apart, but are 128-bits wide, the most significant bits of each limb overlap + * with the least significant bits of the next. + * + * A field element with four limbs is an 'felem'. One with eight limbs is a + * 'longfelem' + * + * A field element with four, 64-bit values is called a 'smallfelem'. Small + * values are used as intermediate values before multiplication. + */ + +#define NLIMBS 4 + +typedef uint128_t limb; +typedef limb felem[NLIMBS]; +typedef limb longfelem[NLIMBS * 2]; +typedef u64 smallfelem[NLIMBS]; + +/* This is the value of the prime as four 64-bit words, little-endian. */ +static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; +static const limb bottom32bits = 0xffffffff; +static const u64 bottom63bits = 0x7ffffffffffffffful; + +/* bin32_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. */ +static void bin32_to_felem(felem out, const u8 in[32]) + { + out[0] = *((u64*) &in[0]); + out[1] = *((u64*) &in[8]); + out[2] = *((u64*) &in[16]); + out[3] = *((u64*) &in[24]); + } + +/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, + * 32 byte array. This assumes that the CPU is little-endian. */ +static void smallfelem_to_bin32(u8 out[32], const smallfelem in) + { + *((u64*) &out[0]) = in[0]; + *((u64*) &out[8]) = in[1]; + *((u64*) &out[16]) = in[2]; + *((u64*) &out[24]) = in[3]; + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin32_to_felem(out, b_out); + return 1; + } + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) + { + felem_bytearray b_in, b_out; + smallfelem_to_bin32(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + + +/* Field operations + * ---------------- */ + +static void smallfelem_one(smallfelem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + } + +static void smallfelem_assign(smallfelem out, const smallfelem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* felem_sum sets out = out + in. */ +static void felem_sum(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* felem_small_sum sets out = out + in. */ +static void felem_small_sum(felem out, const smallfelem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* felem_scalar sets out = out * scalar */ +static void felem_scalar(felem out, const u64 scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + } + +/* longfelem_scalar sets out = out * scalar */ +static void longfelem_scalar(longfelem out, const u64 scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + } + +#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) +#define two105 (((limb)1) << 105) +#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) + +/* zero105 is 0 mod p */ +static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; + +/* smallfelem_neg sets |out| to |-small| + * On exit: + * out[i] < out[i] + 2^105 + */ +static void smallfelem_neg(felem out, const smallfelem small) + { + /* In order to prevent underflow, we subtract from 0 mod p. */ + out[0] = zero105[0] - small[0]; + out[1] = zero105[1] - small[1]; + out[2] = zero105[2] - small[2]; + out[3] = zero105[3] - small[3]; + } + +/* felem_diff subtracts |in| from |out| + * On entry: + * in[i] < 2^104 + * On exit: + * out[i] < out[i] + 2^105 + */ +static void felem_diff(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + out[0] += zero105[0]; + out[1] += zero105[1]; + out[2] += zero105[2]; + out[3] += zero105[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) +#define two107 (((limb)1) << 107) +#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) + +/* zero107 is 0 mod p */ +static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; + +/* An alternative felem_diff for larger inputs |in| + * felem_diff_zero107 subtracts |in| from |out| + * On entry: + * in[i] < 2^106 + * On exit: + * out[i] < out[i] + 2^107 + */ +static void felem_diff_zero107(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + out[0] += zero107[0]; + out[1] += zero107[1]; + out[2] += zero107[2]; + out[3] += zero107[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* longfelem_diff subtracts |in| from |out| + * On entry: + * in[i] < 7*2^67 + * On exit: + * out[i] < out[i] + 2^70 + 2^40 + */ +static void longfelem_diff(longfelem out, const longfelem in) + { + static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); + static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); + static const limb two70 = (((limb)1) << 70); + static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); + static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); + + /* add 0 mod p to avoid underflow */ + out[0] += two70m8p6; + out[1] += two70p40; + out[2] += two70; + out[3] += two70m40m38p6; + out[4] += two70m6; + out[5] += two70m6; + out[6] += two70m6; + out[7] += two70m6; + + /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + out[7] -= in[7]; + } + +#define two64m0 (((limb)1) << 64) - 1 +#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 +#define two64m46 (((limb)1) << 64) - (((limb)1) << 46) +#define two64m32 (((limb)1) << 64) - (((limb)1) << 32) + +/* zero110 is 0 mod p */ +static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; + +/* felem_shrink converts an felem into a smallfelem. The result isn't quite + * minimal as the value may be greater than p. + * + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 2^64 + */ +static void felem_shrink(smallfelem out, const felem in) + { + felem tmp; + u64 a, b, mask; + s64 high, low; + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + + /* Carry 2->3 */ + tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); + /* tmp[3] < 2^110 */ + + tmp[2] = zero110[2] + (u64) in[2]; + tmp[0] = zero110[0] + in[0]; + tmp[1] = zero110[1] + in[1]; + /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ + + /* We perform two partial reductions where we eliminate the + * high-word of tmp[3]. We don't update the other words till the end. + */ + a = tmp[3] >> 64; /* a < 2^46 */ + tmp[3] = (u64) tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb)a) << 32; + /* tmp[3] < 2^79 */ + + b = a; + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ + tmp[3] = (u64) tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb)a) << 32; + /* tmp[3] < 2^64 + 2^47 */ + + /* This adjusts the other two words to complete the two partial + * reductions. */ + tmp[0] += b; + tmp[1] -= (((limb)b) << 32); + + /* In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. */ + high = tmp[3] >> 64; + /* As tmp[3] < 2^65, high is either 1 or 0 */ + high <<= 63; + high >>= 63; + /* high is: + * all ones if the high word of tmp[3] is 1 + * all zeros if the high word of tmp[3] if 0 */ + low = tmp[3]; + mask = low >> 63; + /* mask is: + * all ones if the MSB of low is 1 + * all zeros if the MSB of low if 0 */ + low &= bottom63bits; + low -= kPrime3Test; + /* if low was greater than kPrime3Test then the MSB is zero */ + low = ~low; + low >>= 63; + /* low is: + * all ones if low was > kPrime3Test + * all zeros if low was <= kPrime3Test */ + mask = (mask & low) | high; + tmp[0] -= mask & kPrime[0]; + tmp[1] -= mask & kPrime[1]; + /* kPrime[2] is zero, so omitted */ + tmp[3] -= mask & kPrime[3]; + /* tmp[3] < 2**64 - 2**32 + 1 */ + + tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; + tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; + tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; + /* tmp[i] < 2^64 */ + + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; + } + +/* smallfelem_expand converts a smallfelem to an felem */ +static void smallfelem_expand(felem out, const smallfelem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* smallfelem_square sets |out| = |small|^2 + * On entry: + * small[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_square(longfelem out, const smallfelem small) + { + limb a; + u64 high, low; + + a = ((uint128_t) small[0]) * small[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small[0]) * small[1]; + low = a; + high = a >> 64; + out[1] += low; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small[0]) * small[2]; + low = a; + high = a >> 64; + out[2] += low; + out[2] *= 2; + out[3] = high; + + a = ((uint128_t) small[0]) * small[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small[1]) * small[2]; + low = a; + high = a >> 64; + out[3] += low; + out[3] *= 2; + out[4] += high; + + a = ((uint128_t) small[1]) * small[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small[1]) * small[3]; + low = a; + high = a >> 64; + out[4] += low; + out[4] *= 2; + out[5] = high; + + a = ((uint128_t) small[2]) * small[3]; + low = a; + high = a >> 64; + out[5] += low; + out[5] *= 2; + out[6] = high; + out[6] += high; + + a = ((uint128_t) small[2]) * small[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small[3]) * small[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; + } + +/* felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_square(longfelem out, const felem in) + { + u64 small[4]; + felem_shrink(small, in); + smallfelem_square(out, small); + } + +/* smallfelem_mul sets |out| = |small1| * |small2| + * On entry: + * small1[i] < 2^64 + * small2[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) + { + limb a; + u64 high, low; + + a = ((uint128_t) small1[0]) * small2[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + + a = ((uint128_t) small1[0]) * small2[1]; + low = a; + high = a >> 64; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small1[1]) * small2[0]; + low = a; + high = a >> 64; + out[1] += low; + out[2] += high; + + + a = ((uint128_t) small1[0]) * small2[2]; + low = a; + high = a >> 64; + out[2] += low; + out[3] = high; + + a = ((uint128_t) small1[1]) * small2[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[2]) * small2[0]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + + a = ((uint128_t) small1[0]) * small2[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small1[1]) * small2[2]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[2]) * small2[1]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[3]) * small2[0]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + + a = ((uint128_t) small1[1]) * small2[3]; + low = a; + high = a >> 64; + out[4] += low; + out[5] = high; + + a = ((uint128_t) small1[2]) * small2[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[3]) * small2[1]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + + a = ((uint128_t) small1[2]) * small2[3]; + low = a; + high = a >> 64; + out[5] += low; + out[6] = high; + + a = ((uint128_t) small1[3]) * small2[2]; + low = a; + high = a >> 64; + out[5] += low; + out[6] += high; + + + a = ((uint128_t) small1[3]) * small2[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; + } + +/* felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^109 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_mul(longfelem out, const felem in1, const felem in2) + { + smallfelem small1, small2; + felem_shrink(small1, in1); + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); + } + +/* felem_small_mul sets |out| = |small1| * |in2| + * On entry: + * small1[i] < 2^64 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) + { + smallfelem small2; + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); + } + +#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) +#define two100 (((limb)1) << 100) +#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) +/* zero100 is 0 mod p */ +static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; + +/* Internal function for the different flavours of felem_reduce. + * felem_reduce_ reduces the higher coefficients in[4]-in[7]. + * On entry: + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[1] >= in[7] + 2^32*in[4] + * out[2] >= in[5] + 2^32*in[5] + * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] + * On exit: + * out[0] <= out[0] + in[4] + 2^32*in[5] + * out[1] <= out[1] + in[5] + 2^33*in[6] + * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] + * out[3] <= out[3] + 2^32*in[4] + 3*in[7] + */ +static void felem_reduce_(felem out, const longfelem in) + { + int128_t c; + /* combine common terms from below */ + c = in[4] + (in[5] << 32); + out[0] += c; + out[3] -= c; + + c = in[5] - in[7]; + out[1] += c; + out[2] -= c; + + /* the remaining terms */ + /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ + out[1] -= (in[4] << 32); + out[3] += (in[4] << 32); + + /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ + out[2] -= (in[5] << 32); + + /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ + out[0] -= in[6]; + out[0] -= (in[6] << 32); + out[1] += (in[6] << 33); + out[2] += (in[6] * 2); + out[3] -= (in[6] << 32); + + /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ + out[0] -= in[7]; + out[0] -= (in[7] << 32); + out[2] += (in[7] << 33); + out[3] += (in[7] * 3); + } + +/* felem_reduce converts a longfelem into an felem. + * To be called directly after felem_square or felem_mul. + * On entry: + * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 + * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 + * On exit: + * out[i] < 2^101 + */ +static void felem_reduce(felem out, const longfelem in) + { + out[0] = zero100[0] + in[0]; + out[1] = zero100[1] + in[1]; + out[2] = zero100[2] + in[2]; + out[3] = zero100[3] + in[3]; + + felem_reduce_(out, in); + + /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 + * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 + * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 + * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 + * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 + * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + */ + } + +/* felem_reduce_zero105 converts a larger longfelem into an felem. + * On entry: + * in[0] < 2^71 + * On exit: + * out[i] < 2^106 + */ +static void felem_reduce_zero105(felem out, const longfelem in) + { + out[0] = zero105[0] + in[0]; + out[1] = zero105[1] + in[1]; + out[2] = zero105[2] + in[2]; + out[3] = zero105[3] + in[3]; + + felem_reduce_(out, in); + + /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 + * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 + * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 + * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + */ + } + +/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction + * underflowed. */ +static void subtract_u64(u64* result, u64* carry, u64 v) + { + uint128_t r = *result; + r -= v; + *carry = (r >> 64) & 1; + *result = (u64) r; + } + +/* felem_contract converts |in| to its unique, minimal representation. + * On entry: + * in[i] < 2^109 + */ +static void felem_contract(smallfelem out, const felem in) + { + unsigned i; + u64 all_equal_so_far = 0, result = 0, carry; + + felem_shrink(out, in); + /* small is minimal except that the value might be > p */ + + all_equal_so_far--; + /* We are doing a constant time test if out >= kPrime. We need to + * compare each u64, from most-significant to least significant. For + * each one, if all words so far have been equal (m is all ones) then a + * non-equal result is the answer. Otherwise we continue. */ + for (i = 3; i < 4; i--) + { + u64 equal; + uint128_t a = ((uint128_t) kPrime[i]) - out[i]; + /* if out[i] > kPrime[i] then a will underflow and the high + * 64-bits will all be set. */ + result |= all_equal_so_far & ((u64) (a >> 64)); + + /* if kPrime[i] == out[i] then |equal| will be all zeros and + * the decrement will make it all ones. */ + equal = kPrime[i] ^ out[i]; + equal--; + equal &= equal << 32; + equal &= equal << 16; + equal &= equal << 8; + equal &= equal << 4; + equal &= equal << 2; + equal &= equal << 1; + equal = ((s64) equal) >> 63; + + all_equal_so_far &= equal; + } + + /* if all_equal_so_far is still all ones then the two values are equal + * and so out >= kPrime is true. */ + result |= all_equal_so_far; + + /* if out >= kPrime then we subtract kPrime. */ + subtract_u64(&out[0], &carry, result & kPrime[0]); + subtract_u64(&out[1], &carry, carry); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[1], &carry, result & kPrime[1]); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[2], &carry, result & kPrime[2]); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[3], &carry, result & kPrime[3]); + } + +static void smallfelem_square_contract(smallfelem out, const smallfelem in) + { + longfelem longtmp; + felem tmp; + + smallfelem_square(longtmp, in); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); + } + +static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) + { + longfelem longtmp; + felem tmp; + + smallfelem_mul(longtmp, in1, in2); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); + } + +/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * small[i] < 2^64 + */ +static limb smallfelem_is_zero(const smallfelem small) + { + limb result; + u64 is_p; + + u64 is_zero = small[0] | small[1] | small[2] | small[3]; + is_zero--; + is_zero &= is_zero << 32; + is_zero &= is_zero << 16; + is_zero &= is_zero << 8; + is_zero &= is_zero << 4; + is_zero &= is_zero << 2; + is_zero &= is_zero << 1; + is_zero = ((s64) is_zero) >> 63; + + is_p = (small[0] ^ kPrime[0]) | + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | + (small[3] ^ kPrime[3]); + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = ((s64) is_p) >> 63; + + is_zero |= is_p; + + result = is_zero; + result |= ((limb) is_zero) << 64; + return result; + } + +static int smallfelem_is_zero_int(const smallfelem small) + { + return (int) (smallfelem_is_zero(small) & ((limb)1)); + } + +/* felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2; + /* each e_I will hold |in|^{2^I - 1} */ + felem e2, e4, e8, e16, e32, e64; + longfelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(e2, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_assign(e4, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_assign(e8, ftmp); + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_assign(e16, ftmp); + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_assign(e32, ftmp); + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ + felem_assign(e64, ftmp); + felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + for (i = 0; i < 192; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ + + felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + for (i = 0; i < 4; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ + } + +static void smallfelem_inv_contract(smallfelem out, const smallfelem in) + { + felem tmp; + + smallfelem_expand(tmp, in); + felem_inv(tmp, tmp); + felem_contract(out, tmp); + } + +/* Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates */ + +/* point_double calculates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + longfelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + smallfelem small1, small2; + + felem_assign(ftmp, x_in); + /* ftmp[i] < 2^106 */ + felem_assign(ftmp2, x_in); + /* ftmp2[i] < 2^106 */ + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + /* delta[i] < 2^101 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + /* gamma[i] < 2^101 */ + felem_shrink(small1, gamma); + + /* beta = x*gamma */ + felem_small_mul(tmp, small1, x_in); + felem_reduce(beta, tmp); + /* beta[i] < 2^101 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^105 + 2^106 < 2^107 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^107 < 2^109 */ + felem_mul(tmp, ftmp, ftmp2); + felem_reduce(alpha, tmp); + /* alpha[i] < 2^101 */ + felem_shrink(small2, alpha); + + /* x' = alpha^2 - 8*beta */ + smallfelem_square(tmp, small2); + felem_reduce(x_out, tmp); + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^101 = 2^104 */ + felem_diff(x_out, ftmp); + /* x_out[i] < 2^105 + 2^101 < 2^106 */ + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^101 + 2^101 = 2^102 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^106 + 2^106 = 2^107 */ + felem_square(tmp, ftmp); + felem_reduce(z_out, tmp); + felem_diff(z_out, delta); + /* z_out[i] < 2^105 + 2^101 < 2^106 */ + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^101 = 2^103 */ + felem_diff_zero107(beta, x_out); + /* beta[i] < 2^107 + 2^103 < 2^108 */ + felem_small_mul(tmp, small2, beta); + /* tmp[i] < 7 * 2^64 < 2^67 */ + smallfelem_square(tmp2, small1); + /* tmp2[i] < 7 * 2^64 */ + longfelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + } + +/* point_double_small is the same as point_double, except that it operates on + * smallfelems */ +static void +point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, + const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) + { + felem felem_x_out, felem_y_out, felem_z_out; + felem felem_x_in, felem_y_in, felem_z_in; + + smallfelem_expand(felem_x_in, x_in); + smallfelem_expand(felem_y_in, y_in); + smallfelem_expand(felem_z_in, z_in); + point_double(felem_x_out, felem_y_out, felem_z_out, + felem_x_in, felem_y_in, felem_z_in); + felem_shrink(x_out, felem_x_out); + felem_shrink(y_out, felem_y_out); + felem_shrink(z_out, felem_z_out); + } + +/* copy_conditional copies in to out iff mask is all ones. */ +static void +copy_conditional(felem out, const felem in, limb mask) + { + unsigned i; + for (i = 0; i < NLIMBS; ++i) + { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/* copy_small_conditional copies in to out iff mask is all ones. */ +static void +copy_small_conditional(felem out, const smallfelem in, limb mask) + { + unsigned i; + const u64 mask64 = mask; + for (i = 0; i < NLIMBS; ++i) + { + out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); + } + } + +/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal, (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + longfelem tmp, tmp2; + smallfelem small1, small2, small3, small4, small5; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + felem_shrink(small3, z1); + + z1_is_zero = smallfelem_is_zero(small3); + z2_is_zero = smallfelem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + smallfelem_square(tmp, small3); + felem_reduce(ftmp, tmp); + /* ftmp[i] < 2^101 */ + felem_shrink(small1, ftmp); + + if(!mixed) + { + /* ftmp2 = z2z2 = z2**2 */ + smallfelem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + /* ftmp2[i] < 2^101 */ + felem_shrink(small2, ftmp2); + + felem_shrink(small5, x1); + + /* u1 = ftmp3 = x1*z2z2 */ + smallfelem_mul(tmp, small5, small2); + felem_reduce(ftmp3, tmp); + /* ftmp3[i] < 2^101 */ + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_small_sum(ftmp5, z2); + /* ftmp5[i] < 2^107 */ + + /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ + felem_square(tmp, ftmp5); + felem_reduce(ftmp5, tmp); + /* ftmp2 = z2z2 + z1z1 */ + felem_sum(ftmp2, ftmp); + /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ + felem_diff(ftmp5, ftmp2); + /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ + + /* ftmp2 = z2 * z2z2 */ + smallfelem_mul(tmp, small2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + /* ftmp6[i] < 2^101 */ + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + /* ftmp3[i] < 2^106 */ + + /* ftmp5 = 2z1z2 */ + felem_assign(ftmp5, z1); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2*2^106 = 2^107 */ + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + /* ftmp6[i] < 2^106 */ + } + + /* u2 = x2*z1z1 */ + smallfelem_mul(tmp, x2, small1); + felem_reduce(ftmp4, tmp); + + /* h = ftmp4 = u2 - u1 */ + felem_diff_zero107(ftmp4, ftmp3); + /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ + felem_shrink(small4, ftmp4); + + x_equal = smallfelem_is_zero(small4); + + /* z_out = ftmp5 * h */ + felem_small_mul(tmp, small4, ftmp5); + felem_reduce(z_out, tmp); + /* z_out[i] < 2^101 */ + + /* ftmp = z1 * z1z1 */ + smallfelem_mul(tmp, small1, small3); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_small_mul(tmp, y2, ftmp); + felem_reduce(ftmp5, tmp); + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_zero107(ftmp5, ftmp6); + /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2^109 */ + felem_shrink(small1, ftmp5); + y_equal = smallfelem_is_zero(small1); + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar(ftmp, 2); + /* ftmp[i] < 2*2^108 = 2^109 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + smallfelem_square(tmp, small1); + felem_reduce(x_out, tmp); + felem_assign(ftmp3, ftmp4); + felem_scalar(ftmp4, 2); + felem_sum(ftmp4, ftmp2); + /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ + felem_diff(x_out, ftmp4); + /* x_out[i] < 2^105 + 2^101 */ + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff_zero107(ftmp3, x_out); + /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ + felem_small_mul(tmp, small1, ftmp3); + felem_mul(tmp2, ftmp6, ftmp2); + longfelem_scalar(tmp2, 2); + /* tmp2[i] < 2*2^67 = 2^68 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + + copy_small_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_small_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_small_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* point_add_small is the same as point_add, except that it operates on + * smallfelems */ +static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) + { + felem felem_x3, felem_y3, felem_z3; + felem felem_x1, felem_y1, felem_z1; + smallfelem_expand(felem_x1, x1); + smallfelem_expand(felem_y1, y1); + smallfelem_expand(felem_z1, z1); + point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2); + felem_shrink(x3, felem_x3); + felem_shrink(y3, felem_y3); + felem_shrink(z3, felem_z3); + } + +/* Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^64G + * 3 | 0 0 1 1 | (2^64 + 1)G + * 4 | 0 1 0 0 | 2^128G + * 5 | 0 1 0 1 | (2^128 + 1)G + * 6 | 0 1 1 0 | (2^128 + 2^64)G + * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G + * 8 | 1 0 0 0 | 2^192G + * 9 | 1 0 0 1 | (2^192 + 1)G + * 10 | 1 0 1 0 | (2^192 + 2^64)G + * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G + * 12 | 1 1 0 0 | (2^192 + 2^128)G + * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G + * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G + * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G + * followed by a copy of this with each element multiplied by 2^32. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const smallfelem gmul[2][16][3] = +{{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, + {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, + {1, 0, 0, 0}}, + {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, + {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, + {1, 0, 0, 0}}, + {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, + {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, + {1, 0, 0, 0}}, + {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, + {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, + {1, 0, 0, 0}}, + {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, + {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, + {1, 0, 0, 0}}, + {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, + {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, + {1, 0, 0, 0}}, + {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, + {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, + {1, 0, 0, 0}}, + {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, + {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, + {1, 0, 0, 0}}, + {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, + {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, + {1, 0, 0, 0}}, + {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, + {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, + {1, 0, 0, 0}}, + {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, + {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, + {1, 0, 0, 0}}, + {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, + {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, + {1, 0, 0, 0}}, + {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, + {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, + {1, 0, 0, 0}}, + {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, + {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, + {1, 0, 0, 0}}, + {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, + {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, + {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, + {1, 0, 0, 0}}, + {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, + {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, + {1, 0, 0, 0}}, + {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, + {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, + {1, 0, 0, 0}}, + {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, + {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, + {1, 0, 0, 0}}, + {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, + {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, + {1, 0, 0, 0}}, + {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, + {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, + {1, 0, 0, 0}}, + {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, + {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, + {1, 0, 0, 0}}, + {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, + {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, + {1, 0, 0, 0}}, + {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, + {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, + {1, 0, 0, 0}}, + {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, + {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, + {1, 0, 0, 0}}, + {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, + {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, + {1, 0, 0, 0}}, + {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, + {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, + {1, 0, 0, 0}}, + {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, + {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, + {1, 0, 0, 0}}, + {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, + {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, + {1, 0, 0, 0}}, + {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, + {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, + {1, 0, 0, 0}}}}; + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) + { + unsigned i, j; + u64 *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(smallfelem)); + + for (i = 0; i < size; i++) + { + const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) + { + if ((i < 0) || (i >= 256)) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) + { + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], ftmp; + smallfelem tmp[3]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (two in each of the last 32 rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 255 : 31); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 31)) + { + /* first, look 32 bits upwards */ + bits = get_bit(g_scalar, i + 224) << 3; + bits |= get_bit(g_scalar, i + 160) << 2; + bits |= get_bit(g_scalar, i + 96) << 1; + bits |= get_bit(g_scalar, i + 32); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 192) << 3; + bits |= get_bit(g_scalar, i + 128) << 2; + bits |= get_bit(g_scalar, i + 64) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract, in constant time */ + select_point(digit, 17, pre_comp[num], tmp); + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); + felem_contract(tmp[1], ftmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + +/* Precomputation for the group generator. */ +typedef struct { + smallfelem g_pre_comp[2][16][3]; + int references; +} NISTP256_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp256_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp256_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp256_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp256_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp256_points_mul, + ec_GFp_nistp256_precompute_mult, + ec_GFp_nistp256_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP256_PRE_COMP *nistp256_pre_comp_new() + { + NISTP256_PRE_COMP *ret = NULL; + ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) + { + ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp256_pre_comp_dup(void *src_) + { + NISTP256_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp256_pre_comp_free(void *pre_) + { + int i; + NISTP256_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp256_pre_comp_clear_free(void *pre_) + { + int i; + NISTP256_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp256_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_256; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in; + smallfelem x_out, y_out; + longfelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!smallfelem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!smallfelem_to_BN(y, y_out)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(smallfelem), + tmp_smallfelems, + (void (*)(void *)) smallfelem_one, + (int (*)(const void *)) smallfelem_is_zero_int, + (void (*)(void *, const void *)) smallfelem_assign, + (void (*)(void *, const void *)) smallfelem_square_contract, + (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, + (void (*)(void *, const void *)) smallfelem_inv_contract, + (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + smallfelem (*pre_comp)[17][3] = NULL; + smallfelem *tmp_smallfelems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + smallfelem x_in, y_in, z_in; + felem x_out, y_out, z_out; + NISTP256_PRE_COMP *pre = NULL; + const smallfelem (*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp256_pre_comp_dup, nistp256_pre_comp_free, + nistp256_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points++; + } + if (num_points > 0) + { + if (num_points >= 3) + { + /* unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem)); + if (mixed) + tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* we didn't have a valid precomputation, so we pick + * the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + felem_shrink(pre_comp[i][1][0], x_out); + felem_shrink(pre_comp[i][1][1], y_out); + felem_shrink(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add_small( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double_small( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const smallfelem (*)[17][3]) pre_comp, + g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || + (!smallfelem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_smallfelems != NULL) + OPENSSL_free(tmp_smallfelems); + return ret; + } + +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP256_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + smallfelem tmp_smallfelems[32]; + felem x_tmp, y_tmp, z_tmp; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp256_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(x_tmp, &group->generator->X)) || + (!BN_to_felem(y_tmp, &group->generator->Y)) || + (!BN_to_felem(z_tmp, &group->generator->Z))) + goto err; + felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); + felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); + felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); + /* compute 2^64*G, 2^128*G, 2^192*G for the first table, + * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) + { + point_double_small( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 31; ++j) + { + point_double_small( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double_small( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 31; ++j) + { + point_double_small( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); + } + } + for (i = 0; i < 2; i++) + { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ + point_add_small( + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); + /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) + { + /* odd multiples: add G resp. 2^32*G */ + point_add_small( + pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], pre->g_pre_comp[i][2*j+1][2], + pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp256_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } +#else +static void *dummy=&dummy; +#endif diff --git a/openssl/crypto/ec/ecp_nistp521.c b/openssl/crypto/ec/ecp_nistp521.c new file mode 100644 index 000000000..178b655f7 --- /dev/null +++ b/openssl/crypto/ec/ecp_nistp521.c @@ -0,0 +1,2025 @@ +/* crypto/ec/ecp_nistp521.c */ +/* + * Written by Adam Langley (Google) for the OpenSSL project + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-521 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint64_t u64; +typedef int64_t s64; + +/* The underlying field. + * + * P521 operates over GF(2^521-1). We can serialise an element of this field + * into 66 bytes where the most significant byte contains only a single bit. We + * call this an felem_bytearray. */ + +typedef u8 felem_bytearray[66]; + +/* These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5. + * These values are big-endian. */ +static const felem_bytearray nistp521_curve_params[5] = + { + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* p */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff}, + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* a = -3 */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xfc}, + {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, /* b */ + 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, + 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, + 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, + 0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, + 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, + 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, + 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, + 0x3f, 0x00}, + {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, /* x */ + 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, + 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, + 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, + 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, + 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, + 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, + 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, + 0xbd, 0x66}, + {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, /* y */ + 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, + 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, + 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, + 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, + 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, + 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, + 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, + 0x66, 0x50} + }; + +/* The representation of field elements. + * ------------------------------------ + * + * We represent field elements with nine values. These values are either 64 or + * 128 bits and the field element represented is: + * v[0]*2^0 + v[1]*2^58 + v[2]*2^116 + ... + v[8]*2^464 (mod p) + * Each of the nine values is called a 'limb'. Since the limbs are spaced only + * 58 bits apart, but are greater than 58 bits in length, the most significant + * bits of each limb overlap with the least significant bits of the next. + * + * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a + * 'largefelem' */ + +#define NLIMBS 9 + +typedef uint64_t limb; +typedef limb felem[NLIMBS]; +typedef uint128_t largefelem[NLIMBS]; + +static const limb bottom57bits = 0x1ffffffffffffff; +static const limb bottom58bits = 0x3ffffffffffffff; + +/* bin66_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. */ +static void bin66_to_felem(felem out, const u8 in[66]) + { + out[0] = (*((limb*) &in[0])) & bottom58bits; + out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; + out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; + out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; + out[4] = (*((limb*) &in[29])) & bottom58bits; + out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; + out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; + out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; + out[8] = (*((limb*) &in[58])) & bottom57bits; + } + +/* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte + * array. This assumes that the CPU is little-endian. */ +static void felem_to_bin66(u8 out[66], const felem in) + { + memset(out, 0, 66); + (*((limb*) &out[0])) = in[0]; + (*((limb*) &out[7])) |= in[1] << 2; + (*((limb*) &out[14])) |= in[2] << 4; + (*((limb*) &out[21])) |= in[3] << 6; + (*((limb*) &out[29])) = in[4]; + (*((limb*) &out[36])) |= in[5] << 2; + (*((limb*) &out[43])) |= in[6] << 4; + (*((limb*) &out[50])) |= in[7] << 6; + (*((limb*) &out[58])) = in[8]; + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin66_to_felem(out, b_out); + return 1; + } + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) + { + felem_bytearray b_in, b_out; + felem_to_bin66(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + + +/* Field operations + * ---------------- */ + +static void felem_one(felem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 0; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + out[4] = in[4]; + out[5] = in[5]; + out[6] = in[6]; + out[7] = in[7]; + out[8] = in[8]; + } + +/* felem_sum64 sets out = out + in. */ +static void felem_sum64(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + out[4] += in[4]; + out[5] += in[5]; + out[6] += in[6]; + out[7] += in[7]; + out[8] += in[8]; + } + +/* felem_scalar sets out = in * scalar */ +static void felem_scalar(felem out, const felem in, limb scalar) + { + out[0] = in[0] * scalar; + out[1] = in[1] * scalar; + out[2] = in[2] * scalar; + out[3] = in[3] * scalar; + out[4] = in[4] * scalar; + out[5] = in[5] * scalar; + out[6] = in[6] * scalar; + out[7] = in[7] * scalar; + out[8] = in[8] * scalar; + } + +/* felem_scalar64 sets out = out * scalar */ +static void felem_scalar64(felem out, limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; + } + +/* felem_scalar128 sets out = out * scalar */ +static void felem_scalar128(largefelem out, limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; + } + +/* felem_neg sets |out| to |-in| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < 2^62 + */ +static void felem_neg(felem out, const felem in) + { + /* In order to prevent underflow, we subtract from 0 mod p. */ + static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] = two62m3 - in[0]; + out[1] = two62m2 - in[1]; + out[2] = two62m2 - in[2]; + out[3] = two62m2 - in[3]; + out[4] = two62m2 - in[4]; + out[5] = two62m2 - in[5]; + out[6] = two62m2 - in[6]; + out[7] = two62m2 - in[7]; + out[8] = two62m2 - in[8]; + } + +/* felem_diff64 subtracts |in| from |out| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < out[i] + 2^62 + */ +static void felem_diff64(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] += two62m3 - in[0]; + out[1] += two62m2 - in[1]; + out[2] += two62m2 - in[2]; + out[3] += two62m2 - in[3]; + out[4] += two62m2 - in[4]; + out[5] += two62m2 - in[5]; + out[6] += two62m2 - in[6]; + out[7] += two62m2 - in[7]; + out[8] += two62m2 - in[8]; + } + +/* felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^62 + 2^17 + * On exit: + * out[i] < out[i] + 2^63 + */ +static void felem_diff_128_64(largefelem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] += two63m6 - in[0]; + out[1] += two63m5 - in[1]; + out[2] += two63m5 - in[2]; + out[3] += two63m5 - in[3]; + out[4] += two63m5 - in[4]; + out[5] += two63m5 - in[5]; + out[6] += two63m5 - in[6]; + out[7] += two63m5 - in[7]; + out[8] += two63m5 - in[8]; + } + +/* felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^126 + * On exit: + * out[i] < out[i] + 2^127 - 2^69 + */ +static void felem_diff128(largefelem out, const largefelem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); + static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); + + out[0] += (two127m70 - in[0]); + out[1] += (two127m69 - in[1]); + out[2] += (two127m69 - in[2]); + out[3] += (two127m69 - in[3]); + out[4] += (two127m69 - in[4]); + out[5] += (two127m69 - in[5]); + out[6] += (two127m69 - in[6]); + out[7] += (two127m69 - in[7]); + out[8] += (two127m69 - in[8]); + } + +/* felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^62 + * On exit: + * out[i] < 17 * max(in[i]) * max(in[i]) + */ +static void felem_square(largefelem out, const felem in) + { + felem inx2, inx4; + felem_scalar(inx2, in, 2); + felem_scalar(inx4, in, 4); + + /* We have many cases were we want to do + * in[x] * in[y] + + * in[y] * in[x] + * This is obviously just + * 2 * in[x] * in[y] + * However, rather than do the doubling on the 128 bit result, we + * double one of the inputs to the multiplication by reading from + * |inx2| */ + + out[0] = ((uint128_t) in[0]) * in[0]; + out[1] = ((uint128_t) in[0]) * inx2[1]; + out[2] = ((uint128_t) in[0]) * inx2[2] + + ((uint128_t) in[1]) * in[1]; + out[3] = ((uint128_t) in[0]) * inx2[3] + + ((uint128_t) in[1]) * inx2[2]; + out[4] = ((uint128_t) in[0]) * inx2[4] + + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; + out[5] = ((uint128_t) in[0]) * inx2[5] + + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; + out[6] = ((uint128_t) in[0]) * inx2[6] + + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; + out[7] = ((uint128_t) in[0]) * inx2[7] + + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; + out[8] = ((uint128_t) in[0]) * inx2[8] + + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; + + /* The remaining limbs fall above 2^521, with the first falling at + * 2^522. They correspond to locations one bit up from the limbs + * produced above so we would have to multiply by two to align them. + * Again, rather than operate on the 128-bit result, we double one of + * the inputs to the multiplication. If we want to double for both this + * reason, and the reason above, then we end up multiplying by four. */ + + /* 9 */ + out[0] += ((uint128_t) in[1]) * inx4[8] + + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + + ((uint128_t) in[4]) * inx4[5]; + + /* 10 */ + out[1] += ((uint128_t) in[2]) * inx4[8] + + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + + ((uint128_t) in[5]) * inx2[5]; + + /* 11 */ + out[2] += ((uint128_t) in[3]) * inx4[8] + + ((uint128_t) in[4]) * inx4[7] + + ((uint128_t) in[5]) * inx4[6]; + + /* 12 */ + out[3] += ((uint128_t) in[4]) * inx4[8] + + ((uint128_t) in[5]) * inx4[7] + + ((uint128_t) in[6]) * inx2[6]; + + /* 13 */ + out[4] += ((uint128_t) in[5]) * inx4[8] + + ((uint128_t) in[6]) * inx4[7]; + + /* 14 */ + out[5] += ((uint128_t) in[6]) * inx4[8] + + ((uint128_t) in[7]) * inx2[7]; + + /* 15 */ + out[6] += ((uint128_t) in[7]) * inx4[8]; + + /* 16 */ + out[7] += ((uint128_t) in[8]) * inx2[8]; + } + +/* felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^64 + * in2[i] < 2^63 + * On exit: + * out[i] < 17 * max(in1[i]) * max(in2[i]) + */ +static void felem_mul(largefelem out, const felem in1, const felem in2) + { + felem in2x2; + felem_scalar(in2x2, in2, 2); + + out[0] = ((uint128_t) in1[0]) * in2[0]; + + out[1] = ((uint128_t) in1[0]) * in2[1] + + ((uint128_t) in1[1]) * in2[0]; + + out[2] = ((uint128_t) in1[0]) * in2[2] + + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; + + out[3] = ((uint128_t) in1[0]) * in2[3] + + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; + + out[4] = ((uint128_t) in1[0]) * in2[4] + + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; + + out[5] = ((uint128_t) in1[0]) * in2[5] + + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; + + out[6] = ((uint128_t) in1[0]) * in2[6] + + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; + + out[7] = ((uint128_t) in1[0]) * in2[7] + + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; + + out[8] = ((uint128_t) in1[0]) * in2[8] + + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; + + /* See comment in felem_square about the use of in2x2 here */ + + out[0] += ((uint128_t) in1[1]) * in2x2[8] + + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; + + out[1] += ((uint128_t) in1[2]) * in2x2[8] + + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; + + out[2] += ((uint128_t) in1[3]) * in2x2[8] + + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; + + out[3] += ((uint128_t) in1[4]) * in2x2[8] + + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; + + out[4] += ((uint128_t) in1[5]) * in2x2[8] + + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; + + out[5] += ((uint128_t) in1[6]) * in2x2[8] + + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; + + out[6] += ((uint128_t) in1[7]) * in2x2[8] + + ((uint128_t) in1[8]) * in2x2[7]; + + out[7] += ((uint128_t) in1[8]) * in2x2[8]; + } + +static const limb bottom52bits = 0xfffffffffffff; + +/* felem_reduce converts a largefelem to an felem. + * On entry: + * in[i] < 2^128 + * On exit: + * out[i] < 2^59 + 2^14 + */ +static void felem_reduce(felem out, const largefelem in) + { + u64 overflow1, overflow2; + + out[0] = ((limb) in[0]) & bottom58bits; + out[1] = ((limb) in[1]) & bottom58bits; + out[2] = ((limb) in[2]) & bottom58bits; + out[3] = ((limb) in[3]) & bottom58bits; + out[4] = ((limb) in[4]) & bottom58bits; + out[5] = ((limb) in[5]) & bottom58bits; + out[6] = ((limb) in[6]) & bottom58bits; + out[7] = ((limb) in[7]) & bottom58bits; + out[8] = ((limb) in[8]) & bottom58bits; + + /* out[i] < 2^58 */ + + out[1] += ((limb) in[0]) >> 58; + out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; + /* out[1] < 2^58 + 2^6 + 2^58 + * = 2^59 + 2^6 */ + out[2] += ((limb) (in[0] >> 64)) >> 52; + + out[2] += ((limb) in[1]) >> 58; + out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6; + out[3] += ((limb) (in[1] >> 64)) >> 52; + + out[3] += ((limb) in[2]) >> 58; + out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6; + out[4] += ((limb) (in[2] >> 64)) >> 52; + + out[4] += ((limb) in[3]) >> 58; + out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6; + out[5] += ((limb) (in[3] >> 64)) >> 52; + + out[5] += ((limb) in[4]) >> 58; + out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6; + out[6] += ((limb) (in[4] >> 64)) >> 52; + + out[6] += ((limb) in[5]) >> 58; + out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6; + out[7] += ((limb) (in[5] >> 64)) >> 52; + + out[7] += ((limb) in[6]) >> 58; + out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6; + out[8] += ((limb) (in[6] >> 64)) >> 52; + + out[8] += ((limb) in[7]) >> 58; + out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; + /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 + * < 2^59 + 2^13 */ + overflow1 = ((limb) (in[7] >> 64)) >> 52; + + overflow1 += ((limb) in[8]) >> 58; + overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; + overflow2 = ((limb) (in[8] >> 64)) >> 52; + + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ + + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + + out[1] += out[0] >> 58; out[0] &= bottom58bits; + /* out[0] < 2^58 + * out[1] < 2^59 + 2^6 + 2^13 + 2^2 + * < 2^59 + 2^14 */ + } + +static void felem_square_reduce(felem out, const felem in) + { + largefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); + } + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) + { + largefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); + } + +/* felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2, ftmp3, ftmp4; + largefelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(ftmp2, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + + felem_assign(ftmp2, ftmp3); + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_assign(ftmp4, ftmp3); + felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 8; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 16; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 32; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 64; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 128; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 256; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + + for (i = 0; i < 9; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ +} + +/* This is 2^521-1, expressed as an felem */ +static const felem kPrime = + { + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff + }; + +/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static limb felem_is_zero(const felem in) + { + felem ftmp; + limb is_zero, is_p; + felem_assign(ftmp, in); + + ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; + /* ftmp[8] < 2^57 */ + ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; + /* ftmp[8] < 2^57 + 4 */ + + /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is + * greater than our bound for ftmp[8]. Therefore we only have to check + * if the zero is zero or 2^521-1. */ + + is_zero = 0; + is_zero |= ftmp[0]; + is_zero |= ftmp[1]; + is_zero |= ftmp[2]; + is_zero |= ftmp[3]; + is_zero |= ftmp[4]; + is_zero |= ftmp[5]; + is_zero |= ftmp[6]; + is_zero |= ftmp[7]; + is_zero |= ftmp[8]; + + is_zero--; + /* We know that ftmp[i] < 2^63, therefore the only way that the top bit + * can be set is if is_zero was 0 before the decrement. */ + is_zero = ((s64) is_zero) >> 63; + + is_p = ftmp[0] ^ kPrime[0]; + is_p |= ftmp[1] ^ kPrime[1]; + is_p |= ftmp[2] ^ kPrime[2]; + is_p |= ftmp[3] ^ kPrime[3]; + is_p |= ftmp[4] ^ kPrime[4]; + is_p |= ftmp[5] ^ kPrime[5]; + is_p |= ftmp[6] ^ kPrime[6]; + is_p |= ftmp[7] ^ kPrime[7]; + is_p |= ftmp[8] ^ kPrime[8]; + + is_p--; + is_p = ((s64) is_p) >> 63; + + is_zero |= is_p; + return is_zero; + } + +static int felem_is_zero_int(const felem in) + { + return (int) (felem_is_zero(in) & ((limb)1)); + } + +/* felem_contract converts |in| to its unique, minimal representation. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static void felem_contract(felem out, const felem in) + { + limb is_p, is_greater, sign; + static const limb two58 = ((limb)1) << 58; + + felem_assign(out, in); + + out[0] += out[8] >> 57; out[8] &= bottom57bits; + /* out[8] < 2^57 */ + out[1] += out[0] >> 58; out[0] &= bottom58bits; + out[2] += out[1] >> 58; out[1] &= bottom58bits; + out[3] += out[2] >> 58; out[2] &= bottom58bits; + out[4] += out[3] >> 58; out[3] &= bottom58bits; + out[5] += out[4] >> 58; out[4] &= bottom58bits; + out[6] += out[5] >> 58; out[5] &= bottom58bits; + out[7] += out[6] >> 58; out[6] &= bottom58bits; + out[8] += out[7] >> 58; out[7] &= bottom58bits; + /* out[8] < 2^57 + 4 */ + + /* If the value is greater than 2^521-1 then we have to subtract + * 2^521-1 out. See the comments in felem_is_zero regarding why we + * don't test for other multiples of the prime. */ + + /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ + + is_p = out[0] ^ kPrime[0]; + is_p |= out[1] ^ kPrime[1]; + is_p |= out[2] ^ kPrime[2]; + is_p |= out[3] ^ kPrime[3]; + is_p |= out[4] ^ kPrime[4]; + is_p |= out[5] ^ kPrime[5]; + is_p |= out[6] ^ kPrime[6]; + is_p |= out[7] ^ kPrime[7]; + is_p |= out[8] ^ kPrime[8]; + + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = ((s64) is_p) >> 63; + is_p = ~is_p; + + /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */ + + out[0] &= is_p; + out[1] &= is_p; + out[2] &= is_p; + out[3] &= is_p; + out[4] &= is_p; + out[5] &= is_p; + out[6] &= is_p; + out[7] &= is_p; + out[8] &= is_p; + + /* In order to test that |out| >= 2^521-1 we need only test if out[8] + * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ + is_greater = out[8] >> 57; + is_greater |= is_greater << 32; + is_greater |= is_greater << 16; + is_greater |= is_greater << 8; + is_greater |= is_greater << 4; + is_greater |= is_greater << 2; + is_greater |= is_greater << 1; + is_greater = ((s64) is_greater) >> 63; + + out[0] -= kPrime[0] & is_greater; + out[1] -= kPrime[1] & is_greater; + out[2] -= kPrime[2] & is_greater; + out[3] -= kPrime[3] & is_greater; + out[4] -= kPrime[4] & is_greater; + out[5] -= kPrime[5] & is_greater; + out[6] -= kPrime[6] & is_greater; + out[7] -= kPrime[7] & is_greater; + out[8] -= kPrime[8] & is_greater; + + /* Eliminate negative coefficients */ + sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); + sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); + sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); + sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); + sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); + sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); + sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); + sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); + sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); + sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); + sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); + } + +/* Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates */ + +/* point_double calcuates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + largefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff64(ftmp, delta); + /* ftmp[i] < 2^61 */ + felem_sum64(ftmp2, delta); + /* ftmp2[i] < 2^60 + 2^15 */ + felem_scalar64(ftmp2, 3); + /* ftmp2[i] < 3*2^60 + 3*2^15 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 17(3*2^121 + 3*2^76) + * = 61*2^121 + 61*2^76 + * < 64*2^121 + 64*2^76 + * = 2^127 + 2^82 + * < 2^128 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 17*2^120 + * < 2^125 */ + felem_assign(ftmp, beta); + felem_scalar64(ftmp, 8); + /* ftmp[i] < 2^62 + 2^17 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum64(delta, gamma); + /* delta[i] < 2^60 + 2^15 */ + felem_assign(ftmp, y_in); + felem_sum64(ftmp, z_in); + /* ftmp[i] < 2^60 + 2^15 */ + felem_square(tmp, ftmp); + /* tmp[i] < 17(2^122) + * < 2^127 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^127 + 2^63 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar64(beta, 4); + /* beta[i] < 2^61 + 2^16 */ + felem_diff64(beta, x_out); + /* beta[i] < 2^61 + 2^60 + 2^16 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) + * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) + * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * < 2^128 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 17*(2^59 + 2^14)^2 + * = 17*(2^118 + 2^74 + 2^28) */ + felem_scalar128(tmp2, 8); + /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) + * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 + * < 2^126 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + + * 2^74 + 2^69 + 2^34 + 2^30 + * < 2^128 */ + felem_reduce(y_out, tmp); + } + +/* copy_conditional copies in to out iff mask is all ones. */ +static void +copy_conditional(felem out, const felem in, limb mask) + { + unsigned i; + for (i = 0; i < NLIMBS; ++i) + { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + largefelem tmp, tmp2; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + if (!mixed) + { + /* ftmp2 = z2z2 = z2**2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* u1 = ftmp3 = x1*z2z2 */ + felem_mul(tmp, x1, ftmp2); + felem_reduce(ftmp3, tmp); + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_sum64(ftmp5, z2); + /* ftmp5[i] < 2^61 */ + + /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2 * z2z2 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + + /* ftmp5 = 2*z1z2 */ + felem_scalar(ftmp5, z1, 2); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + } + + /* u2 = x2*z1z1 */ + felem_mul(tmp, x2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* h = ftmp4 = u2 - u1 */ + felem_diff_128_64(tmp, ftmp3); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp4, tmp); + + x_equal = felem_is_zero(ftmp4); + + /* z_out = ftmp5 * h */ + felem_mul(tmp, ftmp5, ftmp4); + felem_reduce(z_out, tmp); + + /* ftmp = z1 * z1z1 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_mul(tmp, y2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_128_64(tmp, ftmp6); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp5, tmp); + y_equal = felem_is_zero(ftmp5); + felem_scalar64(ftmp5, 2); + /* ftmp5[i] < 2^61 */ + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar64(ftmp, 2); + /* ftmp[i] < 2^61 */ + felem_square(tmp, ftmp); + /* tmp[i] < 17*2^122 */ + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_assign(ftmp3, ftmp4); + felem_scalar64(ftmp4, 2); + /* ftmp4[i] < 2^61 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(x_out, tmp); + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff64(ftmp3, x_out); + /* ftmp3[i] < 2^60 + 2^60 + * = 2^61 */ + felem_mul(tmp, ftmp5, ftmp3); + /* tmp[i] < 17*2^122 */ + felem_mul(tmp2, ftmp6, ftmp2); + /* tmp2[i] < 17*2^120 */ + felem_scalar128(tmp2, 2); + /* tmp2[i] < 17*2^121 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^127 - 2^69 + 17*2^122 + * = 2^126 - 2^122 - 2^6 - 2^2 - 1 + * < 2^127 */ + felem_reduce(y_out, tmp); + + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 16 elements: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^130G + * 3 | 0 0 1 1 | (2^130 + 1)G + * 4 | 0 1 0 0 | 2^260G + * 5 | 0 1 0 1 | (2^260 + 1)G + * 6 | 0 1 1 0 | (2^260 + 2^130)G + * 7 | 0 1 1 1 | (2^260 + 2^130 + 1)G + * 8 | 1 0 0 0 | 2^390G + * 9 | 1 0 0 1 | (2^390 + 1)G + * 10 | 1 0 1 0 | (2^390 + 2^130)G + * 11 | 1 0 1 1 | (2^390 + 2^130 + 1)G + * 12 | 1 1 0 0 | (2^390 + 2^260)G + * 13 | 1 1 0 1 | (2^390 + 2^260 + 1)G + * 14 | 1 1 1 0 | (2^390 + 2^260 + 2^130)G + * 15 | 1 1 1 1 | (2^390 + 2^260 + 2^130 + 1)G + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const felem gmul[16][3] = + {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, + 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, + {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, + 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, + 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, + {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, + 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, + 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, + {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, + 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, + 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, + {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, + 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, + 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, + {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, + 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, + 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, + {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, + 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, + 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, + {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, + 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, + 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, + {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, + 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, + 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, + {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, + 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, + 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, + {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, + 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, + 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, + {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, + 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, + 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, + {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, + 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, + 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, + {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, + 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, + 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, + {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, + 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, + 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, + {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, + 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], + felem out[3]) + { + unsigned i, j; + limb *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(felem)); + + for (i = 0; i < size; i++) + { + const limb *inlimbs = &pre_comp[i][0][0]; + limb mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) + { + if (i < 0) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) + { + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + limb bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (last quarter of rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 520 : 130); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 130)) + { + bits = get_bit(g_scalar, i + 390) << 3; + if (i < 130) + { + bits |= get_bit(g_scalar, i + 260) << 2; + bits |= get_bit(g_scalar, i + 130) << 1; + bits |= get_bit(g_scalar, i); + } + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp, tmp); + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract, in constant time */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_conditional(tmp[1], tmp[3], (-(limb) sign)); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + + +/* Precomputation for the group generator. */ +typedef struct { + felem g_pre_comp[16][3]; + int references; +} NISTP521_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp521_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp521_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp521_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp521_points_mul, + ec_GFp_nistp521_precompute_mult, + ec_GFp_nistp521_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP521_PRE_COMP *nistp521_pre_comp_new() + { + NISTP521_PRE_COMP *ret = NULL; + ret = (NISTP521_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP521_PRE_COMP)); + if (!ret) + { + ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp521_pre_comp_dup(void *src_) + { + NISTP521_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp521_pre_comp_free(void *pre_) + { + int i; + NISTP521_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp521_pre_comp_clear_free(void *pre_) + { + int i; + NISTP521_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof(*pre)); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp521_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_521; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in, x_out, y_out; + largefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!felem_to_BN(x, x_out)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!felem_to_BN(y, y_out)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *)) felem_one, + (int (*)(const void *)) felem_is_zero_int, + (void (*)(void *, const void *)) felem_assign, + (void (*)(void *, const void *)) felem_square_reduce, + (void (*)(void *, const void *, const void *)) felem_mul_reduce, + (void (*)(void *, const void *)) felem_inv, + (void (*)(void *, const void *)) felem_contract); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP521_PRE_COMP *pre = NULL; + felem (*g_pre_comp)[3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp521_pre_comp_dup, nistp521_pre_comp_free, + nistp521_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = &pre->g_pre_comp[0]; + else + /* try to use the standard precomputation */ + g_pre_comp = (felem (*)[3]) gmul; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[1][0]) || + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points++; + } + + if (num_points > 0) + { + if (num_points >= 2) + { + /* unless we precompute multiples for just one point, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); + if (mixed) + tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* we didn't have a valid precomputation, so we pick + * the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); + memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); + memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const felem (*)[17][3]) pre_comp, + (const felem (*)[3]) g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_felems != NULL) + OPENSSL_free(tmp_felems); + return ret; + } + +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP521_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[16]; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp521_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) + goto err; + /* compute 2^130*G, 2^260*G, 2^390*G */ + for (i = 1; i <= 4; i <<= 1) + { + point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) + { + point_double(pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2], + pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2]); + } + } + /* g_pre_comp[0] is the point at infinity */ + memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); + /* the remaining multiples */ + /* 2^130*G + 2^260*G */ + point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^130*G + 2^390*G */ + point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); + /* 2^130*G + 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) + { + /* odd multiples: add G */ + point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], + pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], + 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } + make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp521_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } + +#else +static void *dummy=&dummy; +#endif diff --git a/openssl/crypto/ec/ecp_nistputil.c b/openssl/crypto/ec/ecp_nistputil.c new file mode 100644 index 000000000..c8140c807 --- /dev/null +++ b/openssl/crypto/ec/ecp_nistputil.c @@ -0,0 +1,197 @@ +/* crypto/ec/ecp_nistputil.c */ +/* + * Written by Bodo Moeller for the OpenSSL project. + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +/* + * Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c. + */ + +#include <stddef.h> +#include "ec_lcl.h" + +/* Convert an array of points into affine coordinates. + * (If the point at infinity is found (Z = 0), it remains unchanged.) + * This function is essentially an equivalent to EC_POINTs_make_affine(), but + * works with the internal representation of points as used by ecp_nistp###.c + * rather than with (BIGNUM-based) EC_POINT data structures. + * + * point_array is the input/output buffer ('num' points in projective form, + * i.e. three coordinates each), based on an internal representation of + * field elements of size 'felem_size'. + * + * tmp_felems needs to point to a temporary array of 'num'+1 field elements + * for storage of intermediate values. + */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)) + { + int i = 0; + +#define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) +#define X(I) (&((char *)point_array)[3*(I) * felem_size]) +#define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size]) +#define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size]) + + if (!felem_is_zero(Z(0))) + felem_assign(tmp_felem(0), Z(0)); + else + felem_one(tmp_felem(0)); + for (i = 1; i < (int)num; i++) + { + if (!felem_is_zero(Z(i))) + felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); + else + felem_assign(tmp_felem(i), tmp_felem(i-1)); + } + /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: + * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ + + felem_inv(tmp_felem(num-1), tmp_felem(num-1)); + for (i = num - 1; i >= 0; i--) + { + if (i > 0) + /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), + * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) + */ + felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ + else + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + + if (!felem_is_zero(Z(i))) + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); + + /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + felem_contract(X(i), X(i)); + felem_contract(Y(i), Y(i)); + felem_one(Z(i)); + } + else + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_assign(tmp_felem(i-1), tmp_felem(i)); + } + } + } + +/* + * This function looks at 5+1 scalar bits (5 current, 1 adjacent less + * significant bit), and recodes them into a signed digit for use in fast point + * multiplication: the use of signed rather than unsigned digits means that + * fewer points need to be precomputed, given that point inversion is easy + * (a precomputed point dP makes -dP available as well). + * + * BACKGROUND: + * + * Signed digits for multiplication were introduced by Booth ("A signed binary + * multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, + * pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. + * Booth's original encoding did not generally improve the density of nonzero + * digits over the binary representation, and was merely meant to simplify the + * handling of signed factors given in two's complement; but it has since been + * shown to be the basis of various signed-digit representations that do have + * further advantages, including the wNAF, using the following general approach: + * + * (1) Given a binary representation + * + * b_k ... b_2 b_1 b_0, + * + * of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 + * by using bit-wise subtraction as follows: + * + * b_k b_(k-1) ... b_2 b_1 b_0 + * - b_k ... b_3 b_2 b_1 b_0 + * ------------------------------------- + * s_k b_(k-1) ... s_3 s_2 s_1 s_0 + * + * A left-shift followed by subtraction of the original value yields a new + * representation of the same value, using signed bits s_i = b_(i+1) - b_i. + * This representation from Booth's paper has since appeared in the + * literature under a variety of different names including "reversed binary + * form", "alternating greedy expansion", "mutual opposite form", and + * "sign-alternating {+-1}-representation". + * + * An interesting property is that among the nonzero bits, values 1 and -1 + * strictly alternate. + * + * (2) Various window schemes can be applied to the Booth representation of + * integers: for example, right-to-left sliding windows yield the wNAF + * (a signed-digit encoding independently discovered by various researchers + * in the 1990s), and left-to-right sliding windows yield a left-to-right + * equivalent of the wNAF (independently discovered by various researchers + * around 2004). + * + * To prevent leaking information through side channels in point multiplication, + * we need to recode the given integer into a regular pattern: sliding windows + * as in wNAFs won't do, we need their fixed-window equivalent -- which is a few + * decades older: we'll be using the so-called "modified Booth encoding" due to + * MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 + * (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five + * signed bits into a signed digit: + * + * s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) + * + * The sign-alternating property implies that the resulting digit values are + * integers from -16 to 16. + * + * Of course, we don't actually need to compute the signed digits s_i as an + * intermediate step (that's just a nice way to see how this scheme relates + * to the wNAF): a direct computation obtains the recoded digit from the + * six bits b_(4j + 4) ... b_(4j - 1). + * + * This function takes those five bits as an integer (0 .. 63), writing the + * recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute + * value, in the range 0 .. 8). Note that this integer essentially provides the + * input bits "shifted to the left" by one position: for example, the input to + * compute the least significant recoded digit, given that there's no bit b_-1, + * has to be b_4 b_3 b_2 b_1 b_0 0. + * + */ +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) + { + unsigned char s, d; + + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; + } +#else +static void *dummy=&dummy; +#endif diff --git a/openssl/crypto/ec/ecp_oct.c b/openssl/crypto/ec/ecp_oct.c new file mode 100644 index 000000000..374a0ee73 --- /dev/null +++ b/openssl/crypto/ec/ecp_oct.c @@ -0,0 +1,433 @@ +/* crypto/ec/ecp_oct.c */ +/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> + * for the OpenSSL project. + * Includes code written by Bodo Moeller for the OpenSSL project. +*/ +/* ==================================================================== + * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <openssl/err.h> +#include <openssl/symhacks.h> + +#include "ec_lcl.h" + +int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) + { + BN_CTX *new_ctx = NULL; + BIGNUM *tmp1, *tmp2, *x, *y; + int ret = 0; + + /* clear error queue*/ + ERR_clear_error(); + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0); + + BN_CTX_start(ctx); + tmp1 = BN_CTX_get(ctx); + tmp2 = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + /* Recover y. We have a Weierstrass equation + * y^2 = x^3 + a*x + b, + * so y is one of the square roots of x^3 + a*x + b. + */ + + /* tmp1 := x^3 */ + if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; + if (group->meth->field_decode == 0) + { + /* field_{sqr,mul} work on standard representation */ + if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; + if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; + } + else + { + if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; + if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; + } + + /* tmp1 := tmp1 + a*x */ + if (group->a_is_minus3) + { + if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; + if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; + if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + else + { + if (group->meth->field_decode) + { + if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; + if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; + } + else + { + /* field_mul works on standard representation */ + if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; + } + + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + + /* tmp1 := tmp1 + b */ + if (group->meth->field_decode) + { + if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + else + { + if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; + } + + if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) + { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) + { + ERR_clear_error(); + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + } + else + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); + goto err; + } + + if (y_bit != BN_is_odd(y)) + { + if (BN_is_zero(y)) + { + int kron; + + kron = BN_kronecker(x, &group->field, ctx); + if (kron == -2) goto err; + + if (kron == 1) + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); + else + /* BN_mod_sqrt() should have cought this error (not a square) */ + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + goto err; + } + if (!BN_usub(y, &group->field, y)) goto err; + } + if (y_bit != BN_is_odd(y)) + { + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) + { + /* encodes to a single 0 octet */ + if (buf != NULL) + { + if (len < 1) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + + /* ret := required output buffer length */ + field_len = BN_num_bytes(&group->field); + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) + { + if (len < ret) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + + if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) + buf[0] = form + 1; + else + buf[0] = form; + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) + { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return 0; + } + + +int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) + { + if (len != 1) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = BN_num_bytes(&group->field); + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + if (len != enc_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) goto err; + if (BN_ucmp(x, &group->field) >= 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) + { + if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; + } + else + { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; + if (BN_ucmp(y, &group->field) >= 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) + { + if (y_bit != BN_is_odd(y)) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + diff --git a/openssl/crypto/ec/ecp_smpl.c b/openssl/crypto/ec/ecp_smpl.c index 66a92e2a9..7cbb321f9 100644 --- a/openssl/crypto/ec/ecp_smpl.c +++ b/openssl/crypto/ec/ecp_smpl.c @@ -65,11 +65,19 @@ #include <openssl/err.h> #include <openssl/symhacks.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + #include "ec_lcl.h" const EC_METHOD *EC_GFp_simple_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_simple_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_simple_group_init, ec_GFp_simple_group_finish, @@ -88,9 +96,7 @@ const EC_METHOD *EC_GFp_simple_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -110,6 +116,7 @@ const EC_METHOD *EC_GFp_simple_method(void) 0 /* field_set_to_one */ }; return &ret; +#endif } @@ -633,372 +640,6 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P return ret; } - -int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { - BN_CTX *new_ctx = NULL; - BIGNUM *tmp1, *tmp2, *x, *y; - int ret = 0; - - /* clear error queue*/ - ERR_clear_error(); - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - y_bit = (y_bit != 0); - - BN_CTX_start(ctx); - tmp1 = BN_CTX_get(ctx); - tmp2 = BN_CTX_get(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - /* Recover y. We have a Weierstrass equation - * y^2 = x^3 + a*x + b, - * so y is one of the square roots of x^3 + a*x + b. - */ - - /* tmp1 := x^3 */ - if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; - if (group->meth->field_decode == 0) - { - /* field_{sqr,mul} work on standard representation */ - if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; - if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; - } - - /* tmp1 := tmp1 + a*x */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; - if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; - if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; - } - else - { - /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; - } - - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - - /* tmp1 := tmp1 + b */ - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; - } - - if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) - { - unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) - { - ERR_clear_error(); - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); - goto err; - } - - if (y_bit != BN_is_odd(y)) - { - if (BN_is_zero(y)) - { - int kron; - - kron = BN_kronecker(x, &group->field, ctx); - if (kron == -2) goto err; - - if (kron == 1) - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); - else - /* BN_mod_sqrt() should have cought this error (not a square) */ - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - goto err; - } - if (!BN_usub(y, &group->field, y)) goto err; - } - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - -size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - size_t ret; - BN_CTX *new_ctx = NULL; - int used_ctx = 0; - BIGNUM *x, *y; - size_t field_len, i, skip; - - if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); - goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { - /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - buf[0] = 0; - } - return 1; - } - - - /* ret := required output buffer length */ - field_len = BN_num_bytes(&group->field); - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - goto err; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - used_ctx = 1; - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - - if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) - buf[0] = form + 1; - else - buf[0] = form; - - i = 1; - - skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(x, buf + i); - i += skip; - if (i != 1 + field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { - skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(y, buf + i); - i += skip; - } - - if (i != ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - - err: - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return 0; - } - - -int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - point_conversion_form_t form; - int y_bit; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - size_t field_len, enc_len; - int ret = 0; - - if (len == 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - form = buf[0]; - y_bit = form & 1; - form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (form == 0) - { - if (len != 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - return EC_POINT_set_to_infinity(group, point); - } - - field_len = BN_num_bytes(&group->field); - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - if (len != enc_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); - goto err; - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); diff --git a/openssl/crypto/ec/ectest.c b/openssl/crypto/ec/ectest.c index 7509cb9c7..f107782de 100644 --- a/openssl/crypto/ec/ectest.c +++ b/openssl/crypto/ec/ectest.c @@ -94,6 +94,7 @@ int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); retur #include <openssl/objects.h> #include <openssl/rand.h> #include <openssl/bn.h> +#include <openssl/opensslconf.h> #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) /* suppress "too big too optimize" warning */ @@ -107,10 +108,6 @@ int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); retur EXIT(1); \ } while (0) -void prime_field_tests(void); -void char2_field_tests(void); -void internal_curve_test(void); - #define TIMING_BASE_PT 0 #define TIMING_RAND_PT 1 #define TIMING_SIMUL 2 @@ -195,7 +192,50 @@ static void timings(EC_GROUP *group, int type, BN_CTX *ctx) } #endif -void prime_field_tests() +/* test multiplication with group order, long and negative scalars */ +static void group_order_tests(EC_GROUP *group) + { + BIGNUM *n1, *n2, *order; + EC_POINT *P = EC_POINT_new(group); + EC_POINT *Q = EC_POINT_new(group); + BN_CTX *ctx = BN_CTX_new(); + + n1 = BN_new(); n2 = BN_new(); order = BN_new(); + fprintf(stdout, "verify group order ..."); + fflush(stdout); + if (!EC_GROUP_get_order(group, order, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, "."); + fflush(stdout); + if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, " ok\n"); + fprintf(stdout, "long/negative scalar tests ... "); + if (!BN_one(n1)) ABORT; + /* n1 = 1 - order */ + if (!BN_sub(n1, n1, order)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = 1 + order */ + if (!BN_add(n2, order, BN_value_one())) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = (1 - order) * (1 + order) */ + if (!BN_mul(n2, n1, n2, ctx)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + fprintf(stdout, "ok\n"); + EC_POINT_free(P); + EC_POINT_free(Q); + BN_free(n1); + BN_free(n2); + BN_free(order); + BN_CTX_free(ctx); + } + +static void prime_field_tests(void) { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; @@ -321,21 +361,21 @@ void prime_field_tests() if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "Generator as octect string, compressed form:\n "); + fprintf(stdout, "Generator as octet string, compressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); + fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); + fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; @@ -381,17 +421,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 160) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_160, group)) ABORT; @@ -425,17 +455,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 192) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_192, group)) ABORT; @@ -469,17 +489,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 224) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_224, group)) ABORT; @@ -514,17 +524,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 256) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_256, group)) ABORT; @@ -563,18 +563,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 384) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_384, group)) ABORT; @@ -619,18 +609,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 521) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_521, group)) ABORT; @@ -659,6 +639,7 @@ void prime_field_tests() points[2] = Q; points[3] = Q; + if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!BN_add(y, z, BN_value_one())) ABORT; if (BN_is_odd(y)) ABORT; if (!BN_rshift1(y, y)) ABORT; @@ -792,22 +773,14 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); \ if (EC_GROUP_get_degree(group) != _degree) ABORT; \ fprintf(stdout, " ok\n"); \ - fprintf(stdout, "verify group order ..."); \ - fflush(stdout); \ - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, "."); \ - fflush(stdout); \ - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, " ok\n"); \ + group_order_tests(group); \ if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ - if (!EC_GROUP_copy(_variable, group)) ABORT; + if (!EC_GROUP_copy(_variable, group)) ABORT; \ -void char2_field_tests() - { +#ifndef OPENSSL_NO_EC2M + +static void char2_field_tests(void) + { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; EC_GROUP *group; @@ -1239,8 +1212,9 @@ void char2_field_tests() if (C2_B571) EC_GROUP_free(C2_B571); } +#endif -void internal_curve_test(void) +static void internal_curve_test(void) { EC_builtin_curve *curves = NULL; size_t crv_len = 0, n = 0; @@ -1287,13 +1261,189 @@ void internal_curve_test(void) EC_GROUP_free(group); } if (ok) - fprintf(stdout, " ok\n"); + fprintf(stdout, " ok\n\n"); else - fprintf(stdout, " failed\n"); + { + fprintf(stdout, " failed\n\n"); + ABORT; + } OPENSSL_free(curves); return; } +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 +/* nistp_test_params contains magic numbers for testing our optimized + * implementations of several NIST curves with characteristic > 3. */ +struct nistp_test_params + { + const EC_METHOD* (*meth) (); + int degree; + /* Qx, Qy and D are taken from + * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf + * Otherwise, values are standard curve parameters from FIPS 180-3 */ + const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; + }; + +static const struct nistp_test_params nistp_tests_params[] = + { + { + /* P-224 */ + EC_GFp_nistp224_method, + 224, + "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */ + "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */ + "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */ + "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */ + "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */ + "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */ + "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */ + "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */ + "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */ + }, + { + /* P-256 */ + EC_GFp_nistp256_method, + 256, + "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */ + "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */ + "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */ + "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */ + "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */ + "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */ + "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */ + "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */ + "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */ + }, + { + /* P-521 */ + EC_GFp_nistp521_method, + 521, + "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */ + "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */ + "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */ + "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */ + "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */ + "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */ + "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */ + "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */ + "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */ + }, + }; + +void nistp_single_test(const struct nistp_test_params *test) + { + BN_CTX *ctx; + BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; + EC_GROUP *NISTP; + EC_POINT *G, *P, *Q, *Q_CHECK; + + fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree); + ctx = BN_CTX_new(); + p = BN_new(); + a = BN_new(); + b = BN_new(); + x = BN_new(); y = BN_new(); + m = BN_new(); n = BN_new(); order = BN_new(); + + NISTP = EC_GROUP_new(test->meth()); + if(!NISTP) ABORT; + if (!BN_hex2bn(&p, test->p)) ABORT; + if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; + if (!BN_hex2bn(&a, test->a)) ABORT; + if (!BN_hex2bn(&b, test->b)) ABORT; + if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT; + G = EC_POINT_new(NISTP); + P = EC_POINT_new(NISTP); + Q = EC_POINT_new(NISTP); + Q_CHECK = EC_POINT_new(NISTP); + if(!BN_hex2bn(&x, test->Qx)) ABORT; + if(!BN_hex2bn(&y, test->Qy)) ABORT; + if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT; + if (!BN_hex2bn(&x, test->Gx)) ABORT; + if (!BN_hex2bn(&y, test->Gy)) ABORT; + if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT; + if (!BN_hex2bn(&order, test->order)) ABORT; + if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; + + fprintf(stdout, "verify degree ... "); + if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT; + fprintf(stdout, "ok\n"); + + fprintf(stdout, "NIST test vectors ... "); + if (!BN_hex2bn(&n, test->d)) ABORT; + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* set generator to P = 2*G, where G is the standard generator */ + if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT; + if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT; + /* set the scalar to m=n/2, where n is the NIST test scalar */ + if (!BN_rshift(m, n, 1)) ABORT; + + /* test the non-standard generator */ + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* now repeat all tests with precomputation */ + if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT; + + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* reset generator */ + if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + fprintf(stdout, "ok\n"); + group_order_tests(NISTP); +#if 0 + timings(NISTP, TIMING_BASE_PT, ctx); + timings(NISTP, TIMING_RAND_PT, ctx); +#endif + EC_GROUP_free(NISTP); + EC_POINT_free(G); + EC_POINT_free(P); + EC_POINT_free(Q); + EC_POINT_free(Q_CHECK); + BN_free(n); + BN_free(m); + BN_free(p); + BN_free(a); + BN_free(b); + BN_free(x); + BN_free(y); + BN_free(order); + BN_CTX_free(ctx); + } + +void nistp_tests() + { + unsigned i; + + for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++) + { + nistp_single_test(&nistp_tests_params[i]); + } + } +#endif + static const char rnd_seed[] = "string to make the random number generator think it has entropy"; int main(int argc, char *argv[]) @@ -1317,7 +1467,12 @@ int main(int argc, char *argv[]) prime_field_tests(); puts(""); +#ifndef OPENSSL_NO_EC2M char2_field_tests(); +#endif +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + nistp_tests(); +#endif /* test the internal curves */ internal_curve_test(); |