diff options
Diffstat (limited to 'openssl/crypto/ec/ecp_nistp521.c')
| -rw-r--r-- | openssl/crypto/ec/ecp_nistp521.c | 3637 |
1 files changed, 1880 insertions, 1757 deletions
diff --git a/openssl/crypto/ec/ecp_nistp521.c b/openssl/crypto/ec/ecp_nistp521.c index 178b655f7..360b9a351 100644 --- a/openssl/crypto/ec/ecp_nistp521.c +++ b/openssl/crypto/ec/ecp_nistp521.c @@ -29,87 +29,90 @@ #include <openssl/opensslconf.h> #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 -#ifndef OPENSSL_SYS_VMS -#include <stdint.h> -#else -#include <inttypes.h> -#endif +# ifndef OPENSSL_SYS_VMS +# include <stdint.h> +# else +# include <inttypes.h> +# endif -#include <string.h> -#include <openssl/err.h> -#include "ec_lcl.h" +# include <string.h> +# include <openssl/err.h> +# include "ec_lcl.h" -#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) +# 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 __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. */ +/* + * 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. +/* + * 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 @@ -122,7 +125,7 @@ static const felem_bytearray nistp521_curve_params[5] = * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a * 'largefelem' */ -#define NLIMBS 9 +# define NLIMBS 9 typedef uint64_t limb; typedef limb felem[NLIMBS]; @@ -131,350 +134,358 @@ 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. */ +/* + * 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. */ +{ + 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]; - } +{ + 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]; - } +{ + 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_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); - } - +{ + 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 - * ---------------- */ +/*- + * 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; - } +{ + 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]; - } +{ + 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]; - } +{ + 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; - } +{ + 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; - } +{ + 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| +{ + 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| +{ + /* 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| +{ + /* + * 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| +{ + /* + * 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 +{ + /* + * 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| +{ + 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 @@ -482,202 +493,197 @@ static void felem_square(largefelem out, const felem in) * 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]; - } +{ + 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. +/*- + * 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 */ - } +{ + 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); - } +{ + 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); - } +{ + largefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} -/* felem_inv calculates |out| = |in|^{-1} +/*- + * felem_inv calculates |out| = |in|^{-1} * * Based on Fermat's Little Theorem: * a^p = a (mod p) @@ -685,259 +691,335 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2) * 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 */ +{ + 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 +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; - } +{ + 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)); - } +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} -/* felem_contract converts |in| to its unique, minimal representation. +/*- + * 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 +{ + 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) +/*- + * 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 @@ -946,103 +1028,114 @@ static void felem_contract(felem out, const felem in) * 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); - } + 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) +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, @@ -1053,159 +1146,162 @@ copy_conditional(felem out, const felem in, limb mask) * 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 + 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. @@ -1239,787 +1335,814 @@ static void point_add(felem x3, felem y3, felem z3, * 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; - } - } +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. + */ + /* pre_comp below is of the size provided in |size| */ +static void select_point(const limb idx, unsigned int size, + const felem pre_comp[][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]); - } +{ + 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) { + /* The 1 argument below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, 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; + 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; - } - +{ + 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 +/* + * 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; - } +{ + 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_; +{ + NISTP521_PRE_COMP *src = src_; - /* no need to actually copy, these objects never change! */ - CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); - return src_; - } + return src_; +} static void nistp521_pre_comp_free(void *pre_) - { - int i; - NISTP521_PRE_COMP *pre = pre_; +{ + int i; + NISTP521_PRE_COMP *pre = pre_; - if (!pre) - return; + if (!pre) + return; - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - return; + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; - OPENSSL_free(pre); - } + OPENSSL_free(pre); +} static void nistp521_pre_comp_clear_free(void *pre_) - { - int i; - NISTP521_PRE_COMP *pre = pre_; +{ + int i; + NISTP521_PRE_COMP *pre = pre_; - if (!pre) - return; + if (!pre) + return; - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - 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_cleanse(pre, sizeof(*pre)); + OPENSSL_free(pre); +} /******************************************************************************/ -/* OPENSSL EC_METHOD FUNCTIONS +/* + * 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 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) */ + 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). */ + 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; +} + +/* points below is of size |num|, and tmp_felems is of size |num+1/ */ +static void make_points_affine(size_t num, felem points[][3], + felem tmp_felems[]) +{ + /* + * 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; - } + 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; +{ + 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; - } + 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; - } +{ + 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; +static void *dummy = &dummy; #endif |