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Diffstat (limited to 'openssl/crypto/ec/ecp_nistputil.c')
| -rw-r--r-- | openssl/crypto/ec/ecp_nistputil.c | 197 |
1 files changed, 197 insertions, 0 deletions
diff --git a/openssl/crypto/ec/ecp_nistputil.c b/openssl/crypto/ec/ecp_nistputil.c new file mode 100644 index 000000000..c8140c807 --- /dev/null +++ b/openssl/crypto/ec/ecp_nistputil.c @@ -0,0 +1,197 @@ +/* crypto/ec/ecp_nistputil.c */ +/* + * Written by Bodo Moeller for the OpenSSL project. + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +/* + * Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c. + */ + +#include <stddef.h> +#include "ec_lcl.h" + +/* Convert an array of points into affine coordinates. + * (If the point at infinity is found (Z = 0), it remains unchanged.) + * This function is essentially an equivalent to EC_POINTs_make_affine(), but + * works with the internal representation of points as used by ecp_nistp###.c + * rather than with (BIGNUM-based) EC_POINT data structures. + * + * point_array is the input/output buffer ('num' points in projective form, + * i.e. three coordinates each), based on an internal representation of + * field elements of size 'felem_size'. + * + * tmp_felems needs to point to a temporary array of 'num'+1 field elements + * for storage of intermediate values. + */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)) + { + int i = 0; + +#define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) +#define X(I) (&((char *)point_array)[3*(I) * felem_size]) +#define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size]) +#define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size]) + + if (!felem_is_zero(Z(0))) + felem_assign(tmp_felem(0), Z(0)); + else + felem_one(tmp_felem(0)); + for (i = 1; i < (int)num; i++) + { + if (!felem_is_zero(Z(i))) + felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); + else + felem_assign(tmp_felem(i), tmp_felem(i-1)); + } + /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: + * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ + + felem_inv(tmp_felem(num-1), tmp_felem(num-1)); + for (i = num - 1; i >= 0; i--) + { + if (i > 0) + /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), + * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) + */ + felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ + else + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + + if (!felem_is_zero(Z(i))) + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); + + /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + felem_contract(X(i), X(i)); + felem_contract(Y(i), Y(i)); + felem_one(Z(i)); + } + else + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_assign(tmp_felem(i-1), tmp_felem(i)); + } + } + } + +/* + * This function looks at 5+1 scalar bits (5 current, 1 adjacent less + * significant bit), and recodes them into a signed digit for use in fast point + * multiplication: the use of signed rather than unsigned digits means that + * fewer points need to be precomputed, given that point inversion is easy + * (a precomputed point dP makes -dP available as well). + * + * BACKGROUND: + * + * Signed digits for multiplication were introduced by Booth ("A signed binary + * multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, + * pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. + * Booth's original encoding did not generally improve the density of nonzero + * digits over the binary representation, and was merely meant to simplify the + * handling of signed factors given in two's complement; but it has since been + * shown to be the basis of various signed-digit representations that do have + * further advantages, including the wNAF, using the following general approach: + * + * (1) Given a binary representation + * + * b_k ... b_2 b_1 b_0, + * + * of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 + * by using bit-wise subtraction as follows: + * + * b_k b_(k-1) ... b_2 b_1 b_0 + * - b_k ... b_3 b_2 b_1 b_0 + * ------------------------------------- + * s_k b_(k-1) ... s_3 s_2 s_1 s_0 + * + * A left-shift followed by subtraction of the original value yields a new + * representation of the same value, using signed bits s_i = b_(i+1) - b_i. + * This representation from Booth's paper has since appeared in the + * literature under a variety of different names including "reversed binary + * form", "alternating greedy expansion", "mutual opposite form", and + * "sign-alternating {+-1}-representation". + * + * An interesting property is that among the nonzero bits, values 1 and -1 + * strictly alternate. + * + * (2) Various window schemes can be applied to the Booth representation of + * integers: for example, right-to-left sliding windows yield the wNAF + * (a signed-digit encoding independently discovered by various researchers + * in the 1990s), and left-to-right sliding windows yield a left-to-right + * equivalent of the wNAF (independently discovered by various researchers + * around 2004). + * + * To prevent leaking information through side channels in point multiplication, + * we need to recode the given integer into a regular pattern: sliding windows + * as in wNAFs won't do, we need their fixed-window equivalent -- which is a few + * decades older: we'll be using the so-called "modified Booth encoding" due to + * MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 + * (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five + * signed bits into a signed digit: + * + * s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) + * + * The sign-alternating property implies that the resulting digit values are + * integers from -16 to 16. + * + * Of course, we don't actually need to compute the signed digits s_i as an + * intermediate step (that's just a nice way to see how this scheme relates + * to the wNAF): a direct computation obtains the recoded digit from the + * six bits b_(4j + 4) ... b_(4j - 1). + * + * This function takes those five bits as an integer (0 .. 63), writing the + * recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute + * value, in the range 0 .. 8). Note that this integer essentially provides the + * input bits "shifted to the left" by one position: for example, the input to + * compute the least significant recoded digit, given that there's no bit b_-1, + * has to be b_4 b_3 b_2 b_1 b_0 0. + * + */ +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) + { + unsigned char s, d; + + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; + } +#else +static void *dummy=&dummy; +#endif |