+++ /dev/null
-/*
- * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved.
- * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
- *
- * Licensed under the OpenSSL license (the "License"). You may not use
- * this file except in compliance with the License. You can obtain a copy
- * in the file LICENSE in the source distribution or at
- * https://www.openssl.org/source/license.html
- */
-
-#include <openssl/err.h>
-
-#include "internal/bn_int.h"
-#include "ec_lcl.h"
-
-#ifndef OPENSSL_NO_EC2M
-
-/*-
- * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
- * coordinates.
- * Uses algorithm Mdouble in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
- * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
- * modified to not require precomputation of c=b^{2^{m-1}}.
- */
-static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
- BN_CTX *ctx)
-{
- BIGNUM *t1;
- int ret = 0;
-
- /* Since Mdouble is static we can guarantee that ctx != NULL. */
- BN_CTX_start(ctx);
- t1 = BN_CTX_get(ctx);
- if (t1 == NULL)
- goto err;
-
- if (!group->meth->field_sqr(group, x, x, ctx))
- goto err;
- if (!group->meth->field_sqr(group, t1, z, ctx))
- goto err;
- if (!group->meth->field_mul(group, z, x, t1, ctx))
- goto err;
- if (!group->meth->field_sqr(group, x, x, ctx))
- goto err;
- if (!group->meth->field_sqr(group, t1, t1, ctx))
- goto err;
- if (!group->meth->field_mul(group, t1, group->b, t1, ctx))
- goto err;
- if (!BN_GF2m_add(x, x, t1))
- goto err;
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
-}
-
-/*-
- * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
- * projective coordinates.
- * Uses algorithm Madd in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
- * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
- */
-static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1,
- BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2,
- BN_CTX *ctx)
-{
- BIGNUM *t1, *t2;
- int ret = 0;
-
- /* Since Madd is static we can guarantee that ctx != NULL. */
- BN_CTX_start(ctx);
- t1 = BN_CTX_get(ctx);
- t2 = BN_CTX_get(ctx);
- if (t2 == NULL)
- goto err;
-
- if (!BN_copy(t1, x))
- goto err;
- if (!group->meth->field_mul(group, x1, x1, z2, ctx))
- goto err;
- if (!group->meth->field_mul(group, z1, z1, x2, ctx))
- goto err;
- if (!group->meth->field_mul(group, t2, x1, z1, ctx))
- goto err;
- if (!BN_GF2m_add(z1, z1, x1))
- goto err;
- if (!group->meth->field_sqr(group, z1, z1, ctx))
- goto err;
- if (!group->meth->field_mul(group, x1, z1, t1, ctx))
- goto err;
- if (!BN_GF2m_add(x1, x1, t2))
- goto err;
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
-}
-
-/*-
- * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
- * using Montgomery point multiplication algorithm Mxy() in appendix of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
- * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
- * Returns:
- * 0 on error
- * 1 if return value should be the point at infinity
- * 2 otherwise
- */
-static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y,
- BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2,
- BN_CTX *ctx)
-{
- BIGNUM *t3, *t4, *t5;
- int ret = 0;
-
- if (BN_is_zero(z1)) {
- BN_zero(x2);
- BN_zero(z2);
- return 1;
- }
-
- if (BN_is_zero(z2)) {
- if (!BN_copy(x2, x))
- return 0;
- if (!BN_GF2m_add(z2, x, y))
- return 0;
- return 2;
- }
-
- /* Since Mxy is static we can guarantee that ctx != NULL. */
- BN_CTX_start(ctx);
- t3 = BN_CTX_get(ctx);
- t4 = BN_CTX_get(ctx);
- t5 = BN_CTX_get(ctx);
- if (t5 == NULL)
- goto err;
-
- if (!BN_one(t5))
- goto err;
-
- if (!group->meth->field_mul(group, t3, z1, z2, ctx))
- goto err;
-
- if (!group->meth->field_mul(group, z1, z1, x, ctx))
- goto err;
- if (!BN_GF2m_add(z1, z1, x1))
- goto err;
- if (!group->meth->field_mul(group, z2, z2, x, ctx))
- goto err;
- if (!group->meth->field_mul(group, x1, z2, x1, ctx))
- goto err;
- if (!BN_GF2m_add(z2, z2, x2))
- goto err;
-
- if (!group->meth->field_mul(group, z2, z2, z1, ctx))
- goto err;
- if (!group->meth->field_sqr(group, t4, x, ctx))
- goto err;
- if (!BN_GF2m_add(t4, t4, y))
- goto err;
- if (!group->meth->field_mul(group, t4, t4, t3, ctx))
- goto err;
- if (!BN_GF2m_add(t4, t4, z2))
- goto err;
-
- if (!group->meth->field_mul(group, t3, t3, x, ctx))
- goto err;
- if (!group->meth->field_div(group, t3, t5, t3, ctx))
- goto err;
- if (!group->meth->field_mul(group, t4, t3, t4, ctx))
- goto err;
- if (!group->meth->field_mul(group, x2, x1, t3, ctx))
- goto err;
- if (!BN_GF2m_add(z2, x2, x))
- goto err;
-
- if (!group->meth->field_mul(group, z2, z2, t4, ctx))
- goto err;
- if (!BN_GF2m_add(z2, z2, y))
- goto err;
-
- ret = 2;
-
- err:
- BN_CTX_end(ctx);
- return ret;
-}
-
-/*-
- * Computes scalar*point and stores the result in r.
- * point can not equal r.
- * Uses a modified algorithm 2P of
- * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
- * GF(2^m) without precomputation" (CHES '99, LNCS 1717).
- *
- * To protect against side-channel attack the function uses constant time swap,
- * avoiding conditional branches.
- */
-static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group,
- EC_POINT *r,
- const BIGNUM *scalar,
- const EC_POINT *point,
- BN_CTX *ctx)
-{
- BIGNUM *x1, *x2, *z1, *z2;
- int ret = 0, i, group_top;
- BN_ULONG mask, word;
-
- if (r == point) {
- ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
- return 0;
- }
-
- /* if result should be point at infinity */
- if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
- EC_POINT_is_at_infinity(group, point)) {
- return EC_POINT_set_to_infinity(group, r);
- }
-
- /* only support affine coordinates */
- if (!point->Z_is_one)
- return 0;
-
- /*
- * Since point_multiply is static we can guarantee that ctx != NULL.
- */
- BN_CTX_start(ctx);
- x1 = BN_CTX_get(ctx);
- z1 = BN_CTX_get(ctx);
- if (z1 == NULL)
- goto err;
-
- x2 = r->X;
- z2 = r->Y;
-
- group_top = bn_get_top(group->field);
- if (bn_wexpand(x1, group_top) == NULL
- || bn_wexpand(z1, group_top) == NULL
- || bn_wexpand(x2, group_top) == NULL
- || bn_wexpand(z2, group_top) == NULL)
- goto err;
-
- if (!BN_GF2m_mod_arr(x1, point->X, group->poly))
- goto err; /* x1 = x */
- if (!BN_one(z1))
- goto err; /* z1 = 1 */
- if (!group->meth->field_sqr(group, z2, x1, ctx))
- goto err; /* z2 = x1^2 = x^2 */
- if (!group->meth->field_sqr(group, x2, z2, ctx))
- goto err;
- if (!BN_GF2m_add(x2, x2, group->b))
- goto err; /* x2 = x^4 + b */
-
- /* find top most bit and go one past it */
- i = bn_get_top(scalar) - 1;
- mask = BN_TBIT;
- word = bn_get_words(scalar)[i];
- while (!(word & mask))
- mask >>= 1;
- mask >>= 1;
- /* if top most bit was at word break, go to next word */
- if (!mask) {
- i--;
- mask = BN_TBIT;
- }
-
- for (; i >= 0; i--) {
- word = bn_get_words(scalar)[i];
- while (mask) {
- BN_consttime_swap(word & mask, x1, x2, group_top);
- BN_consttime_swap(word & mask, z1, z2, group_top);
- if (!gf2m_Madd(group, point->X, x2, z2, x1, z1, ctx))
- goto err;
- if (!gf2m_Mdouble(group, x1, z1, ctx))
- goto err;
- BN_consttime_swap(word & mask, x1, x2, group_top);
- BN_consttime_swap(word & mask, z1, z2, group_top);
- mask >>= 1;
- }
- mask = BN_TBIT;
- }
-
- /* convert out of "projective" coordinates */
- i = gf2m_Mxy(group, point->X, point->Y, x1, z1, x2, z2, ctx);
- if (i == 0)
- goto err;
- else if (i == 1) {
- if (!EC_POINT_set_to_infinity(group, r))
- goto err;
- } else {
- if (!BN_one(r->Z))
- goto err;
- r->Z_is_one = 1;
- }
-
- /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
- BN_set_negative(r->X, 0);
- BN_set_negative(r->Y, 0);
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
-}
-
-/*-
- * Computes the sum
- * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
- * gracefully ignoring NULL scalar values.
- */
-int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r,
- const BIGNUM *scalar, size_t num,
- const EC_POINT *points[], const BIGNUM *scalars[],
- BN_CTX *ctx)
-{
- BN_CTX *new_ctx = NULL;
- int ret = 0;
- size_t i;
- EC_POINT *p = NULL;
- EC_POINT *acc = NULL;
-
- if (ctx == NULL) {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- /*
- * This implementation is more efficient than the wNAF implementation for
- * 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more
- * points, or if we can perform a fast multiplication based on
- * precomputation.
- */
- if ((scalar && (num > 1)) || (num > 2)
- || (num == 0 && EC_GROUP_have_precompute_mult(group))) {
- ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
- goto err;
- }
-
- if ((p = EC_POINT_new(group)) == NULL)
- goto err;
- if ((acc = EC_POINT_new(group)) == NULL)
- goto err;
-
- if (!EC_POINT_set_to_infinity(group, acc))
- goto err;
-
- if (scalar) {
- if (!ec_GF2m_montgomery_point_multiply
- (group, p, scalar, group->generator, ctx))
- goto err;
- if (BN_is_negative(scalar))
- if (!group->meth->invert(group, p, ctx))
- goto err;
- if (!group->meth->add(group, acc, acc, p, ctx))
- goto err;
- }
-
- for (i = 0; i < num; i++) {
- if (!ec_GF2m_montgomery_point_multiply
- (group, p, scalars[i], points[i], ctx))
- goto err;
- if (BN_is_negative(scalars[i]))
- if (!group->meth->invert(group, p, ctx))
- goto err;
- if (!group->meth->add(group, acc, acc, p, ctx))
- goto err;
- }
-
- if (!EC_POINT_copy(r, acc))
- goto err;
-
- ret = 1;
-
- err:
- EC_POINT_free(p);
- EC_POINT_free(acc);
- BN_CTX_free(new_ctx);
- return ret;
-}
-
-/*
- * Precomputation for point multiplication: fall back to wNAF methods because
- * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate
- */
-
-int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
-{
- return ec_wNAF_precompute_mult(group, ctx);
-}
-
-int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
-{
- return ec_wNAF_have_precompute_mult(group);
-}
-
-#endif
projects / oweals / openssl.git / commitdiff