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Zhi Guan
2015-08-15 15:02:15 +08:00
parent 06df2fab54
commit 3bdc0ea895
2536 changed files with 417052 additions and 271997 deletions
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571
crypto/ec/ec2_mult.c
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@@ -21,7 +21,7 @@
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
@@ -71,316 +71,393 @@
#include "ec_lcl.h"
#ifndef OPENSSL_NO_EC2M
/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
/*-
* 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
* 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;
static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z,
BN_CTX *ctx)
{
BIGNUM *t1;
int ret = 0;
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;
/* Since Mdouble is static we can guarantee that ctx != NULL. */
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
if (t1 == NULL)
goto err;
ret = 1;
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;
}
BN_CTX_end(ctx);
return ret;
}
/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
/*-
* 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
* 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;
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;
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;
/* 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;
ret = 1;
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;
}
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
/*-
* 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;
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_one(t5)) goto err;
if (BN_is_zero(z1)) {
BN_zero(x2);
BN_zero(z2);
return 1;
}
if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
if (BN_is_zero(z2)) {
if (!BN_copy(x2, x))
return 0;
if (!BN_GF2m_add(z2, x, y))
return 0;
return 2;
}
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;
/* 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 (!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 (!BN_one(t5))
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, t3, z1, z2, ctx))
goto err;
if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
if (!BN_GF2m_add(z2, z2, y)) 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;
ret = 2;
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;
}
BN_CTX_end(ctx);
return ret;
}
/* Computes scalar*point and stores the result in r.
/*-
* Computes scalar*point and stores the result in r.
* point can not equal r.
* Uses algorithm 2P of
* Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
* 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;
BN_ULONG mask,word;
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;
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);
}
if (r == point) {
ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
return 0;
}
/* only support affine coordinates */
if (!point->Z_is_one) 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);
}
/* 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;
/* only support affine coordinates */
if (!point->Z_is_one)
return 0;
x2 = &r->X;
z2 = &r->Y;
/*
* 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;
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 */
x2 = &r->X;
z2 = &r->Y;
/* find top most bit and go one past it */
i = scalar->top - 1;
mask = BN_TBIT;
word = scalar->d[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;
}
bn_wexpand(x1, group->field.top);
bn_wexpand(z1, group->field.top);
bn_wexpand(x2, group->field.top);
bn_wexpand(z2, group->field.top);
for (; i >= 0; i--)
{
word = scalar->d[i];
while (mask)
{
if (word & mask)
{
if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err;
if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err;
}
else
{
if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
}
mask >>= 1;
}
mask = BN_TBIT;
}
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 */
/* 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;
}
/* find top most bit and go one past it */
i = scalar->top - 1;
mask = BN_TBIT;
word = scalar->d[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;
}
/* GF(2^m) field elements should always have BIGNUM::neg = 0 */
BN_set_negative(&r->X, 0);
BN_set_negative(&r->Y, 0);
for (; i >= 0; i--) {
word = scalar->d[i];
while (mask) {
BN_consttime_swap(word & mask, x1, x2, group->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.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->field.top);
BN_consttime_swap(word & mask, z1, z2, group->field.top);
mask >>= 1;
}
mask = BN_TBIT;
}
ret = 1;
/* 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;
}
BN_CTX_end(ctx);
return ret;
}
/* Computes the sum
/*-
* 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;
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;
}
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;
}
/*
* 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 ((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 (!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;
}
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;
}
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;
if (!EC_POINT_copy(r, acc))
goto err;
ret = 1;
ret = 1;
err:
if (p) EC_POINT_free(p);
if (acc) EC_POINT_free(acc);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
}
err:
if (p)
EC_POINT_free(p);
if (acc)
EC_POINT_free(acc);
if (new_ctx != NULL)
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 */
/*
* 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);
}
{
return ec_wNAF_precompute_mult(group, ctx);
}
int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
{
return ec_wNAF_have_precompute_mult(group);
}
{
return ec_wNAF_have_precompute_mult(group);
}
#endif