/* crypto/ec/ecp_smpl.c */
/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
- * for the OpenSSL project. */
+ * for the OpenSSL project.
+ * Includes code written by Bodo Moeller for the OpenSSL project.
+*/
/* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
+ * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* Hudson (tjh@cryptsoft.com).
*
*/
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ * Portions of this software developed by SUN MICROSYSTEMS, INC.,
+ * and contributed to the OpenSSL project.
+ */
#include <openssl/err.h>
+#include <openssl/symhacks.h>
#include "ec_lcl.h"
-
const EC_METHOD *EC_GFp_simple_method(void)
{
static const EC_METHOD ret = {
+ NID_X9_62_prime_field,
ec_GFp_simple_group_init,
- ec_GFp_simple_group_set_curve_GFp,
ec_GFp_simple_group_finish,
ec_GFp_simple_group_clear_finish,
ec_GFp_simple_group_copy,
- ec_GFp_simple_group_set_generator,
- /* TODO: 'set' and 'get' functions for EC_GROUPs */
+ ec_GFp_simple_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_set_to_infinity,
ec_GFp_simple_set_Jprojective_coordinates_GFp,
ec_GFp_simple_get_Jprojective_coordinates_GFp,
- ec_GFp_simple_point_set_affine_coordinates_GFp,
- ec_GFp_simple_point_get_affine_coordinates_GFp,
- ec_GFp_simple_set_compressed_coordinates_GFp,
+ ec_GFp_simple_point_set_affine_coordinates,
+ ec_GFp_simple_point_get_affine_coordinates,
+ ec_GFp_simple_set_compressed_coordinates,
ec_GFp_simple_point2oct,
ec_GFp_simple_oct2point,
ec_GFp_simple_add,
ec_GFp_simple_is_on_curve,
ec_GFp_simple_cmp,
ec_GFp_simple_make_affine,
+ ec_GFp_simple_points_make_affine,
+ 0 /* mul */,
+ 0 /* precompute_mult */,
+ 0 /* have_precompute_mult */,
ec_GFp_simple_field_mul,
ec_GFp_simple_field_sqr,
+ 0 /* field_div */,
0 /* field_encode */,
- 0 /* field_decode */ };
+ 0 /* field_decode */,
+ 0 /* field_set_to_one */ };
return &ret;
}
+/* Most method functions in this file are designed to work with
+ * non-trivial representations of field elements if necessary
+ * (see ecp_mont.c): while standard modular addition and subtraction
+ * are used, the field_mul and field_sqr methods will be used for
+ * multiplication, and field_encode and field_decode (if defined)
+ * will be used for converting between representations.
+
+ * Functions ec_GFp_simple_points_make_affine() and
+ * ec_GFp_simple_point_get_affine_coordinates() specifically assume
+ * that if a non-trivial representation is used, it is a Montgomery
+ * representation (i.e. 'encoding' means multiplying by some factor R).
+ */
+
+
int ec_GFp_simple_group_init(EC_GROUP *group)
{
BN_init(&group->field);
BN_init(&group->a);
BN_init(&group->b);
group->a_is_minus3 = 0;
- group->generator = NULL;
- BN_init(&group->order);
- BN_init(&group->cofactor);
return 1;
}
-int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+ {
+ BN_free(&group->field);
+ BN_free(&group->a);
+ BN_free(&group->b);
+ }
+
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+ {
+ BN_clear_free(&group->field);
+ BN_clear_free(&group->a);
+ BN_clear_free(&group->b);
+ }
+
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+ {
+ if (!BN_copy(&dest->field, &src->field)) return 0;
+ if (!BN_copy(&dest->a, &src->a)) return 0;
+ if (!BN_copy(&dest->b, &src->b)) return 0;
+
+ dest->a_is_minus3 = src->a_is_minus3;
+
+ return 1;
+ }
+
+
+int ec_GFp_simple_group_set_curve(EC_GROUP *group,
const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
/* p must be a prime > 3 */
if (BN_num_bits(p) <= 2 || !BN_is_odd(p))
{
- ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE_GFP, EC_R_INVALID_FIELD);
+ ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD);
return 0;
}
/* group->field */
if (!BN_copy(&group->field, p)) goto err;
- group->field.neg = 0;
+ BN_set_negative(&group->field, 0);
/* group->a */
if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
}
-void ec_GFp_simple_group_finish(EC_GROUP *group)
+int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
{
- BN_free(&group->field);
- BN_free(&group->a);
- BN_free(&group->b);
- if (group->generator != NULL)
- EC_POINT_free(group->generator);
- BN_free(&group->order);
- BN_free(&group->cofactor);
- }
-
-
-void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
- {
- BN_clear_free(&group->field);
- BN_clear_free(&group->a);
- BN_clear_free(&group->b);
- if (group->generator != NULL)
+ int ret = 0;
+ BN_CTX *new_ctx = NULL;
+
+ if (p != NULL)
{
- EC_POINT_clear_free(group->generator);
- group->generator = NULL;
+ if (!BN_copy(p, &group->field)) return 0;
}
- BN_clear_free(&group->order);
- BN_clear_free(&group->cofactor);
- }
-
-
-int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
- {
- if (!BN_copy(&dest->field, &src->field)) return 0;
- if (!BN_copy(&dest->a, &src->a)) return 0;
- if (!BN_copy(&dest->b, &src->b)) return 0;
-
- dest->a_is_minus3 = src->a_is_minus3;
- if (src->generator != NULL)
+ if (a != NULL || b != NULL)
{
- if (dest->generator == NULL)
+ if (group->meth->field_decode)
{
- dest->generator = EC_POINT_new(dest);
- if (dest->generator == NULL) return 0;
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+ if (a != NULL)
+ {
+ if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+ }
+ if (b != NULL)
+ {
+ if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+ }
}
- if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
- }
- else
- {
- /* src->generator == NULL */
- if (dest->generator != NULL)
+ else
{
- EC_POINT_clear_free(dest->generator);
- dest->generator = NULL;
+ if (a != NULL)
+ {
+ if (!BN_copy(a, &group->a)) goto err;
+ }
+ if (b != NULL)
+ {
+ if (!BN_copy(b, &group->b)) goto err;
+ }
}
}
+
+ ret = 1;
+
+ err:
+ if (new_ctx)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
- if (!BN_copy(&dest->order, &src->order)) return 0;
- if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
- return 1;
+int ec_GFp_simple_group_get_degree(const EC_GROUP *group)
+ {
+ return BN_num_bits(&group->field);
}
-int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
- const BIGNUM *order, const BIGNUM *cofactor)
+int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx)
{
- if (generator)
+ int ret = 0;
+ BIGNUM *a,*b,*order,*tmp_1,*tmp_2;
+ const BIGNUM *p = &group->field;
+ BN_CTX *new_ctx = NULL;
+
+ if (ctx == NULL)
{
- ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER);
- return 0 ;
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, ERR_R_MALLOC_FAILURE);
+ goto err;
+ }
}
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ tmp_1 = BN_CTX_get(ctx);
+ tmp_2 = BN_CTX_get(ctx);
+ order = BN_CTX_get(ctx);
+ if (order == NULL) goto err;
- if (group->generator == NULL)
+ if (group->meth->field_decode)
{
- group->generator = EC_POINT_new(group);
- if (group->generator == NULL) return 0;
+ if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+ if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
}
- if (!EC_POINT_copy(group->generator, generator)) return 0;
-
- if (order != NULL)
- { if (!BN_copy(&group->order, order)) return 0; }
else
- { if (!BN_zero(&group->order)) return 0; }
+ {
+ if (!BN_copy(a, &group->a)) goto err;
+ if (!BN_copy(b, &group->b)) goto err;
+ }
+
+ /* check the discriminant:
+ * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p)
+ * 0 =< a, b < p */
+ if (BN_is_zero(a))
+ {
+ if (BN_is_zero(b)) goto err;
+ }
+ else if (!BN_is_zero(b))
+ {
+ if (!BN_mod_sqr(tmp_1, a, p, ctx)) goto err;
+ if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) goto err;
+ if (!BN_lshift(tmp_1, tmp_2, 2)) goto err;
+ /* tmp_1 = 4*a^3 */
- if (cofactor != NULL)
- { if (!BN_copy(&group->cofactor, cofactor)) return 0; }
- else
- { if (!BN_zero(&group->cofactor)) return 0; }
-
- return 1;
- }
+ if (!BN_mod_sqr(tmp_2, b, p, ctx)) goto err;
+ if (!BN_mul_word(tmp_2, 27)) goto err;
+ /* tmp_2 = 27*b^2 */
+ if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) goto err;
+ if (BN_is_zero(a)) goto err;
+ }
+ ret = 1;
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
+err:
+ if (ctx != NULL)
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
int ec_GFp_simple_point_init(EC_POINT *point)
int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, EC_POINT *point)
{
point->Z_is_one = 0;
- return (BN_zero(&point->Z));
+ BN_zero(&point->Z);
+ return 1;
}
int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
-/* TODO */
+ const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+ if (x != NULL)
+ {
+ if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
+ if (group->meth->field_encode)
+ {
+ if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
+ }
+ }
+
+ if (y != NULL)
+ {
+ if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
+ if (group->meth->field_encode)
+ {
+ if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
+ }
+ }
+
+ if (z != NULL)
+ {
+ int Z_is_one;
-int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
- BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
-/* TODO */
+ if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
+ Z_is_one = BN_is_one(&point->Z);
+ if (group->meth->field_encode)
+ {
+ if (Z_is_one && (group->meth->field_set_to_one != 0))
+ {
+ if (!group->meth->field_set_to_one(group, &point->Z, ctx)) goto err;
+ }
+ else
+ {
+ if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+ }
+ }
+ point->Z_is_one = Z_is_one;
+ }
+ if (BN_cmp(&point->X, x) || BN_cmp(&point->Y, y))
+ ret = 2;
+ else
+ ret = 1;
+
+ err:
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
-int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+ BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
int ret = 0;
-
- if (!BN_copy(&point->X, x)) goto err;
- if (!BN_copy(&point->Y, y)) goto err;
- if (!BN_one(&point->Z)) goto err;
-
- if (group->meth->field_encode)
+
+ if (group->meth->field_decode != 0)
{
if (ctx == NULL)
{
if (ctx == NULL)
return 0;
}
-
- if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
- if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
- if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
- }
- point->Z_is_one = 1;
+ if (x != NULL)
+ {
+ if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+ }
+ if (z != NULL)
+ {
+ if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
+ }
+ }
+ else
+ {
+ if (x != NULL)
+ {
+ if (!BN_copy(x, &point->X)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!BN_copy(y, &point->Y)) goto err;
+ }
+ if (z != NULL)
+ {
+ if (!BN_copy(z, &point->Z)) goto err;
+ }
+ }
+ ret = 1;
+
err:
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
}
-int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
+ const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+ {
+ if (x == NULL || y == NULL)
+ {
+ /* unlike for projective coordinates, we do not tolerate this */
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, ERR_R_PASSED_NULL_PARAMETER);
+ return 0;
+ }
+
+ return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
+ }
+
+
+int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
- BIGNUM *X, *Y, *Z, *Z_1, *Z_2, *Z_3;
- const BIGNUM *X_, *Y_, *Z_;
+ BIGNUM *Z, *Z_1, *Z_2, *Z_3;
+ const BIGNUM *Z_;
int ret = 0;
if (EC_POINT_is_at_infinity(group, point))
{
- ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, EC_R_POINT_AT_INFINITY);
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, EC_R_POINT_AT_INFINITY);
return 0;
}
}
BN_CTX_start(ctx);
- X = BN_CTX_get(ctx);
- Y = BN_CTX_get(ctx);
Z = BN_CTX_get(ctx);
Z_1 = BN_CTX_get(ctx);
Z_2 = BN_CTX_get(ctx);
if (group->meth->field_decode)
{
- if (!group->meth->field_decode(group, X, &point->X, ctx)) goto err;
- if (!group->meth->field_decode(group, Y, &point->Y, ctx)) goto err;
if (!group->meth->field_decode(group, Z, &point->Z, ctx)) goto err;
- X_ = X; Y_ = Y; Z_ = Z;
+ Z_ = Z;
}
else
{
- X_ = &point->X;
- Y_ = &point->Y;
Z_ = &point->Z;
}
if (BN_is_one(Z_))
{
- if (x != NULL)
+ if (group->meth->field_decode)
{
- if (!BN_copy(x, X_)) goto err;
+ if (x != NULL)
+ {
+ if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+ }
}
- if (y != NULL)
+ else
{
- if (!BN_copy(y, Y_)) goto err;
+ if (x != NULL)
+ {
+ if (!BN_copy(x, &point->X)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!BN_copy(y, &point->Y)) goto err;
+ }
}
}
else
{
if (!BN_mod_inverse(Z_1, Z_, &group->field, ctx))
{
- ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES_GFP, ERR_R_BN_LIB);
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
goto err;
}
- if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
+
+ if (group->meth->field_encode == 0)
+ {
+ /* field_sqr works on standard representation */
+ if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_sqr(Z_2, Z_1, &group->field, ctx)) goto err;
+ }
if (x != NULL)
{
- if (!BN_mod_mul(x, X_, Z_2, &group->field, ctx)) goto err;
+ /* in the Montgomery case, field_mul will cancel out Montgomery factor in X: */
+ if (!group->meth->field_mul(group, x, &point->X, Z_2, ctx)) goto err;
}
if (y != NULL)
{
- if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
- if (!BN_mod_mul(y, Y_, Z_3, &group->field, ctx)) goto err;
+ if (group->meth->field_encode == 0)
+ {
+ /* field_mul works on standard representation */
+ if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_mul(Z_3, Z_2, Z_1, &group->field, ctx)) goto err;
+ }
+
+ /* in the Montgomery case, field_mul will cancel out Montgomery factor in Y: */
+ if (!group->meth->field_mul(group, y, &point->Y, Z_3, ctx)) goto err;
}
}
}
-int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, int y_bit, BN_CTX *);
-/* TODO */
+int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
+ const BIGNUM *x_, int y_bit, BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *x, *y;
+ int ret = 0;
+
+ /* clear error queue*/
+ ERR_clear_error();
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ y_bit = (y_bit != 0);
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ x = BN_CTX_get(ctx);
+ y = BN_CTX_get(ctx);
+ if (y == NULL) goto err;
+
+ /* Recover y. We have a Weierstrass equation
+ * y^2 = x^3 + a*x + b,
+ * so y is one of the square roots of x^3 + a*x + b.
+ */
+
+ /* tmp1 := x^3 */
+ if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
+ if (group->meth->field_decode == 0)
+ {
+ /* field_{sqr,mul} work on standard representation */
+ if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
+ if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
+ if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
+ }
+
+ /* tmp1 := tmp1 + a*x */
+ if (group->a_is_minus3)
+ {
+ if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
+ if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
+ if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+ else
+ {
+ if (group->meth->field_decode)
+ {
+ if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
+ if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
+ }
+ else
+ {
+ /* field_mul works on standard representation */
+ if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
+ }
+
+ if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+
+ /* tmp1 := tmp1 + b */
+ if (group->meth->field_decode)
+ {
+ if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
+ if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
+ }
+
+ if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
+ {
+ unsigned long err = ERR_peek_last_error();
+
+ if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
+ {
+ ERR_clear_error();
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+ }
+ else
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
+ goto err;
+ }
+
+ if (y_bit != BN_is_odd(y))
+ {
+ if (BN_is_zero(y))
+ {
+ int kron;
+
+ kron = BN_kronecker(x, &group->field, ctx);
+ if (kron == -2) goto err;
+
+ if (kron == 1)
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
+ else
+ /* BN_mod_sqrt() should have cought this error (not a square) */
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
+ goto err;
+ }
+ if (!BN_usub(y, &group->field, y)) goto err;
+ }
+ if (y_bit != BN_is_odd(y))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
size_t field_len, enc_len;
int ret = 0;
- if (len <= 0)
+ if (len == 0)
{
ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
return 0;
}
form = buf[0];
y_bit = form & 1;
- form = form & ~1;
+ form = form & ~1U;
if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
&& (form != POINT_CONVERSION_UNCOMPRESSED)
&& (form != POINT_CONVERSION_HYBRID))
goto err;
}
- if (form != POINT_CONVERSION_COMPRESSED)
+ if (form == POINT_CONVERSION_COMPRESSED)
+ {
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
+ }
+ else
{
if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
if (BN_ucmp(y, &group->field) >= 0)
goto err;
}
}
- }
-
- if (form == POINT_CONVERSION_COMPRESSED)
- {
- /* Recover y. We have a Weierstrass equation
- * y^2 = x^3 + a*x + b,
- * so y is one of the square roots of x^3 + a*x + b.
- */
-
- BIGNUM *tmp1, *tmp2;
-
- tmp1 = BN_CTX_get(ctx);
- tmp2 = BN_CTX_get(ctx);
- if (tmp2 == NULL) goto err;
-
- /* tmp1 := x^3 */
- if (!BN_mod_sqr(tmp2, x, &group->field, ctx)) goto err;
- if (!BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) goto err;
-
- /* tmp1 := tmp1 + a*x */
- if (group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
- if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
-
- /* tmp1 := tmp1 + b */
- if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
-
- if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_BN_LIB);
- goto err;
- }
- if (y_bit != BN_is_odd(y))
- {
- if (BN_is_zero(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- if (!BN_usub(y, &group->field, y)) goto err;
- }
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
}
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
{
ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
else
{
/* a is the inverse of b */
- if (!BN_zero(&r->Z)) goto end;
+ BN_zero(&r->Z);
r->Z_is_one = 0;
ret = 1;
goto end;
if (EC_POINT_is_at_infinity(group, a))
{
- if (!BN_zero(&r->Z)) return 0;
+ BN_zero(&r->Z);
r->Z_is_one = 0;
return 1;
}
}
-int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
-/* TODO */
+int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+ {
+ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
+ /* point is its own inverse */
+ return 1;
+
+ return BN_usub(&point->Y, &group->field, &point->Y);
+ }
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
const BIGNUM *p;
BN_CTX *new_ctx = NULL;
- BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
+ BIGNUM *rh, *tmp, *Z4, *Z6;
int ret = -1;
if (EC_POINT_is_at_infinity(group, point))
BN_CTX_start(ctx);
rh = BN_CTX_get(ctx);
- tmp1 = BN_CTX_get(ctx);
- tmp2 = BN_CTX_get(ctx);
+ tmp = BN_CTX_get(ctx);
Z4 = BN_CTX_get(ctx);
Z6 = BN_CTX_get(ctx);
if (Z6 == NULL) goto err;
* To test this, we add up the right-hand side in 'rh'.
*/
- /* rh := X^3 */
+ /* rh := X^2 */
if (!field_sqr(group, rh, &point->X, ctx)) goto err;
- if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
if (!point->Z_is_one)
{
- if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
- if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
- if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
+ if (!field_sqr(group, tmp, &point->Z, ctx)) goto err;
+ if (!field_sqr(group, Z4, tmp, ctx)) goto err;
+ if (!field_mul(group, Z6, Z4, tmp, ctx)) goto err;
- /* rh := rh + a*X*Z^4 */
- if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
- if (&group->a_is_minus3)
+ /* rh := (rh + a*Z^4)*X */
+ if (group->a_is_minus3)
{
- if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
- if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
+ if (!BN_mod_lshift1_quick(tmp, Z4, p)) goto err;
+ if (!BN_mod_add_quick(tmp, tmp, Z4, p)) goto err;
+ if (!BN_mod_sub_quick(rh, rh, tmp, p)) goto err;
+ if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
}
else
{
- if (!field_mul(group, tmp2, tmp1, &group->a, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
+ if (!field_mul(group, tmp, Z4, &group->a, ctx)) goto err;
+ if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
+ if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
}
/* rh := rh + b*Z^6 */
- if (!field_mul(group, tmp1, &group->b, Z6, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
+ if (!field_mul(group, tmp, &group->b, Z6, ctx)) goto err;
+ if (!BN_mod_add_quick(rh, rh, tmp, p)) goto err;
}
else
{
/* point->Z_is_one */
- /* rh := rh + a*X */
- if (&group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
- if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
- }
- else
- {
- if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
- }
-
+ /* rh := (rh + a)*X */
+ if (!BN_mod_add_quick(rh, rh, &group->a, p)) goto err;
+ if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
/* rh := rh + b */
if (!BN_mod_add_quick(rh, rh, &group->b, p)) goto err;
}
/* 'lh' := Y^2 */
- if (!field_sqr(group, tmp1, &point->Y, ctx)) goto err;
+ if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
- ret = (0 == BN_cmp(tmp1, rh));
+ ret = (0 == BN_ucmp(tmp, rh));
err:
BN_CTX_end(ctx);
}
-int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
-/* TODO */
+int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+ {
+ /* return values:
+ * -1 error
+ * 0 equal (in affine coordinates)
+ * 1 not equal
+ */
+
+ int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+ int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
+ const BIGNUM *tmp1_, *tmp2_;
+ int ret = -1;
+
+ if (EC_POINT_is_at_infinity(group, a))
+ {
+ return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
+ }
+
+ if (EC_POINT_is_at_infinity(group, b))
+ return 1;
+
+ if (a->Z_is_one && b->Z_is_one)
+ {
+ return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
+ }
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return -1;
+ }
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ Za23 = BN_CTX_get(ctx);
+ Zb23 = BN_CTX_get(ctx);
+ if (Zb23 == NULL) goto end;
+
+ /* We have to decide whether
+ * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
+ * or equivalently, whether
+ * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
+ */
+
+ if (!b->Z_is_one)
+ {
+ if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
+ if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
+ tmp1_ = tmp1;
+ }
+ else
+ tmp1_ = &a->X;
+ if (!a->Z_is_one)
+ {
+ if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
+ if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
+ tmp2_ = tmp2;
+ }
+ else
+ tmp2_ = &b->X;
+
+ /* compare X_a*Z_b^2 with X_b*Z_a^2 */
+ if (BN_cmp(tmp1_, tmp2_) != 0)
+ {
+ ret = 1; /* points differ */
+ goto end;
+ }
+ if (!b->Z_is_one)
+ {
+ if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
+ if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
+ /* tmp1_ = tmp1 */
+ }
+ else
+ tmp1_ = &a->Y;
+ if (!a->Z_is_one)
+ {
+ if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
+ if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
+ /* tmp2_ = tmp2 */
+ }
+ else
+ tmp2_ = &b->Y;
+
+ /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
+ if (BN_cmp(tmp1_, tmp2_) != 0)
+ {
+ ret = 1; /* points differ */
+ goto end;
+ }
+
+ /* points are equal */
+ ret = 0;
+
+ end:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
+
int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
}
+int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp0, *tmp1;
+ size_t pow2 = 0;
+ BIGNUM **heap = NULL;
+ size_t i;
+ int ret = 0;
+
+ if (num == 0)
+ return 1;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ BN_CTX_start(ctx);
+ tmp0 = BN_CTX_get(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ if (tmp0 == NULL || tmp1 == NULL) goto err;
+
+ /* Before converting the individual points, compute inverses of all Z values.
+ * Modular inversion is rather slow, but luckily we can do with a single
+ * explicit inversion, plus about 3 multiplications per input value.
+ */
+
+ pow2 = 1;
+ while (num > pow2)
+ pow2 <<= 1;
+ /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
+ * We need twice that. */
+ pow2 <<= 1;
+
+ heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
+ if (heap == NULL) goto err;
+
+ /* The array is used as a binary tree, exactly as in heapsort:
+ *
+ * heap[1]
+ * heap[2] heap[3]
+ * heap[4] heap[5] heap[6] heap[7]
+ * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
+ *
+ * We put the Z's in the last line;
+ * then we set each other node to the product of its two child-nodes (where
+ * empty or 0 entries are treated as ones);
+ * then we invert heap[1];
+ * then we invert each other node by replacing it by the product of its
+ * parent (after inversion) and its sibling (before inversion).
+ */
+ heap[0] = NULL;
+ for (i = pow2/2 - 1; i > 0; i--)
+ heap[i] = NULL;
+ for (i = 0; i < num; i++)
+ heap[pow2/2 + i] = &points[i]->Z;
+ for (i = pow2/2 + num; i < pow2; i++)
+ heap[i] = NULL;
+
+ /* set each node to the product of its children */
+ for (i = pow2/2 - 1; i > 0; i--)
+ {
+ heap[i] = BN_new();
+ if (heap[i] == NULL) goto err;
+
+ if (heap[2*i] != NULL)
+ {
+ if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
+ {
+ if (!BN_copy(heap[i], heap[2*i])) goto err;
+ }
+ else
+ {
+ if (BN_is_zero(heap[2*i]))
+ {
+ if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
+ }
+ else
+ {
+ if (!group->meth->field_mul(group, heap[i],
+ heap[2*i], heap[2*i + 1], ctx)) goto err;
+ }
+ }
+ }
+ }
+
+ /* invert heap[1] */
+ if (!BN_is_zero(heap[1]))
+ {
+ if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
+ goto err;
+ }
+ }
+ if (group->meth->field_encode != 0)
+ {
+ /* in the Montgomery case, we just turned R*H (representing H)
+ * into 1/(R*H), but we need R*(1/H) (representing 1/H);
+ * i.e. we have need to multiply by the Montgomery factor twice */
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+ if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+ }
+
+ /* set other heap[i]'s to their inverses */
+ for (i = 2; i < pow2/2 + num; i += 2)
+ {
+ /* i is even */
+ if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
+ {
+ if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
+ if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
+ if (!BN_copy(heap[i], tmp0)) goto err;
+ if (!BN_copy(heap[i + 1], tmp1)) goto err;
+ }
+ else
+ {
+ if (!BN_copy(heap[i], heap[i/2])) goto err;
+ }
+ }
+
+ /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
+ for (i = 0; i < num; i++)
+ {
+ EC_POINT *p = points[i];
+
+ if (!BN_is_zero(&p->Z))
+ {
+ /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
+
+ if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
+ if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
+
+ if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
+ if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
+
+ if (group->meth->field_set_to_one != 0)
+ {
+ if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_one(&p->Z)) goto err;
+ }
+ p->Z_is_one = 1;
+ }
+ }
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ if (heap != NULL)
+ {
+ /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
+ for (i = pow2/2 - 1; i > 0; i--)
+ {
+ if (heap[i] != NULL)
+ BN_clear_free(heap[i]);
+ }
+ OPENSSL_free(heap);
+ }
+ return ret;
+ }
+
+
int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
return BN_mod_mul(r, a, b, &group->field, ctx);
projects / openssl.git / blobdiff