| /* |
| * Copyright 2001-2017 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 <openssl/symhacks.h> |
| |
| #include "ec_lcl.h" |
| |
| const EC_METHOD *EC_GFp_simple_method(void) |
| { |
| static const EC_METHOD ret = { |
| EC_FLAGS_DEFAULT_OCT, |
| NID_X9_62_prime_field, |
| ec_GFp_simple_group_init, |
| ec_GFp_simple_group_finish, |
| ec_GFp_simple_group_clear_finish, |
| ec_GFp_simple_group_copy, |
| ec_GFp_simple_group_set_curve, |
| ec_GFp_simple_group_get_curve, |
| ec_GFp_simple_group_get_degree, |
| ec_group_simple_order_bits, |
| 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_simple_point_get_affine_coordinates, |
| 0, 0, 0, |
| 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, |
| 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_set_to_one */ |
| ec_key_simple_priv2oct, |
| ec_key_simple_oct2priv, |
| 0, /* set private */ |
| ec_key_simple_generate_key, |
| ec_key_simple_check_key, |
| ec_key_simple_generate_public_key, |
| 0, /* keycopy */ |
| 0, /* keyfinish */ |
| ecdh_simple_compute_key |
| }; |
| |
| 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) |
| { |
| group->field = BN_new(); |
| group->a = BN_new(); |
| group->b = BN_new(); |
| if (group->field == NULL || group->a == NULL || group->b == NULL) { |
| BN_free(group->field); |
| BN_free(group->a); |
| BN_free(group->b); |
| return 0; |
| } |
| group->a_is_minus3 = 0; |
| return 1; |
| } |
| |
| 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; |
| BN_CTX *new_ctx = NULL; |
| BIGNUM *tmp_a; |
| |
| /* 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, EC_R_INVALID_FIELD); |
| return 0; |
| } |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| tmp_a = BN_CTX_get(ctx); |
| if (tmp_a == NULL) |
| goto err; |
| |
| /* group->field */ |
| if (!BN_copy(group->field, p)) |
| goto err; |
| BN_set_negative(group->field, 0); |
| |
| /* group->a */ |
| if (!BN_nnmod(tmp_a, a, p, ctx)) |
| goto err; |
| if (group->meth->field_encode) { |
| if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) |
| goto err; |
| } else if (!BN_copy(group->a, tmp_a)) |
| goto err; |
| |
| /* group->b */ |
| if (!BN_nnmod(group->b, b, p, ctx)) |
| goto err; |
| if (group->meth->field_encode) |
| if (!group->meth->field_encode(group, group->b, group->b, ctx)) |
| goto err; |
| |
| /* group->a_is_minus3 */ |
| if (!BN_add_word(tmp_a, 3)) |
| goto err; |
| group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, |
| BIGNUM *b, BN_CTX *ctx) |
| { |
| int ret = 0; |
| BN_CTX *new_ctx = NULL; |
| |
| if (p != NULL) { |
| if (!BN_copy(p, group->field)) |
| return 0; |
| } |
| |
| if (a != NULL || b != NULL) { |
| if (group->meth->field_decode) { |
| 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; |
| } |
| } else { |
| 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: |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| int ec_GFp_simple_group_get_degree(const EC_GROUP *group) |
| { |
| return BN_num_bits(group->field); |
| } |
| |
| int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) |
| { |
| int ret = 0; |
| BIGNUM *a, *b, *order, *tmp_1, *tmp_2; |
| const BIGNUM *p = group->field; |
| BN_CTX *new_ctx = NULL; |
| |
| if (ctx == NULL) { |
| 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->meth->field_decode) { |
| if (!group->meth->field_decode(group, a, group->a, ctx)) |
| goto err; |
| if (!group->meth->field_decode(group, b, group->b, ctx)) |
| goto err; |
| } else { |
| 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 (!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; |
| |
| err: |
| if (ctx != NULL) |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| int ec_GFp_simple_point_init(EC_POINT *point) |
| { |
| point->X = BN_new(); |
| point->Y = BN_new(); |
| point->Z = BN_new(); |
| point->Z_is_one = 0; |
| |
| if (point->X == NULL || point->Y == NULL || point->Z == NULL) { |
| BN_free(point->X); |
| BN_free(point->Y); |
| BN_free(point->Z); |
| return 0; |
| } |
| return 1; |
| } |
| |
| void ec_GFp_simple_point_finish(EC_POINT *point) |
| { |
| BN_free(point->X); |
| BN_free(point->Y); |
| BN_free(point->Z); |
| } |
| |
| void ec_GFp_simple_point_clear_finish(EC_POINT *point) |
| { |
| BN_clear_free(point->X); |
| BN_clear_free(point->Y); |
| BN_clear_free(point->Z); |
| point->Z_is_one = 0; |
| } |
| |
| int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) |
| { |
| if (!BN_copy(dest->X, src->X)) |
| return 0; |
| if (!BN_copy(dest->Y, src->Y)) |
| return 0; |
| if (!BN_copy(dest->Z, src->Z)) |
| return 0; |
| dest->Z_is_one = src->Z_is_one; |
| |
| return 1; |
| } |
| |
| int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, |
| EC_POINT *point) |
| { |
| point->Z_is_one = 0; |
| 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) |
| { |
| 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; |
| |
| 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; |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| 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 (group->meth->field_decode != 0) { |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| 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: |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| 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 *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, |
| EC_R_POINT_AT_INFINITY); |
| return 0; |
| } |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| Z = BN_CTX_get(ctx); |
| Z_1 = BN_CTX_get(ctx); |
| Z_2 = BN_CTX_get(ctx); |
| Z_3 = BN_CTX_get(ctx); |
| if (Z_3 == NULL) |
| goto err; |
| |
| /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ |
| |
| if (group->meth->field_decode) { |
| if (!group->meth->field_decode(group, Z, point->Z, ctx)) |
| goto err; |
| Z_ = Z; |
| } else { |
| Z_ = point->Z; |
| } |
| |
| if (BN_is_one(Z_)) { |
| if (group->meth->field_decode) { |
| 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; |
| } |
| } else { |
| 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, |
| ERR_R_BN_LIB); |
| 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) { |
| /* |
| * 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 (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; |
| } |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
| const EC_POINT *b, BN_CTX *ctx) |
| { |
| int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
| const BIGNUM *, BN_CTX *); |
| int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| const BIGNUM *p; |
| BN_CTX *new_ctx = NULL; |
| BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; |
| int ret = 0; |
| |
| if (a == b) |
| return EC_POINT_dbl(group, r, a, ctx); |
| if (EC_POINT_is_at_infinity(group, a)) |
| return EC_POINT_copy(r, b); |
| if (EC_POINT_is_at_infinity(group, b)) |
| return EC_POINT_copy(r, a); |
| |
| field_mul = group->meth->field_mul; |
| field_sqr = group->meth->field_sqr; |
| p = group->field; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| n0 = BN_CTX_get(ctx); |
| n1 = BN_CTX_get(ctx); |
| n2 = BN_CTX_get(ctx); |
| n3 = BN_CTX_get(ctx); |
| n4 = BN_CTX_get(ctx); |
| n5 = BN_CTX_get(ctx); |
| n6 = BN_CTX_get(ctx); |
| if (n6 == NULL) |
| goto end; |
| |
| /* |
| * Note that in this function we must not read components of 'a' or 'b' |
| * once we have written the corresponding components of 'r'. ('r' might |
| * be one of 'a' or 'b'.) |
| */ |
| |
| /* n1, n2 */ |
| if (b->Z_is_one) { |
| if (!BN_copy(n1, a->X)) |
| goto end; |
| if (!BN_copy(n2, a->Y)) |
| goto end; |
| /* n1 = X_a */ |
| /* n2 = Y_a */ |
| } else { |
| if (!field_sqr(group, n0, b->Z, ctx)) |
| goto end; |
| if (!field_mul(group, n1, a->X, n0, ctx)) |
| goto end; |
| /* n1 = X_a * Z_b^2 */ |
| |
| if (!field_mul(group, n0, n0, b->Z, ctx)) |
| goto end; |
| if (!field_mul(group, n2, a->Y, n0, ctx)) |
| goto end; |
| /* n2 = Y_a * Z_b^3 */ |
| } |
| |
| /* n3, n4 */ |
| if (a->Z_is_one) { |
| if (!BN_copy(n3, b->X)) |
| goto end; |
| if (!BN_copy(n4, b->Y)) |
| goto end; |
| /* n3 = X_b */ |
| /* n4 = Y_b */ |
| } else { |
| if (!field_sqr(group, n0, a->Z, ctx)) |
| goto end; |
| if (!field_mul(group, n3, b->X, n0, ctx)) |
| goto end; |
| /* n3 = X_b * Z_a^2 */ |
| |
| if (!field_mul(group, n0, n0, a->Z, ctx)) |
| goto end; |
| if (!field_mul(group, n4, b->Y, n0, ctx)) |
| goto end; |
| /* n4 = Y_b * Z_a^3 */ |
| } |
| |
| /* n5, n6 */ |
| if (!BN_mod_sub_quick(n5, n1, n3, p)) |
| goto end; |
| if (!BN_mod_sub_quick(n6, n2, n4, p)) |
| goto end; |
| /* n5 = n1 - n3 */ |
| /* n6 = n2 - n4 */ |
| |
| if (BN_is_zero(n5)) { |
| if (BN_is_zero(n6)) { |
| /* a is the same point as b */ |
| BN_CTX_end(ctx); |
| ret = EC_POINT_dbl(group, r, a, ctx); |
| ctx = NULL; |
| goto end; |
| } else { |
| /* a is the inverse of b */ |
| BN_zero(r->Z); |
| r->Z_is_one = 0; |
| ret = 1; |
| goto end; |
| } |
| } |
| |
| /* 'n7', 'n8' */ |
| if (!BN_mod_add_quick(n1, n1, n3, p)) |
| goto end; |
| if (!BN_mod_add_quick(n2, n2, n4, p)) |
| goto end; |
| /* 'n7' = n1 + n3 */ |
| /* 'n8' = n2 + n4 */ |
| |
| /* Z_r */ |
| if (a->Z_is_one && b->Z_is_one) { |
| if (!BN_copy(r->Z, n5)) |
| goto end; |
| } else { |
| if (a->Z_is_one) { |
| if (!BN_copy(n0, b->Z)) |
| goto end; |
| } else if (b->Z_is_one) { |
| if (!BN_copy(n0, a->Z)) |
| goto end; |
| } else { |
| if (!field_mul(group, n0, a->Z, b->Z, ctx)) |
| goto end; |
| } |
| if (!field_mul(group, r->Z, n0, n5, ctx)) |
| goto end; |
| } |
| r->Z_is_one = 0; |
| /* Z_r = Z_a * Z_b * n5 */ |
| |
| /* X_r */ |
| if (!field_sqr(group, n0, n6, ctx)) |
| goto end; |
| if (!field_sqr(group, n4, n5, ctx)) |
| goto end; |
| if (!field_mul(group, n3, n1, n4, ctx)) |
| goto end; |
| if (!BN_mod_sub_quick(r->X, n0, n3, p)) |
| goto end; |
| /* X_r = n6^2 - n5^2 * 'n7' */ |
| |
| /* 'n9' */ |
| if (!BN_mod_lshift1_quick(n0, r->X, p)) |
| goto end; |
| if (!BN_mod_sub_quick(n0, n3, n0, p)) |
| goto end; |
| /* n9 = n5^2 * 'n7' - 2 * X_r */ |
| |
| /* Y_r */ |
| if (!field_mul(group, n0, n0, n6, ctx)) |
| goto end; |
| if (!field_mul(group, n5, n4, n5, ctx)) |
| goto end; /* now n5 is n5^3 */ |
| if (!field_mul(group, n1, n2, n5, ctx)) |
| goto end; |
| if (!BN_mod_sub_quick(n0, n0, n1, p)) |
| goto end; |
| if (BN_is_odd(n0)) |
| if (!BN_add(n0, n0, p)) |
| goto end; |
| /* now 0 <= n0 < 2*p, and n0 is even */ |
| if (!BN_rshift1(r->Y, n0)) |
| goto end; |
| /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ |
| |
| ret = 1; |
| |
| end: |
| if (ctx) /* otherwise we already called BN_CTX_end */ |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, |
| BN_CTX *ctx) |
| { |
| int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
| const BIGNUM *, BN_CTX *); |
| int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| const BIGNUM *p; |
| BN_CTX *new_ctx = NULL; |
| BIGNUM *n0, *n1, *n2, *n3; |
| int ret = 0; |
| |
| if (EC_POINT_is_at_infinity(group, a)) { |
| BN_zero(r->Z); |
| r->Z_is_one = 0; |
| return 1; |
| } |
| |
| field_mul = group->meth->field_mul; |
| field_sqr = group->meth->field_sqr; |
| p = group->field; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| n0 = BN_CTX_get(ctx); |
| n1 = BN_CTX_get(ctx); |
| n2 = BN_CTX_get(ctx); |
| n3 = BN_CTX_get(ctx); |
| if (n3 == NULL) |
| goto err; |
| |
| /* |
| * Note that in this function we must not read components of 'a' once we |
| * have written the corresponding components of 'r'. ('r' might the same |
| * as 'a'.) |
| */ |
| |
| /* n1 */ |
| if (a->Z_is_one) { |
| if (!field_sqr(group, n0, a->X, ctx)) |
| goto err; |
| if (!BN_mod_lshift1_quick(n1, n0, p)) |
| goto err; |
| if (!BN_mod_add_quick(n0, n0, n1, p)) |
| goto err; |
| if (!BN_mod_add_quick(n1, n0, group->a, p)) |
| goto err; |
| /* n1 = 3 * X_a^2 + a_curve */ |
| } else if (group->a_is_minus3) { |
| if (!field_sqr(group, n1, a->Z, ctx)) |
| goto err; |
| if (!BN_mod_add_quick(n0, a->X, n1, p)) |
| goto err; |
| if (!BN_mod_sub_quick(n2, a->X, n1, p)) |
| goto err; |
| if (!field_mul(group, n1, n0, n2, ctx)) |
| goto err; |
| if (!BN_mod_lshift1_quick(n0, n1, p)) |
| goto err; |
| if (!BN_mod_add_quick(n1, n0, n1, p)) |
| goto err; |
| /*- |
| * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) |
| * = 3 * X_a^2 - 3 * Z_a^4 |
| */ |
| } else { |
| if (!field_sqr(group, n0, a->X, ctx)) |
| goto err; |
| if (!BN_mod_lshift1_quick(n1, n0, p)) |
| goto err; |
| if (!BN_mod_add_quick(n0, n0, n1, p)) |
| goto err; |
| if (!field_sqr(group, n1, a->Z, ctx)) |
| goto err; |
| if (!field_sqr(group, n1, n1, ctx)) |
| goto err; |
| if (!field_mul(group, n1, n1, group->a, ctx)) |
| goto err; |
| if (!BN_mod_add_quick(n1, n1, n0, p)) |
| goto err; |
| /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ |
| } |
| |
| /* Z_r */ |
| if (a->Z_is_one) { |
| if (!BN_copy(n0, a->Y)) |
| goto err; |
| } else { |
| if (!field_mul(group, n0, a->Y, a->Z, ctx)) |
| goto err; |
| } |
| if (!BN_mod_lshift1_quick(r->Z, n0, p)) |
| goto err; |
| r->Z_is_one = 0; |
| /* Z_r = 2 * Y_a * Z_a */ |
| |
| /* n2 */ |
| if (!field_sqr(group, n3, a->Y, ctx)) |
| goto err; |
| if (!field_mul(group, n2, a->X, n3, ctx)) |
| goto err; |
| if (!BN_mod_lshift_quick(n2, n2, 2, p)) |
| goto err; |
| /* n2 = 4 * X_a * Y_a^2 */ |
| |
| /* X_r */ |
| if (!BN_mod_lshift1_quick(n0, n2, p)) |
| goto err; |
| if (!field_sqr(group, r->X, n1, ctx)) |
| goto err; |
| if (!BN_mod_sub_quick(r->X, r->X, n0, p)) |
| goto err; |
| /* X_r = n1^2 - 2 * n2 */ |
| |
| /* n3 */ |
| if (!field_sqr(group, n0, n3, ctx)) |
| goto err; |
| if (!BN_mod_lshift_quick(n3, n0, 3, p)) |
| goto err; |
| /* n3 = 8 * Y_a^4 */ |
| |
| /* Y_r */ |
| if (!BN_mod_sub_quick(n0, n2, r->X, p)) |
| goto err; |
| if (!field_mul(group, n0, n1, n0, ctx)) |
| goto err; |
| if (!BN_mod_sub_quick(r->Y, n0, n3, p)) |
| goto err; |
| /* Y_r = n1 * (n2 - X_r) - n3 */ |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| 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) |
| { |
| return BN_is_zero(point->Z); |
| } |
| |
| int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, |
| BN_CTX *ctx) |
| { |
| int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, |
| const BIGNUM *, BN_CTX *); |
| int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); |
| const BIGNUM *p; |
| BN_CTX *new_ctx = NULL; |
| BIGNUM *rh, *tmp, *Z4, *Z6; |
| int ret = -1; |
| |
| if (EC_POINT_is_at_infinity(group, point)) |
| return 1; |
| |
| field_mul = group->meth->field_mul; |
| field_sqr = group->meth->field_sqr; |
| p = group->field; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return -1; |
| } |
| |
| BN_CTX_start(ctx); |
| rh = BN_CTX_get(ctx); |
| tmp = BN_CTX_get(ctx); |
| Z4 = BN_CTX_get(ctx); |
| Z6 = BN_CTX_get(ctx); |
| if (Z6 == NULL) |
| goto err; |
| |
| /*- |
| * We have a curve defined by a Weierstrass equation |
| * y^2 = x^3 + a*x + b. |
| * The point to consider is given in Jacobian projective coordinates |
| * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). |
| * Substituting this and multiplying by Z^6 transforms the above equation into |
| * Y^2 = X^3 + a*X*Z^4 + b*Z^6. |
| * To test this, we add up the right-hand side in 'rh'. |
| */ |
| |
| /* rh := X^2 */ |
| if (!field_sqr(group, rh, point->X, ctx)) |
| goto err; |
| |
| if (!point->Z_is_one) { |
| 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*Z^4)*X */ |
| if (group->a_is_minus3) { |
| 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, 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, 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 (!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, tmp, point->Y, ctx)) |
| goto err; |
| |
| ret = (0 == BN_ucmp(tmp, rh)); |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| 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); |
| 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; |
| BIGNUM *x, *y; |
| int ret = 0; |
| |
| if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) |
| return 1; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| x = BN_CTX_get(ctx); |
| y = BN_CTX_get(ctx); |
| if (y == NULL) |
| goto err; |
| |
| if (!EC_POINT_get_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 (!point->Z_is_one) { |
| ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); |
| goto err; |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| 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 *tmp, *tmp_Z; |
| BIGNUM **prod_Z = 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); |
| tmp = BN_CTX_get(ctx); |
| tmp_Z = BN_CTX_get(ctx); |
| if (tmp_Z == NULL) |
| goto err; |
| |
| prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); |
| if (prod_Z == NULL) |
| goto err; |
| for (i = 0; i < num; i++) { |
| prod_Z[i] = BN_new(); |
| if (prod_Z[i] == NULL) |
| goto err; |
| } |
| |
| /* |
| * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, |
| * skipping any zero-valued inputs (pretend that they're 1). |
| */ |
| |
| if (!BN_is_zero(points[0]->Z)) { |
| if (!BN_copy(prod_Z[0], points[0]->Z)) |
| goto err; |
| } else { |
| if (group->meth->field_set_to_one != 0) { |
| if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) |
| goto err; |
| } else { |
| if (!BN_one(prod_Z[0])) |
| goto err; |
| } |
| } |
| |
| for (i = 1; i < num; i++) { |
| if (!BN_is_zero(points[i]->Z)) { |
| if (!group-> |
| meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, |
| ctx)) |
| goto err; |
| } else { |
| if (!BN_copy(prod_Z[i], prod_Z[i - 1])) |
| goto err; |
| } |
| } |
| |
| /* |
| * Now use a single explicit inversion to replace every non-zero |
| * points[i]->Z by its inverse. |
| */ |
| |
| if (!BN_mod_inverse(tmp, prod_Z[num - 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 need to |
| * multiply by the Montgomery factor twice. |
| */ |
| if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
| goto err; |
| if (!group->meth->field_encode(group, tmp, tmp, ctx)) |
| goto err; |
| } |
| |
| for (i = num - 1; i > 0; --i) { |
| /* |
| * Loop invariant: tmp is the product of the inverses of points[0]->Z |
| * .. points[i]->Z (zero-valued inputs skipped). |
| */ |
| if (!BN_is_zero(points[i]->Z)) { |
| /* |
| * Set tmp_Z to the inverse of points[i]->Z (as product of Z |
| * inverses 0 .. i, Z values 0 .. i - 1). |
| */ |
| if (!group-> |
| meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) |
| goto err; |
| /* |
| * Update tmp to satisfy the loop invariant for i - 1. |
| */ |
| if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) |
| goto err; |
| /* Replace points[i]->Z by its inverse. */ |
| if (!BN_copy(points[i]->Z, tmp_Z)) |
| goto err; |
| } |
| } |
| |
| if (!BN_is_zero(points[0]->Z)) { |
| /* Replace points[0]->Z by its inverse. */ |
| if (!BN_copy(points[0]->Z, tmp)) |
| goto err; |
| } |
| |
| /* Finally, fix up the X and Y coordinates for all 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, tmp, p->Z, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) |
| goto err; |
| |
| if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) |
| goto err; |
| if (!group->meth->field_mul(group, p->Y, p->Y, tmp, 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); |
| BN_CTX_free(new_ctx); |
| if (prod_Z != NULL) { |
| for (i = 0; i < num; i++) { |
| if (prod_Z[i] == NULL) |
| break; |
| BN_clear_free(prod_Z[i]); |
| } |
| OPENSSL_free(prod_Z); |
| } |
| 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); |
| } |
| |
| int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, |
| BN_CTX *ctx) |
| { |
| return BN_mod_sqr(r, a, group->field, ctx); |
| } |
