diff options
Diffstat (limited to 'roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ecp_smpl.c')
| -rw-r--r-- | roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ecp_smpl.c | 1716 |
1 files changed, 1716 insertions, 0 deletions
diff --git a/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ecp_smpl.c b/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ecp_smpl.c new file mode 100644 index 000000000..b3110ec89 --- /dev/null +++ b/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ecp_smpl.c @@ -0,0 +1,1716 @@ +/* + * Copyright 2001-2020 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_local.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 */ , + ec_GFp_simple_field_inv, + 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, + 0, /* field_inverse_mod_ord */ + ec_GFp_simple_blind_coordinates, + ec_GFp_simple_ladder_pre, + ec_GFp_simple_ladder_step, + ec_GFp_simple_ladder_post + }; + + 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: + 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; + dest->curve_name = src->curve_name; + + 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 (!group->meth->field_inv(group, Z_1, Z_, 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: + 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(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates(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 (!group->meth->field_inv(group, tmp, prod_Z[num - 1], 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); +} + +/*- + * Computes the multiplicative inverse of a in GF(p), storing the result in r. + * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error. + * Since we don't have a Mont structure here, SCA hardening is with blinding. + * NB: "a" must be in _decoded_ form. (i.e. field_decode must precede.) + */ +int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + BIGNUM *e = NULL; + BN_CTX *new_ctx = NULL; + int ret = 0; + + if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL) + return 0; + + BN_CTX_start(ctx); + if ((e = BN_CTX_get(ctx)) == NULL) + goto err; + + do { + if (!BN_priv_rand_range(e, group->field)) + goto err; + } while (BN_is_zero(e)); + + /* r := a * e */ + if (!group->meth->field_mul(group, r, a, e, ctx)) + goto err; + /* r := 1/(a * e) */ + if (!BN_mod_inverse(r, r, group->field, ctx)) { + ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT); + goto err; + } + /* r := e/(a * e) = 1/a */ + if (!group->meth->field_mul(group, r, r, e, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/*- + * Apply randomization of EC point projective coordinates: + * + * (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z) + * lambda = [1,group->field) + * + */ +int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p, + BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *lambda = NULL; + BIGNUM *temp = NULL; + + BN_CTX_start(ctx); + lambda = BN_CTX_get(ctx); + temp = BN_CTX_get(ctx); + if (temp == NULL) { + ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE); + goto end; + } + + /*- + * Make sure lambda is not zero. + * If the RNG fails, we cannot blind but nevertheless want + * code to continue smoothly and not clobber the error stack. + */ + do { + ERR_set_mark(); + ret = BN_priv_rand_range(lambda, group->field); + ERR_pop_to_mark(); + if (ret == 0) { + ret = 1; + goto end; + } + } while (BN_is_zero(lambda)); + + /* if field_encode defined convert between representations */ + if ((group->meth->field_encode != NULL + && !group->meth->field_encode(group, lambda, lambda, ctx)) + || !group->meth->field_mul(group, p->Z, p->Z, lambda, ctx) + || !group->meth->field_sqr(group, temp, lambda, ctx) + || !group->meth->field_mul(group, p->X, p->X, temp, ctx) + || !group->meth->field_mul(group, temp, temp, lambda, ctx) + || !group->meth->field_mul(group, p->Y, p->Y, temp, ctx)) + goto end; + + p->Z_is_one = 0; + ret = 1; + + end: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Input: + * - p: affine coordinates + * + * Output: + * - s := p, r := 2p: blinded projective (homogeneous) coordinates + * + * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve + * multiplication resistant against side channel attacks" appendix, described at + * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2 + * simplified for Z1=1. + * + * Blinding uses the equivalence relation (\lambda X, \lambda Y, \lambda Z) + * for any non-zero \lambda that holds for projective (homogeneous) coords. + */ +int ec_GFp_simple_ladder_pre(const EC_GROUP *group, + EC_POINT *r, EC_POINT *s, + EC_POINT *p, BN_CTX *ctx) +{ + BIGNUM *t1, *t2, *t3, *t4, *t5 = NULL; + + t1 = s->Z; + t2 = r->Z; + t3 = s->X; + t4 = r->X; + t5 = s->Y; + + if (!p->Z_is_one /* r := 2p */ + || !group->meth->field_sqr(group, t3, p->X, ctx) + || !BN_mod_sub_quick(t4, t3, group->a, group->field) + || !group->meth->field_sqr(group, t4, t4, ctx) + || !group->meth->field_mul(group, t5, p->X, group->b, ctx) + || !BN_mod_lshift_quick(t5, t5, 3, group->field) + /* r->X coord output */ + || !BN_mod_sub_quick(r->X, t4, t5, group->field) + || !BN_mod_add_quick(t1, t3, group->a, group->field) + || !group->meth->field_mul(group, t2, p->X, t1, ctx) + || !BN_mod_add_quick(t2, group->b, t2, group->field) + /* r->Z coord output */ + || !BN_mod_lshift_quick(r->Z, t2, 2, group->field)) + return 0; + + /* make sure lambda (r->Y here for storage) is not zero */ + do { + if (!BN_priv_rand_range(r->Y, group->field)) + return 0; + } while (BN_is_zero(r->Y)); + + /* make sure lambda (s->Z here for storage) is not zero */ + do { + if (!BN_priv_rand_range(s->Z, group->field)) + return 0; + } while (BN_is_zero(s->Z)); + + /* if field_encode defined convert between representations */ + if (group->meth->field_encode != NULL + && (!group->meth->field_encode(group, r->Y, r->Y, ctx) + || !group->meth->field_encode(group, s->Z, s->Z, ctx))) + return 0; + + /* blind r and s independently */ + if (!group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) + || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx) + || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) /* s := p */ + return 0; + + r->Z_is_one = 0; + s->Z_is_one = 0; + + return 1; +} + +/*- + * Input: + * - s, r: projective (homogeneous) coordinates + * - p: affine coordinates + * + * Output: + * - s := r + s, r := 2r: projective (homogeneous) coordinates + * + * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi + * "A fast parallel elliptic curve multiplication resistant against side channel + * attacks", as described at + * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-mladd-2002-it-4 + */ +int ec_GFp_simple_ladder_step(const EC_GROUP *group, + EC_POINT *r, EC_POINT *s, + EC_POINT *p, BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; + + BN_CTX_start(ctx); + t0 = BN_CTX_get(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + t3 = BN_CTX_get(ctx); + t4 = BN_CTX_get(ctx); + t5 = BN_CTX_get(ctx); + t6 = BN_CTX_get(ctx); + + if (t6 == NULL + || !group->meth->field_mul(group, t6, r->X, s->X, ctx) + || !group->meth->field_mul(group, t0, r->Z, s->Z, ctx) + || !group->meth->field_mul(group, t4, r->X, s->Z, ctx) + || !group->meth->field_mul(group, t3, r->Z, s->X, ctx) + || !group->meth->field_mul(group, t5, group->a, t0, ctx) + || !BN_mod_add_quick(t5, t6, t5, group->field) + || !BN_mod_add_quick(t6, t3, t4, group->field) + || !group->meth->field_mul(group, t5, t6, t5, ctx) + || !group->meth->field_sqr(group, t0, t0, ctx) + || !BN_mod_lshift_quick(t2, group->b, 2, group->field) + || !group->meth->field_mul(group, t0, t2, t0, ctx) + || !BN_mod_lshift1_quick(t5, t5, group->field) + || !BN_mod_sub_quick(t3, t4, t3, group->field) + /* s->Z coord output */ + || !group->meth->field_sqr(group, s->Z, t3, ctx) + || !group->meth->field_mul(group, t4, s->Z, p->X, ctx) + || !BN_mod_add_quick(t0, t0, t5, group->field) + /* s->X coord output */ + || !BN_mod_sub_quick(s->X, t0, t4, group->field) + || !group->meth->field_sqr(group, t4, r->X, ctx) + || !group->meth->field_sqr(group, t5, r->Z, ctx) + || !group->meth->field_mul(group, t6, t5, group->a, ctx) + || !BN_mod_add_quick(t1, r->X, r->Z, group->field) + || !group->meth->field_sqr(group, t1, t1, ctx) + || !BN_mod_sub_quick(t1, t1, t4, group->field) + || !BN_mod_sub_quick(t1, t1, t5, group->field) + || !BN_mod_sub_quick(t3, t4, t6, group->field) + || !group->meth->field_sqr(group, t3, t3, ctx) + || !group->meth->field_mul(group, t0, t5, t1, ctx) + || !group->meth->field_mul(group, t0, t2, t0, ctx) + /* r->X coord output */ + || !BN_mod_sub_quick(r->X, t3, t0, group->field) + || !BN_mod_add_quick(t3, t4, t6, group->field) + || !group->meth->field_sqr(group, t4, t5, ctx) + || !group->meth->field_mul(group, t4, t4, t2, ctx) + || !group->meth->field_mul(group, t1, t1, t3, ctx) + || !BN_mod_lshift1_quick(t1, t1, group->field) + /* r->Z coord output */ + || !BN_mod_add_quick(r->Z, t4, t1, group->field)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Input: + * - s, r: projective (homogeneous) coordinates + * - p: affine coordinates + * + * Output: + * - r := (x,y): affine coordinates + * + * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass + * Elliptic Curves and Side-Channel Attacks", modified to work in mixed + * projective coords, i.e. p is affine and (r,s) in projective (homogeneous) + * coords, and return r in affine coordinates. + * + * X4 = two*Y1*X2*Z3*Z2; + * Y4 = two*b*Z3*SQR(Z2) + Z3*(a*Z2+X1*X2)*(X1*Z2+X2) - X3*SQR(X1*Z2-X2); + * Z4 = two*Y1*Z3*SQR(Z2); + * + * Z4 != 0 because: + * - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch); + * - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch); + * - Y1==0 implies p has order 2, so either r or s are infinity and handled by + * one of the BN_is_zero(...) branches. + */ +int ec_GFp_simple_ladder_post(const EC_GROUP *group, + EC_POINT *r, EC_POINT *s, + EC_POINT *p, BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL; + + if (BN_is_zero(r->Z)) + return EC_POINT_set_to_infinity(group, r); + + if (BN_is_zero(s->Z)) { + if (!EC_POINT_copy(r, p) + || !EC_POINT_invert(group, r, ctx)) + return 0; + return 1; + } + + BN_CTX_start(ctx); + t0 = BN_CTX_get(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + t3 = BN_CTX_get(ctx); + t4 = BN_CTX_get(ctx); + t5 = BN_CTX_get(ctx); + t6 = BN_CTX_get(ctx); + + if (t6 == NULL + || !BN_mod_lshift1_quick(t4, p->Y, group->field) + || !group->meth->field_mul(group, t6, r->X, t4, ctx) + || !group->meth->field_mul(group, t6, s->Z, t6, ctx) + || !group->meth->field_mul(group, t5, r->Z, t6, ctx) + || !BN_mod_lshift1_quick(t1, group->b, group->field) + || !group->meth->field_mul(group, t1, s->Z, t1, ctx) + || !group->meth->field_sqr(group, t3, r->Z, ctx) + || !group->meth->field_mul(group, t2, t3, t1, ctx) + || !group->meth->field_mul(group, t6, r->Z, group->a, ctx) + || !group->meth->field_mul(group, t1, p->X, r->X, ctx) + || !BN_mod_add_quick(t1, t1, t6, group->field) + || !group->meth->field_mul(group, t1, s->Z, t1, ctx) + || !group->meth->field_mul(group, t0, p->X, r->Z, ctx) + || !BN_mod_add_quick(t6, r->X, t0, group->field) + || !group->meth->field_mul(group, t6, t6, t1, ctx) + || !BN_mod_add_quick(t6, t6, t2, group->field) + || !BN_mod_sub_quick(t0, t0, r->X, group->field) + || !group->meth->field_sqr(group, t0, t0, ctx) + || !group->meth->field_mul(group, t0, t0, s->X, ctx) + || !BN_mod_sub_quick(t0, t6, t0, group->field) + || !group->meth->field_mul(group, t1, s->Z, t4, ctx) + || !group->meth->field_mul(group, t1, t3, t1, ctx) + || (group->meth->field_decode != NULL + && !group->meth->field_decode(group, t1, t1, ctx)) + || !group->meth->field_inv(group, t1, t1, ctx) + || (group->meth->field_encode != NULL + && !group->meth->field_encode(group, t1, t1, ctx)) + || !group->meth->field_mul(group, r->X, t5, t1, ctx) + || !group->meth->field_mul(group, r->Y, t0, t1, ctx)) + goto err; + + if (group->meth->field_set_to_one != NULL) { + if (!group->meth->field_set_to_one(group, r->Z, ctx)) + goto err; + } else { + if (!BN_one(r->Z)) + goto err; + } + + r->Z_is_one = 1; + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} |