diff options
Diffstat (limited to 'roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ec2_smpl.c')
| -rw-r--r-- | roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ec2_smpl.c | 969 |
1 files changed, 969 insertions, 0 deletions
diff --git a/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ec2_smpl.c b/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ec2_smpl.c new file mode 100644 index 000000000..84e5537a0 --- /dev/null +++ b/roms/edk2/CryptoPkg/Library/OpensslLib/openssl/crypto/ec/ec2_smpl.c @@ -0,0 +1,969 @@ +/* + * Copyright 2002-2019 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 "crypto/bn.h" +#include "ec_local.h" + +#ifndef OPENSSL_NO_EC2M + +/* + * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members + * are handled by EC_GROUP_new. + */ +int ec_GF2m_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; + } + return 1; +} + +/* + * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are + * handled by EC_GROUP_free. + */ +void ec_GF2m_simple_group_finish(EC_GROUP *group) +{ + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); +} + +/* + * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other + * members are handled by EC_GROUP_clear_free. + */ +void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) +{ + BN_clear_free(group->field); + BN_clear_free(group->a); + BN_clear_free(group->b); + group->poly[0] = 0; + group->poly[1] = 0; + group->poly[2] = 0; + group->poly[3] = 0; + group->poly[4] = 0; + group->poly[5] = -1; +} + +/* + * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are + * handled by EC_GROUP_copy. + */ +int ec_GF2m_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->poly[0] = src->poly[0]; + dest->poly[1] = src->poly[1]; + dest->poly[2] = src->poly[2]; + dest->poly[3] = src->poly[3]; + dest->poly[4] = src->poly[4]; + dest->poly[5] = src->poly[5]; + if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == + NULL) + return 0; + if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == + NULL) + return 0; + bn_set_all_zero(dest->a); + bn_set_all_zero(dest->b); + return 1; +} + +/* Set the curve parameters of an EC_GROUP structure. */ +int ec_GF2m_simple_group_set_curve(EC_GROUP *group, + const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0, i; + + /* group->field */ + if (!BN_copy(group->field, p)) + goto err; + i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1; + if ((i != 5) && (i != 3)) { + ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); + goto err; + } + + /* group->a */ + if (!BN_GF2m_mod_arr(group->a, a, group->poly)) + goto err; + if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) + == NULL) + goto err; + bn_set_all_zero(group->a); + + /* group->b */ + if (!BN_GF2m_mod_arr(group->b, b, group->poly)) + goto err; + if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) + == NULL) + goto err; + bn_set_all_zero(group->b); + + ret = 1; + err: + return ret; +} + +/* + * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL + * then there values will not be set but the method will return with success. + */ +int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, + BIGNUM *a, BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + + if (p != NULL) { + if (!BN_copy(p, group->field)) + return 0; + } + + 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: + return ret; +} + +/* + * Gets the degree of the field. For a curve over GF(2^m) this is the value + * m. + */ +int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) +{ + return BN_num_bits(group->field) - 1; +} + +/* + * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an + * elliptic curve <=> b != 0 (mod p) + */ +int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, + BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *b; + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, + ERR_R_MALLOC_FAILURE); + goto err; + } + } + BN_CTX_start(ctx); + b = BN_CTX_get(ctx); + if (b == NULL) + goto err; + + if (!BN_GF2m_mod_arr(b, group->b, group->poly)) + goto err; + + /* + * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic + * curve <=> b != 0 (mod p) + */ + if (BN_is_zero(b)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* Initializes an EC_POINT. */ +int ec_GF2m_simple_point_init(EC_POINT *point) +{ + point->X = BN_new(); + point->Y = BN_new(); + point->Z = BN_new(); + + 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; +} + +/* Frees an EC_POINT. */ +void ec_GF2m_simple_point_finish(EC_POINT *point) +{ + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); +} + +/* Clears and frees an EC_POINT. */ +void ec_GF2m_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; +} + +/* + * Copy the contents of one EC_POINT into another. Assumes dest is + * initialized. + */ +int ec_GF2m_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; +} + +/* + * Set an EC_POINT to the point at infinity. A point at infinity is + * represented by having Z=0. + */ +int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, + EC_POINT *point) +{ + point->Z_is_one = 0; + BN_zero(point->Z); + return 1; +} + +/* + * Set the coordinates of an EC_POINT using affine coordinates. Note that + * the simple implementation only uses affine coordinates. + */ +int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) +{ + int ret = 0; + if (x == NULL || y == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (!BN_copy(point->X, x)) + goto err; + BN_set_negative(point->X, 0); + if (!BN_copy(point->Y, y)) + goto err; + BN_set_negative(point->Y, 0); + if (!BN_copy(point->Z, BN_value_one())) + goto err; + BN_set_negative(point->Z, 0); + point->Z_is_one = 1; + ret = 1; + + err: + return ret; +} + +/* + * Gets the affine coordinates of an EC_POINT. Note that the simple + * implementation only uses affine coordinates. + */ +int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + int ret = 0; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + + if (BN_cmp(point->Z, BN_value_one())) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (x != NULL) { + if (!BN_copy(x, point->X)) + goto err; + BN_set_negative(x, 0); + } + if (y != NULL) { + if (!BN_copy(y, point->Y)) + goto err; + BN_set_negative(y, 0); + } + ret = 1; + + err: + return ret; +} + +/* + * Computes a + b and stores the result in r. r could be a or b, a could be + * b. Uses algorithm A.10.2 of IEEE P1363. + */ +int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, a)) { + if (!EC_POINT_copy(r, b)) + return 0; + return 1; + } + + if (EC_POINT_is_at_infinity(group, b)) { + if (!EC_POINT_copy(r, a)) + return 0; + return 1; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x0 = BN_CTX_get(ctx); + y0 = BN_CTX_get(ctx); + x1 = BN_CTX_get(ctx); + y1 = BN_CTX_get(ctx); + x2 = BN_CTX_get(ctx); + y2 = BN_CTX_get(ctx); + s = BN_CTX_get(ctx); + t = BN_CTX_get(ctx); + if (t == NULL) + goto err; + + if (a->Z_is_one) { + if (!BN_copy(x0, a->X)) + goto err; + if (!BN_copy(y0, a->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates(group, a, x0, y0, ctx)) + goto err; + } + if (b->Z_is_one) { + if (!BN_copy(x1, b->X)) + goto err; + if (!BN_copy(y1, b->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates(group, b, x1, y1, ctx)) + goto err; + } + + if (BN_GF2m_cmp(x0, x1)) { + if (!BN_GF2m_add(t, x0, x1)) + goto err; + if (!BN_GF2m_add(s, y0, y1)) + goto err; + if (!group->meth->field_div(group, s, s, t, ctx)) + goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, group->a)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, t)) + goto err; + } else { + if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + ret = 1; + goto err; + } + if (!group->meth->field_div(group, s, y1, x1, ctx)) + goto err; + if (!BN_GF2m_add(s, s, x1)) + goto err; + + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, group->a)) + goto err; + } + + if (!BN_GF2m_add(y2, x1, x2)) + goto err; + if (!group->meth->field_mul(group, y2, y2, s, ctx)) + goto err; + if (!BN_GF2m_add(y2, y2, x2)) + goto err; + if (!BN_GF2m_add(y2, y2, y1)) + goto err; + + if (!EC_POINT_set_affine_coordinates(group, r, x2, y2, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Computes 2 * a and stores the result in r. r could be a. Uses algorithm + * A.10.2 of IEEE P1363. + */ +int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ + return ec_GF2m_simple_add(group, r, a, a, ctx); +} + +int ec_GF2m_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; + + if (!EC_POINT_make_affine(group, point, ctx)) + return 0; + return BN_GF2m_add(point->Y, point->X, point->Y); +} + +/* Indicates whether the given point is the point at infinity. */ +int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, + const EC_POINT *point) +{ + return BN_is_zero(point->Z); +} + +/*- + * Determines whether the given EC_POINT is an actual point on the curve defined + * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: + * y^2 + x*y = x^3 + a*x^2 + b. + */ +int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, + BN_CTX *ctx) +{ + int ret = -1; + BN_CTX *new_ctx = NULL; + BIGNUM *lh, *y2; + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + + if (EC_POINT_is_at_infinity(group, point)) + return 1; + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + + /* only support affine coordinates */ + if (!point->Z_is_one) + return -1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + y2 = BN_CTX_get(ctx); + lh = BN_CTX_get(ctx); + if (lh == NULL) + goto err; + + /*- + * We have a curve defined by a Weierstrass equation + * y^2 + x*y = x^3 + a*x^2 + b. + * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 + * <=> ((x + a) * x + y ) * x + b + y^2 = 0 + */ + if (!BN_GF2m_add(lh, point->X, group->a)) + goto err; + if (!field_mul(group, lh, lh, point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, point->Y)) + goto err; + if (!field_mul(group, lh, lh, point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, group->b)) + goto err; + if (!field_sqr(group, y2, point->Y, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, y2)) + goto err; + ret = BN_is_zero(lh); + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/*- + * Indicates whether two points are equal. + * Return values: + * -1 error + * 0 equal (in affine coordinates) + * 1 not equal + */ +int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + BIGNUM *aX, *aY, *bX, *bY; + BN_CTX *new_ctx = NULL; + 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; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + aX = BN_CTX_get(ctx); + aY = BN_CTX_get(ctx); + bX = BN_CTX_get(ctx); + bY = BN_CTX_get(ctx); + if (bY == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates(group, a, aX, aY, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates(group, b, bX, bY, ctx)) + goto err; + ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* Forces the given EC_POINT to internally use affine coordinates. */ +int ec_GF2m_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 (!BN_copy(point->X, x)) + goto err; + if (!BN_copy(point->Y, y)) + goto err; + if (!BN_one(point->Z)) + goto err; + point->Z_is_one = 1; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Forces each of the EC_POINTs in the given array to use affine coordinates. + */ +int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ + size_t i; + + for (i = 0; i < num; i++) { + if (!group->meth->make_affine(group, points[i], ctx)) + return 0; + } + + return 1; +} + +/* Wrapper to simple binary polynomial field multiplication implementation. */ +int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); +} + +/* Wrapper to simple binary polynomial field squaring implementation. */ +int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); +} + +/* Wrapper to simple binary polynomial field division implementation. */ +int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + return BN_GF2m_mod_div(r, a, b, group->field, ctx); +} + +/*- + * Lopez-Dahab ladder, pre step. + * See e.g. "Guide to ECC" Alg 3.40. + * Modified to blind s and r independently. + * s:= p, r := 2p + */ +static +int ec_GF2m_simple_ladder_pre(const EC_GROUP *group, + EC_POINT *r, EC_POINT *s, + EC_POINT *p, BN_CTX *ctx) +{ + /* if p is not affine, something is wrong */ + if (p->Z_is_one == 0) + return 0; + + /* s blinding: make sure lambda (s->Z here) is not zero */ + do { + if (!BN_priv_rand(s->Z, BN_num_bits(group->field) - 1, + BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) { + ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB); + 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, s->Z, s->Z, ctx)) + || !group->meth->field_mul(group, s->X, p->X, s->Z, ctx)) + return 0; + + /* r blinding: make sure lambda (r->Y here for storage) is not zero */ + do { + if (!BN_priv_rand(r->Y, BN_num_bits(group->field) - 1, + BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY)) { + ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_PRE, ERR_R_BN_LIB); + return 0; + } + } while (BN_is_zero(r->Y)); + + if ((group->meth->field_encode != NULL + && !group->meth->field_encode(group, r->Y, r->Y, ctx)) + || !group->meth->field_sqr(group, r->Z, p->X, ctx) + || !group->meth->field_sqr(group, r->X, r->Z, ctx) + || !BN_GF2m_add(r->X, r->X, group->b) + || !group->meth->field_mul(group, r->Z, r->Z, r->Y, ctx) + || !group->meth->field_mul(group, r->X, r->X, r->Y, ctx)) + return 0; + + s->Z_is_one = 0; + r->Z_is_one = 0; + + return 1; +} + +/*- + * Ladder step: differential addition-and-doubling, mixed Lopez-Dahab coords. + * http://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3 + * s := r + s, r := 2r + */ +static +int ec_GF2m_simple_ladder_step(const EC_GROUP *group, + EC_POINT *r, EC_POINT *s, + EC_POINT *p, BN_CTX *ctx) +{ + if (!group->meth->field_mul(group, r->Y, r->Z, s->X, ctx) + || !group->meth->field_mul(group, s->X, r->X, s->Z, ctx) + || !group->meth->field_sqr(group, s->Y, r->Z, ctx) + || !group->meth->field_sqr(group, r->Z, r->X, ctx) + || !BN_GF2m_add(s->Z, r->Y, s->X) + || !group->meth->field_sqr(group, s->Z, s->Z, ctx) + || !group->meth->field_mul(group, s->X, r->Y, s->X, ctx) + || !group->meth->field_mul(group, r->Y, s->Z, p->X, ctx) + || !BN_GF2m_add(s->X, s->X, r->Y) + || !group->meth->field_sqr(group, r->Y, r->Z, ctx) + || !group->meth->field_mul(group, r->Z, r->Z, s->Y, ctx) + || !group->meth->field_sqr(group, s->Y, s->Y, ctx) + || !group->meth->field_mul(group, s->Y, s->Y, group->b, ctx) + || !BN_GF2m_add(r->X, r->Y, s->Y)) + return 0; + + return 1; +} + +/*- + * Recover affine (x,y) result from Lopez-Dahab r and s, affine p. + * See e.g. "Fast Multiplication on Elliptic Curves over GF(2**m) + * without Precomputation" (Lopez and Dahab, CHES 1999), + * Appendix Alg Mxy. + */ +static +int ec_GF2m_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 = 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)) { + ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_EC_LIB); + return 0; + } + return 1; + } + + BN_CTX_start(ctx); + t0 = BN_CTX_get(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + if (t2 == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_LADDER_POST, ERR_R_MALLOC_FAILURE); + goto err; + } + + if (!group->meth->field_mul(group, t0, r->Z, s->Z, ctx) + || !group->meth->field_mul(group, t1, p->X, r->Z, ctx) + || !BN_GF2m_add(t1, r->X, t1) + || !group->meth->field_mul(group, t2, p->X, s->Z, ctx) + || !group->meth->field_mul(group, r->Z, r->X, t2, ctx) + || !BN_GF2m_add(t2, t2, s->X) + || !group->meth->field_mul(group, t1, t1, t2, ctx) + || !group->meth->field_sqr(group, t2, p->X, ctx) + || !BN_GF2m_add(t2, p->Y, t2) + || !group->meth->field_mul(group, t2, t2, t0, ctx) + || !BN_GF2m_add(t1, t2, t1) + || !group->meth->field_mul(group, t2, p->X, t0, ctx) + || !group->meth->field_inv(group, t2, t2, ctx) + || !group->meth->field_mul(group, t1, t1, t2, ctx) + || !group->meth->field_mul(group, r->X, r->Z, t2, ctx) + || !BN_GF2m_add(t2, p->X, r->X) + || !group->meth->field_mul(group, t2, t2, t1, ctx) + || !BN_GF2m_add(r->Y, p->Y, t2) + || !BN_one(r->Z)) + goto err; + + r->Z_is_one = 1; + + /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ + BN_set_negative(r->X, 0); + BN_set_negative(r->Y, 0); + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} + +static +int ec_GF2m_simple_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], + BN_CTX *ctx) +{ + int ret = 0; + EC_POINT *t = NULL; + + /*- + * We limit use of the ladder only to the following cases: + * - r := scalar * G + * Fixed point mul: scalar != NULL && num == 0; + * - r := scalars[0] * points[0] + * Variable point mul: scalar == NULL && num == 1; + * - r := scalar * G + scalars[0] * points[0] + * used, e.g., in ECDSA verification: scalar != NULL && num == 1 + * + * In any other case (num > 1) we use the default wNAF implementation. + * + * We also let the default implementation handle degenerate cases like group + * order or cofactor set to 0. + */ + if (num > 1 || BN_is_zero(group->order) || BN_is_zero(group->cofactor)) + return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); + + if (scalar != NULL && num == 0) + /* Fixed point multiplication */ + return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx); + + if (scalar == NULL && num == 1) + /* Variable point multiplication */ + return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx); + + /*- + * Double point multiplication: + * r := scalar * G + scalars[0] * points[0] + */ + + if ((t = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINTS_MUL, ERR_R_MALLOC_FAILURE); + return 0; + } + + if (!ec_scalar_mul_ladder(group, t, scalar, NULL, ctx) + || !ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx) + || !EC_POINT_add(group, r, t, r, ctx)) + goto err; + + ret = 1; + + err: + EC_POINT_free(t); + return ret; +} + +/*- + * Computes the multiplicative inverse of a in GF(2^m), storing the result in r. + * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error. + * SCA hardening is with blinding: BN_GF2m_mod_inv does that. + */ +static int ec_GF2m_simple_field_inv(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + int ret; + + if (!(ret = BN_GF2m_mod_inv(r, a, group->field, ctx))) + ECerr(EC_F_EC_GF2M_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT); + return ret; +} + +const EC_METHOD *EC_GF2m_simple_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_characteristic_two_field, + ec_GF2m_simple_group_init, + ec_GF2m_simple_group_finish, + ec_GF2m_simple_group_clear_finish, + ec_GF2m_simple_group_copy, + ec_GF2m_simple_group_set_curve, + ec_GF2m_simple_group_get_curve, + ec_GF2m_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GF2m_simple_group_check_discriminant, + ec_GF2m_simple_point_init, + ec_GF2m_simple_point_finish, + ec_GF2m_simple_point_clear_finish, + ec_GF2m_simple_point_copy, + ec_GF2m_simple_point_set_to_infinity, + 0, /* set_Jprojective_coordinates_GFp */ + 0, /* get_Jprojective_coordinates_GFp */ + ec_GF2m_simple_point_set_affine_coordinates, + ec_GF2m_simple_point_get_affine_coordinates, + 0, /* point_set_compressed_coordinates */ + 0, /* point2oct */ + 0, /* oct2point */ + ec_GF2m_simple_add, + ec_GF2m_simple_dbl, + ec_GF2m_simple_invert, + ec_GF2m_simple_is_at_infinity, + ec_GF2m_simple_is_on_curve, + ec_GF2m_simple_cmp, + ec_GF2m_simple_make_affine, + ec_GF2m_simple_points_make_affine, + ec_GF2m_simple_points_mul, + 0, /* precompute_mult */ + 0, /* have_precompute_mult */ + ec_GF2m_simple_field_mul, + ec_GF2m_simple_field_sqr, + ec_GF2m_simple_field_div, + ec_GF2m_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 */ + 0, /* blind_coordinates */ + ec_GF2m_simple_ladder_pre, + ec_GF2m_simple_ladder_step, + ec_GF2m_simple_ladder_post + }; + + return &ret; +} + +#endif |