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3712436071
openssl/crypto/ec/ecp_smpl.c
Nicola Tuveri 3712436071 EC point multiplication: add ladder scaffold 
for specialized Montgomery ladder implementations

PR #6009 and #6070 replaced the default EC point multiplication path for
prime and binary curves with a unified Montgomery ladder implementation
with various timing attack defenses (for the common paths when a secret
scalar is feed to the point multiplication).
The newly introduced default implementation directly used
EC_POINT_add/dbl in the main loop.

The scaffolding introduced by this commit allows EC_METHODs to define a
specialized `ladder_step` function to improve performances by taking
advantage of efficient formulas for differential addition-and-doubling
and different coordinate systems.

- `ladder_pre` is executed before the main loop of the ladder: by
  default it copies the input point P into S, and doubles it into R.
  Specialized implementations could, e.g., use this hook to transition
  to different coordinate systems before copying and doubling;
- `ladder_step` is the core of the Montgomery ladder loop: by default it
  computes `S := R+S; R := 2R;`, but specific implementations could,
  e.g., implement a more efficient formula for differential
  addition-and-doubling;
- `ladder_post` is executed after the Montgomery ladder loop: by default
  it's a noop, but specialized implementations could, e.g., use this
  hook to transition back from the coordinate system used for optimizing
  the differential addition-and-doubling or recover the y coordinate of
  the result point.

This commit also renames `ec_mul_consttime` to `ec_scalar_mul_ladder`,
as it better corresponds to what this function does: nothing can be
truly said about the constant-timeness of the overall execution of this
function, given that the underlying operations are not necessarily
constant-time themselves.
What this implementation ensures is that the same fixed sequence of
operations is executed for each scalar multiplication (for a given
EC_GROUP), with no dependency on the value of the input scalar.

Co-authored-by: Sohaib ul Hassan <soh.19.hassan@gmail.com>
Co-authored-by: Billy Brumley <bbrumley@gmail.com>

Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/6690)
2018-07-16 10:17:40 +01:00

1424 lines
38 KiB
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/*
* Copyright 2001-2018 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,
0, /* field_inverse_mod_ord */
ec_GFp_simple_blind_coordinates,
0, /* ladder_pre */
0, /* ladder_step */
0 /* 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:
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;
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 (!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);
}
/*-
* 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 err;
}
/* make sure lambda is not zero */
do {
if (!BN_priv_rand_range(lambda, group->field)) {
ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
goto err;
}
} 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))
goto err;
if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
goto err;
if (!group->meth->field_sqr(group, temp, lambda, ctx))
goto err;
if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
goto err;
if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
goto err;
if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
goto err;
p->Z_is_one = 0;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
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