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openssl/crypto/ec/ec2_smpl.c
Sohaib ul Hassan f667820c16 Implement coordinate blinding for EC_POINT 
This commit implements coordinate blinding, i.e., it randomizes the
representative of an elliptic curve point in its equivalence class, for
prime curves implemented through EC_GFp_simple_method,
EC_GFp_mont_method, and EC_GFp_nist_method.

This commit is derived from the patch
https://marc.info/?l=openssl-dev&m=131194808413635 by Billy Brumley.

Coordinate blinding is a generally useful side-channel countermeasure
and is (mostly) free. The function itself takes a few field
multiplicationss, but is usually only necessary at the beginning of a
scalar multiplication (as implemented in the patch). When used this way,
it makes the values that variables take (i.e., field elements in an
algorithm state) unpredictable.

For instance, this mitigates chosen EC point side-channel attacks for
settings such as ECDH and EC private key decryption, for the
aforementioned curves.

For EC_METHODs using different coordinate representations this commit
does nothing, but the corresponding coordinate blinding function can be
easily added in the future to extend these changes to such curves.

Co-authored-by: Nicola Tuveri <nic.tuv@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/6501)
2018-06-19 11:43:59 +01:00

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/*
* Copyright 2002-2018 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 "internal/bn_int.h"
#include "ec_lcl.h"
#ifndef OPENSSL_NO_EC2M
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, 0, 0,
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,
0 /* mul */,
0 /* precompute_mul */,
0 /* have_precompute_mul */,
ec_GF2m_simple_field_mul,
ec_GF2m_simple_field_sqr,
ec_GF2m_simple_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 */
0 /* blind_coordinates */
};
return &ret;
}
/*
* 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:
if (ctx != NULL)
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_GF2m(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_GF2m(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_GF2m(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_GF2m(group, a, aX, aY, ctx))
goto err;
if (!EC_POINT_get_affine_coordinates_GF2m(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_GF2m(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);
}
#endif
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