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openssl/crypto/ec/ec2_smpl.c
Billy Brumley 48e82c8e22 SCA hardening for mod. field inversion in EC_GROUP 
This commit adds a dedicated function in `EC_METHOD` to access a modular
field inversion implementation suitable for the specifics of the
implemented curve, featuring SCA countermeasures.

The new pointer is defined as:
`int (*field_inv)(const EC_GROUP*, BIGNUM *r, const BIGNUM *a, BN_CTX*)`
and computes the multiplicative inverse of `a` in the underlying field,
storing the result in `r`.

Three implementations are included, each including specific SCA
countermeasures:
  - `ec_GFp_simple_field_inv()`, featuring SCA hardening through
    blinding.
  - `ec_GFp_mont_field_inv()`, featuring SCA hardening through Fermat's
    Little Theorem (FLT) inversion.
  - `ec_GF2m_simple_field_inv()`, that uses `BN_GF2m_mod_inv()` which
    already features SCA hardening through blinding.

From a security point of view, this also helps addressing a leakage
previously affecting conversions from projective to affine coordinates.

This commit also adds a new error reason code (i.e.,
`EC_R_CANNOT_INVERT`) to improve consistency between the three
implementations as all of them could fail for the same reason but
through different code paths resulting in inconsistent error stack
states.

Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>

(cherry picked from commit e0033efc30)

Reviewed-by: Matt Caswell <matt@openssl.org>
Reviewed-by: Nicola Tuveri <nic.tuv@gmail.com>
(Merged from https://github.com/openssl/openssl/pull/8262)
2019-02-20 19:54:19 +02:00

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/*
* 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 "internal/bn_int.h"
#include "ec_lcl.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:
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(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
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