/*

 * Copyright 2002-2021 The OpenSSL Project Authors. All Rights Reserved.

 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved

 *

 * Licensed under the Apache License 2.0 (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

 */

/*

 * ECDSA low-level APIs are deprecated for public use, but still ok for

 * internal use.

 */

#include "internal/deprecated.h"

#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 ossl_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 ossl_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 ossl_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 ossl_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 ossl_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)) {

        ERR_raise(ERR_LIB_EC, 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 ossl_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 ossl_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 ossl_ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group,

                                                 BN_CTX *ctx)

{

    int ret = 0;

    BIGNUM *b;

#ifndef FIPS_MODULE

    BN_CTX *new_ctx = NULL;

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        if (ctx == NULL) {

            ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);

            goto err;

        }

    }

#endif

    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);

#ifndef FIPS_MODULE

    BN_CTX_free(new_ctx);

#endif

    return ret;

}

/* Initializes an EC_POINT. */

int ossl_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 ossl_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 ossl_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 ossl_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 ossl_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 ossl_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) {

        ERR_raise(ERR_LIB_EC, 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 ossl_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)) {

        ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);

        return 0;

    }

    if (BN_cmp(point->Z, BN_value_one())) {

        ERR_raise(ERR_LIB_EC, 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 ossl_ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r,

                            const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)

{

    BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t;

    int ret = 0;

#ifndef FIPS_MODULE

    BN_CTX *new_ctx = NULL;

#endif

    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;

    }

#ifndef FIPS_MODULE

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        if (ctx == NULL)

            return 0;

    }

#endif

    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);

#ifndef FIPS_MODULE

    BN_CTX_free(new_ctx);

#endif

    return ret;

}

/*

 * Computes 2 * a and stores the result in r.  r could be a. Uses algorithm

 * A.10.2 of IEEE P1363.

 */

int ossl_ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r,

                            const EC_POINT *a, BN_CTX *ctx)

{

    return ossl_ec_GF2m_simple_add(group, r, a, a, ctx);

}

int ossl_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 (group->meth->make_affine == NULL

        || !group->meth->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 ossl_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 ossl_ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point,

                                    BN_CTX *ctx)

{

    int ret = -1;

    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 *);

#ifndef FIPS_MODULE

    BN_CTX *new_ctx = NULL;

#endif

    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;

#ifndef FIPS_MODULE

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        if (ctx == NULL)

            return -1;

    }

#endif

    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);

#ifndef FIPS_MODULE

    BN_CTX_free(new_ctx);

#endif

    return ret;

}

/*-

 * Indicates whether two points are equal.

 * Return values:

 *  -1   error

 *   0   equal (in affine coordinates)

 *   1   not equal

 */

int ossl_ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a,

                            const EC_POINT *b, BN_CTX *ctx)

{

    BIGNUM *aX, *aY, *bX, *bY;

    int ret = -1;

#ifndef FIPS_MODULE

    BN_CTX *new_ctx = NULL;

#endif

    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;

    }

#ifndef FIPS_MODULE

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        if (ctx == NULL)

            return -1;

    }

#endif

    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);

#ifndef FIPS_MODULE

    BN_CTX_free(new_ctx);

#endif

    return ret;

}

/* Forces the given EC_POINT to internally use affine coordinates. */

int ossl_ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point,

                                    BN_CTX *ctx)

{

    BIGNUM *x, *y;

    int ret = 0;

#ifndef FIPS_MODULE

    BN_CTX *new_ctx = NULL;

#endif

    if (point->Z_is_one || EC_POINT_is_at_infinity(group, point))

        return 1;

#ifndef FIPS_MODULE

    if (ctx == NULL) {

        ctx = new_ctx = BN_CTX_new();

        if (ctx == NULL)

            return 0;

    }

#endif

    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);

#ifndef FIPS_MODULE

    BN_CTX_free(new_ctx);

#endif

    return ret;

}

/*

 * Forces each of the EC_POINTs in the given array to use affine coordinates.

 */

int ossl_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 ossl_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 ossl_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 ossl_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_ex(s->Z, BN_num_bits(group->field) - 1,

                             BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, 0, ctx)) {

            ERR_raise(ERR_LIB_EC, 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_ex(r->Y, BN_num_bits(group->field) - 1,

                             BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, 0, ctx)) {

            ERR_raise(ERR_LIB_EC, 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)) {

            ERR_raise(ERR_LIB_EC, 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) {

        ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);

        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 ossl_ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);

    if (scalar != NULL && num == 0)

        /* Fixed point multiplication */

        return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);

    if (scalar == NULL && num == 1)

        /* Variable point multiplication */

        return ossl_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) {

        ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);

        return 0;

    }

    if (!ossl_ec_scalar_mul_ladder(group, t, scalar, NULL, ctx)

        || !ossl_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 an 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)))

        ERR_raise(ERR_LIB_EC, 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,

        ossl_ec_GF2m_simple_group_init,

        ossl_ec_GF2m_simple_group_finish,

        ossl_ec_GF2m_simple_group_clear_finish,

        ossl_ec_GF2m_simple_group_copy,

        ossl_ec_GF2m_simple_group_set_curve,

        ossl_ec_GF2m_simple_group_get_curve,

        ossl_ec_GF2m_simple_group_get_degree,

        ossl_ec_group_simple_order_bits,

        ossl_ec_GF2m_simple_group_check_discriminant,

        ossl_ec_GF2m_simple_point_init,

        ossl_ec_GF2m_simple_point_finish,

        ossl_ec_GF2m_simple_point_clear_finish,

        ossl_ec_GF2m_simple_point_copy,

        ossl_ec_GF2m_simple_point_set_to_infinity,

        ossl_ec_GF2m_simple_point_set_affine_coordinates,

        ossl_ec_GF2m_simple_point_get_affine_coordinates,

        0, /* point_set_compressed_coordinates */

        0, /* point2oct */

        0, /* oct2point */

        ossl_ec_GF2m_simple_add,

        ossl_ec_GF2m_simple_dbl,

        ossl_ec_GF2m_simple_invert,

        ossl_ec_GF2m_simple_is_at_infinity,

        ossl_ec_GF2m_simple_is_on_curve,

        ossl_ec_GF2m_simple_cmp,

        ossl_ec_GF2m_simple_make_affine,

        ossl_ec_GF2m_simple_points_make_affine,

        ec_GF2m_simple_points_mul,

        0, /* precompute_mult */

        0, /* have_precompute_mult */

        ossl_ec_GF2m_simple_field_mul,

        ossl_ec_GF2m_simple_field_sqr,

        ossl_ec_GF2m_simple_field_div,

        ec_GF2m_simple_field_inv,

        0, /* field_encode */

        0, /* field_decode */

        0, /* field_set_to_one */

        ossl_ec_key_simple_priv2oct,

        ossl_ec_key_simple_oct2priv,

        0, /* set private */

        ossl_ec_key_simple_generate_key,

        ossl_ec_key_simple_check_key,

        ossl_ec_key_simple_generate_public_key,

        0, /* keycopy */

        0, /* keyfinish */

        ossl_ecdh_simple_compute_key,

        ossl_ecdsa_simple_sign_setup,