+ 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(group, point, x, y, ctx))
+ goto err;
+ if (!EC_POINT_set_affine_coordinates(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 (!group->meth->field_inv(group, tmp, prod_Z[num - 1], 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);
+}
+
+/*-
+ * Computes the multiplicative inverse of a in GF(p), storing the result in r.
+ * If a is zero (or equivalent), you'll get a EC_R_CANNOT_INVERT error.
+ * Since we don't have a Mont structure here, SCA hardening is with blinding.
+ */
+int ec_GFp_simple_field_inv(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
+ BN_CTX *ctx)
+{
+ BIGNUM *e = NULL;
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL && (ctx = new_ctx = BN_CTX_secure_new()) == NULL)
+ return 0;
+
+ BN_CTX_start(ctx);
+ if ((e = BN_CTX_get(ctx)) == NULL)
+ goto err;
+
+ do {
+ if (!BN_priv_rand_range(e, group->field))
+ goto err;
+ } while (BN_is_zero(e));
+
+ /* r := a * e */
+ if (!group->meth->field_mul(group, r, a, e, ctx))
+ goto err;
+ /* r := 1/(a * e) */
+ if (!BN_mod_inverse(r, r, group->field, ctx)) {
+ ECerr(EC_F_EC_GFP_SIMPLE_FIELD_INV, EC_R_CANNOT_INVERT);
+ goto err;
+ }
+ /* r := e/(a * e) = 1/a */
+ if (!group->meth->field_mul(group, r, r, e, ctx))
+ goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ BN_CTX_free(new_ctx);
+ return ret;
+}
+
+/*-
+ * 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;
+}
+
+/*-
+ * Set s := p, r := 2p.
+ *
+ * For doubling we use Formula 3 from Izu-Takagi "A fast parallel elliptic curve
+ * multiplication resistant against side channel attacks" appendix, as described
+ * at
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
+ *
+ * The input point p will be in randomized Jacobian projective coords:
+ * x = X/Z**2, y=Y/Z**3
+ *
+ * The output points p, s, and r are converted to standard (homogeneous)
+ * projective coords:
+ * x = X/Z, y=Y/Z
+ */
+int ec_GFp_simple_ladder_pre(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ BIGNUM *t1, *t2, *t3, *t4, *t5, *t6 = NULL;
+
+ t1 = r->Z;
+ t2 = r->Y;
+ t3 = s->X;
+ t4 = r->X;
+ t5 = s->Y;
+ t6 = s->Z;
+
+ /* convert p: (X,Y,Z) -> (XZ,Y,Z**3) */
+ if (!group->meth->field_mul(group, p->X, p->X, p->Z, ctx)
+ || !group->meth->field_sqr(group, t1, p->Z, ctx)
+ || !group->meth->field_mul(group, p->Z, p->Z, t1, ctx)
+ /* r := 2p */
+ || !group->meth->field_sqr(group, t2, p->X, ctx)
+ || !group->meth->field_sqr(group, t3, p->Z, ctx)
+ || !group->meth->field_mul(group, t4, t3, group->a, ctx)
+ || !BN_mod_sub_quick(t5, t2, t4, group->field)
+ || !BN_mod_add_quick(t2, t2, t4, group->field)
+ || !group->meth->field_sqr(group, t5, t5, ctx)
+ || !group->meth->field_mul(group, t6, t3, group->b, ctx)
+ || !group->meth->field_mul(group, t1, p->X, p->Z, ctx)
+ || !group->meth->field_mul(group, t4, t1, t6, ctx)
+ || !BN_mod_lshift_quick(t4, t4, 3, group->field)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t5, t4, group->field)
+ || !group->meth->field_mul(group, t1, t1, t2, ctx)
+ || !group->meth->field_mul(group, t2, t3, t6, ctx)
+ || !BN_mod_add_quick(t1, t1, t2, group->field)
+ /* r->Z coord output */
+ || !BN_mod_lshift_quick(r->Z, t1, 2, group->field)
+ || !EC_POINT_copy(s, p))
+ return 0;
+
+ r->Z_is_one = 0;
+ s->Z_is_one = 0;
+ p->Z_is_one = 0;
+
+ return 1;
+}
+
+/*-
+ * Differential addition-and-doubling using Eq. (9) and (10) from Izu-Takagi
+ * "A fast parallel elliptic curve multiplication resistant against side channel
+ * attacks", as described at
+ * https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
+ */
+int ec_GFp_simple_ladder_step(const EC_GROUP *group,
+ EC_POINT *r, EC_POINT *s,
+ EC_POINT *p, BN_CTX *ctx)
+{
+ int ret = 0;
+ BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6, *t7 = NULL;
+
+ BN_CTX_start(ctx);
+ t0 = BN_CTX_get(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ t3 = BN_CTX_get(ctx);
+ t4 = BN_CTX_get(ctx);
+ t5 = BN_CTX_get(ctx);
+ t6 = BN_CTX_get(ctx);
+ t7 = BN_CTX_get(ctx);
+
+ if (t7 == NULL
+ || !group->meth->field_mul(group, t0, r->X, s->X, ctx)
+ || !group->meth->field_mul(group, t1, r->Z, s->Z, ctx)
+ || !group->meth->field_mul(group, t2, r->X, s->Z, ctx)
+ || !group->meth->field_mul(group, t3, r->Z, s->X, ctx)
+ || !group->meth->field_mul(group, t4, group->a, t1, ctx)
+ || !BN_mod_add_quick(t0, t0, t4, group->field)
+ || !BN_mod_add_quick(t4, t3, t2, group->field)
+ || !group->meth->field_mul(group, t0, t4, t0, ctx)
+ || !group->meth->field_sqr(group, t1, t1, ctx)
+ || !BN_mod_lshift_quick(t7, group->b, 2, group->field)
+ || !group->meth->field_mul(group, t1, t7, t1, ctx)
+ || !BN_mod_lshift1_quick(t0, t0, group->field)
+ || !BN_mod_add_quick(t0, t1, t0, group->field)
+ || !BN_mod_sub_quick(t1, t2, t3, group->field)
+ || !group->meth->field_sqr(group, t1, t1, ctx)
+ || !group->meth->field_mul(group, t3, t1, p->X, ctx)
+ || !group->meth->field_mul(group, t0, p->Z, t0, ctx)
+ /* s->X coord output */
+ || !BN_mod_sub_quick(s->X, t0, t3, group->field)
+ /* s->Z coord output */
+ || !group->meth->field_mul(group, s->Z, p->Z, t1, ctx)
+ || !group->meth->field_sqr(group, t3, r->X, ctx)
+ || !group->meth->field_sqr(group, t2, r->Z, ctx)
+ || !group->meth->field_mul(group, t4, t2, group->a, ctx)
+ || !BN_mod_add_quick(t5, r->X, r->Z, group->field)
+ || !group->meth->field_sqr(group, t5, t5, ctx)
+ || !BN_mod_sub_quick(t5, t5, t3, group->field)
+ || !BN_mod_sub_quick(t5, t5, t2, group->field)
+ || !BN_mod_sub_quick(t6, t3, t4, group->field)
+ || !group->meth->field_sqr(group, t6, t6, ctx)
+ || !group->meth->field_mul(group, t0, t2, t5, ctx)
+ || !group->meth->field_mul(group, t0, t7, t0, ctx)
+ /* r->X coord output */
+ || !BN_mod_sub_quick(r->X, t6, t0, group->field)
+ || !BN_mod_add_quick(t6, t3, t4, group->field)
+ || !group->meth->field_sqr(group, t3, t2, ctx)
+ || !group->meth->field_mul(group, t7, t3, t7, ctx)
+ || !group->meth->field_mul(group, t5, t5, t6, ctx)
+ || !BN_mod_lshift1_quick(t5, t5, group->field)
+ /* r->Z coord output */
+ || !BN_mod_add_quick(r->Z, t7, t5, group->field))
+ goto err;
+
+ ret = 1;