}
-/* Most method functions in this file are designed to work with
+/*
+ * 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
/* group->field */
if (!BN_copy(&group->field, p)) goto err;
- BN_set_sign(&group->field, 0);
+ BN_set_negative(&group->field, 0);
/* group->a */
if (!BN_nnmod(tmp_a, a, p, ctx)) goto err;
if (!BN_copy(b, &group->b)) goto err;
}
- /* check the discriminant:
+ /*-
+ * 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 */
+ * 0 =< a, b < p
+ */
if (BN_is_zero(a))
{
if (BN_is_zero(b)) goto err;
ret = 1;
err:
- BN_CTX_end(ctx);
+ if (ctx != NULL)
+ BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
BIGNUM *tmp1, *tmp2, *x, *y;
int ret = 0;
+ /* clear error queue*/
+ ERR_clear_error();
+
if (ctx == NULL)
{
ctx = new_ctx = BN_CTX_new();
y = BN_CTX_get(ctx);
if (y == NULL) goto err;
- /* Recover y. We have a Weierstrass equation
+ /*-
+ * Recover y. We have a Weierstrass equation
* y^2 = x^3 + a*x + b,
* so y is one of the square roots of x^3 + a*x + b.
*/
if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
{
- unsigned long err = ERR_peek_error();
+ unsigned long err = ERR_peek_last_error();
if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
{
- (void)ERR_get_error();
+ ERR_clear_error();
ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
}
else
if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
}
- if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
+ /* test required by X9.62 */
+ if (!EC_POINT_is_on_curve(group, point, ctx))
{
ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
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 */
+ /*-
+ * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2)
+ * = 3 * X_a^2 - 3 * Z_a^4
+ */
}
else
{
int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
const BIGNUM *p;
BN_CTX *new_ctx = NULL;
- BIGNUM *rh, *tmp1, *tmp2, *Z4, *Z6;
+ BIGNUM *rh, *tmp, *Z4, *Z6;
int ret = -1;
if (EC_POINT_is_at_infinity(group, point))
BN_CTX_start(ctx);
rh = BN_CTX_get(ctx);
- tmp1 = BN_CTX_get(ctx);
- tmp2 = 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
+ /*-
+ * 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).
* To test this, we add up the right-hand side in 'rh'.
*/
- /* rh := X^3 */
+ /* rh := X^2 */
if (!field_sqr(group, rh, &point->X, ctx)) goto err;
- if (!field_mul(group, rh, rh, &point->X, ctx)) goto err;
if (!point->Z_is_one)
{
- if (!field_sqr(group, tmp1, &point->Z, ctx)) goto err;
- if (!field_sqr(group, Z4, tmp1, ctx)) goto err;
- if (!field_mul(group, Z6, Z4, tmp1, ctx)) goto err;
+ 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*X*Z^4 */
- if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
+ /* rh := (rh + a*Z^4)*X */
if (group->a_is_minus3)
{
- if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
- if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
+ 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, tmp2, tmp1, &group->a, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
+ 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, tmp1, &group->b, Z6, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp1, p)) goto err;
+ 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 (group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
- if (!BN_mod_sub_quick(rh, rh, tmp2, p)) goto err;
- }
- else
- {
- if (!field_mul(group, tmp2, &point->X, &group->a, ctx)) goto err;
- if (!BN_mod_add_quick(rh, rh, tmp2, p)) goto err;
- }
-
+ /* 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, tmp1, &point->Y, ctx)) goto err;
+ if (!field_sqr(group, tmp, &point->Y, ctx)) goto err;
- ret = (0 == BN_cmp(tmp1, rh));
+ ret = (0 == BN_ucmp(tmp, rh));
err:
BN_CTX_end(ctx);
int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
{
- /* return values:
+ /*-
+ * return values:
* -1 error
* 0 equal (in affine coordinates)
* 1 not equal
{
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)
{
Zb23 = BN_CTX_get(ctx);
if (Zb23 == NULL) goto end;
- /* We have to decide whether
+ /*-
+ * 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).
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 *tmp0, *tmp1;
- size_t pow2 = 0;
- BIGNUM **heap = NULL;
+ BIGNUM *tmp, *tmp_Z;
+ BIGNUM **prod_Z = NULL;
size_t i;
int ret = 0;
}
BN_CTX_start(ctx);
- tmp0 = BN_CTX_get(ctx);
- tmp1 = BN_CTX_get(ctx);
- if (tmp0 == NULL || tmp1 == NULL) goto err;
+ tmp = BN_CTX_get(ctx);
+ tmp_Z = BN_CTX_get(ctx);
+ if (tmp == NULL || tmp_Z == NULL) goto err;
- /* Before converting the individual points, compute inverses of all Z values.
- * Modular inversion is rather slow, but luckily we can do with a single
- * explicit inversion, plus about 3 multiplications per input value.
- */
+ 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;
+ }
- pow2 = 1;
- while (num > pow2)
- pow2 <<= 1;
- /* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
- * We need twice that. */
- pow2 <<= 1;
+ /* 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). */
- heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
- if (heap == NULL) goto err;
-
- /* The array is used as a binary tree, exactly as in heapsort:
- *
- * heap[1]
- * heap[2] heap[3]
- * heap[4] heap[5] heap[6] heap[7]
- * heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
- *
- * We put the Z's in the last line;
- * then we set each other node to the product of its two child-nodes (where
- * empty or 0 entries are treated as ones);
- * then we invert heap[1];
- * then we invert each other node by replacing it by the product of its
- * parent (after inversion) and its sibling (before inversion).
- */
- heap[0] = NULL;
- for (i = pow2/2 - 1; i > 0; i--)
- heap[i] = NULL;
- for (i = 0; i < num; i++)
- heap[pow2/2 + i] = &points[i]->Z;
- for (i = pow2/2 + num; i < pow2; i++)
- heap[i] = NULL;
-
- /* set each node to the product of its children */
- for (i = pow2/2 - 1; i > 0; i--)
+ if (!BN_is_zero(&points[0]->Z))
{
- heap[i] = BN_new();
- if (heap[i] == NULL) goto err;
-
- if (heap[2*i] != NULL)
+ if (!BN_copy(prod_Z[0], &points[0]->Z)) goto err;
+ }
+ else
+ {
+ if (group->meth->field_set_to_one != 0)
{
- if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
- {
- if (!BN_copy(heap[i], heap[2*i])) goto err;
- }
- else
- {
- if (BN_is_zero(heap[2*i]))
- {
- if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
- }
- else
- {
- if (!group->meth->field_mul(group, heap[i],
- heap[2*i], heap[2*i + 1], ctx)) goto err;
- }
- }
+ if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
+ }
+ else
+ {
+ if (!BN_one(prod_Z[0])) goto err;
}
}
- /* invert heap[1] */
- if (!BN_is_zero(heap[1]))
+ for (i = 1; i < num; i++)
{
- if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
+ if (!BN_is_zero(&points[i]->Z))
{
- ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
- goto err;
+ 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)
+ /* 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 have need to multiply by the Montgomery factor twice */
- if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
- if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
+ * 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;
}
- /* set other heap[i]'s to their inverses */
- for (i = 2; i < pow2/2 + num; i += 2)
+ for (i = num - 1; i > 0; --i)
{
- /* i is even */
- if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
- {
- if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
- if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
- if (!BN_copy(heap[i], tmp0)) goto err;
- if (!BN_copy(heap[i + 1], tmp1)) goto err;
- }
- else
+ /* 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))
{
- if (!BN_copy(heap[i], heap[i/2])) goto err;
+ /* 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;
}
}
- /* we have replaced all non-zero Z's by their inverses, now fix up all the points */
+ 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, tmp1, &p->Z, ctx)) goto err;
- if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
+ 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_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
- if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
-
if (group->meth->field_set_to_one != 0)
{
if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
}
ret = 1;
-
+
err:
BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
- if (heap != NULL)
+ if (prod_Z != NULL)
{
- /* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
- for (i = pow2/2 - 1; i > 0; i--)
+ for (i = 0; i < num; i++)
{
- if (heap[i] != NULL)
- BN_clear_free(heap[i]);
+ if (prod_Z[i] == NULL) break;
+ BN_clear_free(prod_Z[i]);
}
- OPENSSL_free(heap);
+ OPENSSL_free(prod_Z);
}
return ret;
}
projects / thirdparty / openssl.git / blobdiff