* and contributed to the OpenSSL project.
*/
+#define OPENSSL_FIPSAPI
+
#include <openssl/err.h>
#include <openssl/symhacks.h>
const EC_METHOD *EC_GFp_simple_method(void)
{
static const EC_METHOD ret = {
+ EC_FLAGS_DEFAULT_OCT,
NID_X9_62_prime_field,
ec_GFp_simple_group_init,
ec_GFp_simple_group_finish,
ec_GFp_simple_get_Jprojective_coordinates_GFp,
ec_GFp_simple_point_set_affine_coordinates,
ec_GFp_simple_point_get_affine_coordinates,
- ec_GFp_simple_set_compressed_coordinates,
- ec_GFp_simple_point2oct,
- ec_GFp_simple_oct2point,
+ 0,0,0,
ec_GFp_simple_add,
ec_GFp_simple_dbl,
ec_GFp_simple_invert,
/* 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;
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;
return ret;
}
-
-int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x_, int y_bit, BN_CTX *ctx)
- {
- BN_CTX *new_ctx = NULL;
- BIGNUM *tmp1, *tmp2, *x, *y;
- int ret = 0;
-
- if (ctx == NULL)
- {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- y_bit = (y_bit != 0);
-
- BN_CTX_start(ctx);
- tmp1 = BN_CTX_get(ctx);
- tmp2 = BN_CTX_get(ctx);
- x = BN_CTX_get(ctx);
- y = BN_CTX_get(ctx);
- if (y == NULL) goto err;
-
- /* 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.
- */
-
- /* tmp1 := x^3 */
- if (!BN_nnmod(x, x_, &group->field,ctx)) goto err;
- if (group->meth->field_decode == 0)
- {
- /* field_{sqr,mul} work on standard representation */
- if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err;
- if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err;
- }
- else
- {
- if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err;
- if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err;
- }
-
- /* tmp1 := tmp1 + a*x */
- if (group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
- if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (group->meth->field_decode)
- {
- if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err;
- if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err;
- }
- else
- {
- /* field_mul works on standard representation */
- if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err;
- }
-
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
-
- /* tmp1 := tmp1 + b */
- if (group->meth->field_decode)
- {
- if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err;
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
- }
-
- if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
- {
- unsigned long err = ERR_peek_error();
-
- if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE)
- {
- (void)ERR_get_error();
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
- }
- else
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB);
- goto err;
- }
-
- if (y_bit != BN_is_odd(y))
- {
- if (BN_is_zero(y))
- {
- int kron;
-
- kron = BN_kronecker(x, &group->field, ctx);
- if (kron == -2) goto err;
-
- if (kron == 1)
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT);
- else
- /* BN_mod_sqrt() should have cought this error (not a square) */
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT);
- goto err;
- }
- if (!BN_usub(y, &group->field, y)) goto err;
- }
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR);
- goto err;
- }
-
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
- }
-
-
-size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
- unsigned char *buf, size_t len, BN_CTX *ctx)
- {
- size_t ret;
- BN_CTX *new_ctx = NULL;
- int used_ctx = 0;
- BIGNUM *x, *y;
- size_t field_len, i, skip;
-
- if ((form != POINT_CONVERSION_COMPRESSED)
- && (form != POINT_CONVERSION_UNCOMPRESSED)
- && (form != POINT_CONVERSION_HYBRID))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM);
- goto err;
- }
-
- if (EC_POINT_is_at_infinity(group, point))
- {
- /* encodes to a single 0 octet */
- if (buf != NULL)
- {
- if (len < 1)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
- return 0;
- }
- buf[0] = 0;
- }
- return 1;
- }
-
-
- /* ret := required output buffer length */
- field_len = BN_num_bytes(&group->field);
- ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
- /* if 'buf' is NULL, just return required length */
- if (buf != NULL)
- {
- if (len < ret)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL);
- goto err;
- }
-
- if (ctx == NULL)
- {
- ctx = new_ctx = BN_CTX_new();
- if (ctx == NULL)
- return 0;
- }
-
- BN_CTX_start(ctx);
- used_ctx = 1;
- x = BN_CTX_get(ctx);
- y = BN_CTX_get(ctx);
- if (y == NULL) goto err;
-
- if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
- if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y))
- buf[0] = form + 1;
- else
- buf[0] = form;
-
- i = 1;
-
- skip = field_len - BN_num_bytes(x);
- if (skip > field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- while (skip > 0)
- {
- buf[i++] = 0;
- skip--;
- }
- skip = BN_bn2bin(x, buf + i);
- i += skip;
- if (i != 1 + field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
-
- if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID)
- {
- skip = field_len - BN_num_bytes(y);
- if (skip > field_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- while (skip > 0)
- {
- buf[i++] = 0;
- skip--;
- }
- skip = BN_bn2bin(y, buf + i);
- i += skip;
- }
-
- if (i != ret)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
- }
-
- if (used_ctx)
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
-
- err:
- if (used_ctx)
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return 0;
- }
-
-
-int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
- const unsigned char *buf, size_t len, BN_CTX *ctx)
- {
- point_conversion_form_t form;
- int y_bit;
- BN_CTX *new_ctx = NULL;
- BIGNUM *x, *y;
- size_t field_len, enc_len;
- int ret = 0;
-
- if (len == 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL);
- return 0;
- }
- form = buf[0];
- y_bit = form & 1;
- form = form & ~1;
- if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED)
- && (form != POINT_CONVERSION_UNCOMPRESSED)
- && (form != POINT_CONVERSION_HYBRID))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
- if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- if (form == 0)
- {
- if (len != 1)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- return EC_POINT_set_to_infinity(group, point);
- }
-
- field_len = BN_num_bytes(&group->field);
- enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len;
-
- if (len != enc_len)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- return 0;
- }
-
- 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 (!BN_bin2bn(buf + 1, field_len, x)) goto err;
- if (BN_ucmp(x, &group->field) >= 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
-
- if (form == POINT_CONVERSION_COMPRESSED)
- {
- if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
- }
- else
- {
- if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
- if (BN_ucmp(y, &group->field) >= 0)
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- if (form == POINT_CONVERSION_HYBRID)
- {
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- }
-
- 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 */
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
- goto err;
- }
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- if (new_ctx != NULL)
- BN_CTX_free(new_ctx);
- return ret;
- }
-
-
int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
{
int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
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;
* 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);
{
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)
{
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]))
+ /* 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 (!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
- {
- 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 / openssl.git / blobdiff