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Simplify ec_GFp_simple_points_make_affine.

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Replace the tree-like structure by a linear approach, with fewer special
cases to handle value 0.

(Imported from upstream's d5213519c0ed87c71136084e7e843a4125ecc024.)

Change-Id: Icdd4815066bdbab0d2c0020db6a8cacc49b3d82a
Reviewed-on: https://boringssl-review.googlesource.com/1400
Reviewed-by: Adam Langley <agl@google.com>
This commit is contained in:
Adam Langley 2014-08-04 16:06:09 -07:00 committed by Adam Langley
parent 43ec06f705
commit 993fde5162
1 changed files with 106 additions and 128 deletions
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234
crypto/ec/simple.c
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@ -1195,159 +1195,135 @@ err:
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;
if (num == 0)
if (num == 0) {
return 1;
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
if (ctx == NULL) {
return 0;
}
}
BN_CTX_start(ctx);
tmp0 = BN_CTX_get(ctx);
tmp1 = BN_CTX_get(ctx);
if (tmp0 == NULL || tmp1 == NULL)
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.
*/
pow2 = 1;
while (num > pow2)
pow2 <<= 1;
/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
* We need twice that. */
pow2 <<= 1;
heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
if (heap == NULL)
prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0]));
if (prod_Z == NULL) {
goto err;
/* TODO(bmoeller): There is no reason to use this tree structure.
* We should instead proceed sequentially, exactly as in
* ec_GFp_nistp_points_make_affine_internal, which makes everything
* much simpler. */
/* 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--) {
heap[i] = BN_new();
if (heap[i] == NULL)
goto err;
if (heap[2 * i] != NULL) {
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;
}
}
}
}
/* invert heap[1] */
if (!BN_is_zero(heap[1])) {
if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx)) {
OPENSSL_PUT_ERROR(EC, 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 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)) {
memset(prod_Z, 0, num * sizeof(prod_Z[0]));
for (i = 0; i < num; i++) {
prod_Z[i] = BN_new();
if (prod_Z[i] == NULL) {
goto err;
}
}
/* set other heap[i]'s to their inverses */
for (i = 2; i < pow2 / 2 + num; i += 2) {
/* i is even */
if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1])) {
if (!BN_is_zero(heap[i])) {
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 + 1], heap[i / 2]))
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_copy(heap[i], heap[i / 2]))
if (!BN_one(prod_Z[0])) {
goto err;
}
}
}
/* we have replaced all non-zero Z's by their inverses, now fix up all the
* points */
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 (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx)) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_points_make_affine, ERR_R_BN_LIB);
goto err;
}
if (group->meth->field_encode != NULL) {
/* 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) ||
!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)) {
continue;
}
/* 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) ||
/* Update tmp to satisfy the loop invariant for i - 1. */
!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx) ||
/* Replace points[i]->Z by its inverse. */
!BN_copy(&points[i]->Z, tmp_Z)) {
goto err;
}
}
/* Replace points[0]->Z by its inverse. */
if (!BN_is_zero(&points[0]->Z) && !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) */
/* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1). */
if (!group->meth->field_sqr(group, tmp, &p->Z, ctx) ||
!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx) ||
!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx) ||
!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) {
goto err;
}
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_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))
if (group->meth->field_set_to_one != NULL) {
if (!group->meth->field_set_to_one(group, &p->Z, ctx)) {
goto err;
}
} else {
if (!BN_one(&p->Z))
if (!BN_one(&p->Z)) {
goto err;
}
}
p->Z_is_one = 1;
}
@ -1357,16 +1333,18 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num,
err:
BN_CTX_end(ctx);
if (new_ctx != NULL)
if (new_ctx != NULL) {
BN_CTX_free(new_ctx);
if (heap != NULL) {
/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
for (i = pow2 / 2 - 1; i > 0; i--) {
if (heap[i] != NULL)
BN_clear_free(heap[i]);
}
OPENSSL_free(heap);
}
if (prod_Z != NULL) {
for (i = 0; i < num; i++) {
if (prod_Z[i] != NULL) {
BN_clear_free(prod_Z[i]);
}
}
OPENSSL_free(prod_Z);
}
return ret;
}