Simplify and fix ec_GFp_simple_points_make_affine
(which didn't always handle value 0 correctly). Reviewed-by: emilia@openssl.org
This commit is contained in:
Bodo Moeller
parent
e0fc7961c4
commit
0fe73d6c36
3 changed files with 138 additions and 120 deletions
5
CHANGES
5
CHANGES
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@ -310,6 +310,11 @@
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Changes between 1.0.1e and 1.0.2 [xx XXX xxxx]
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*) Fix ec_GFp_simple_points_make_affine (thus, EC_POINTs_mul etc.)
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for corner cases. (Certain input points at infinity could lead to
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bogus results, with non-infinity inputs mapped to infinity too.)
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[Bodo Moeller]
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*) Initial support for PowerISA 2.0.7, first implemented in POWER8.
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This covers AES, SHA256/512 and GHASH. "Initial" means that most
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common cases are optimized and there still is room for further
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@ -1175,9 +1175,8 @@ int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct
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int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx)
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{
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BN_CTX *new_ctx = NULL;
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BIGNUM *tmp0, *tmp1;
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size_t pow2 = 0;
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BIGNUM **heap = NULL;
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BIGNUM *tmp, *tmp_Z;
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BIGNUM **prod_Z = NULL;
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size_t i;
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int ret = 0;
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@ -1192,124 +1191,104 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT
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}
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BN_CTX_start(ctx);
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tmp0 = BN_CTX_get(ctx);
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tmp1 = BN_CTX_get(ctx);
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if (tmp0 == NULL || tmp1 == NULL) goto err;
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tmp = BN_CTX_get(ctx);
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tmp_Z = BN_CTX_get(ctx);
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if (tmp == NULL || tmp_Z == NULL) goto err;
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/* Before converting the individual points, compute inverses of all Z values.
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* Modular inversion is rather slow, but luckily we can do with a single
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* explicit inversion, plus about 3 multiplications per input value.
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*/
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pow2 = 1;
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while (num > pow2)
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pow2 <<= 1;
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/* Now pow2 is the smallest power of 2 satifsying pow2 >= num.
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* We need twice that. */
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pow2 <<= 1;
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heap = OPENSSL_malloc(pow2 * sizeof heap[0]);
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if (heap == NULL) goto err;
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/* The array is used as a binary tree, exactly as in heapsort:
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*
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* heap[1]
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* heap[2] heap[3]
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* heap[4] heap[5] heap[6] heap[7]
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* heap[8]heap[9] heap[10]heap[11] heap[12]heap[13] heap[14] heap[15]
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*
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* We put the Z's in the last line;
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* then we set each other node to the product of its two child-nodes (where
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* empty or 0 entries are treated as ones);
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* then we invert heap[1];
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* then we invert each other node by replacing it by the product of its
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* parent (after inversion) and its sibling (before inversion).
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*/
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heap[0] = NULL;
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for (i = pow2/2 - 1; i > 0; i--)
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heap[i] = NULL;
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prod_Z = OPENSSL_malloc(num * sizeof prod_Z[0]);
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if (prod_Z == NULL) goto err;
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for (i = 0; i < num; i++)
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heap[pow2/2 + i] = &points[i]->Z;
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for (i = pow2/2 + num; i < pow2; i++)
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heap[i] = NULL;
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/* set each node to the product of its children */
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for (i = pow2/2 - 1; i > 0; i--)
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{
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heap[i] = BN_new();
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if (heap[i] == NULL) goto err;
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if (heap[2*i] != NULL)
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{
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if ((heap[2*i + 1] == NULL) || BN_is_zero(heap[2*i + 1]))
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{
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if (!BN_copy(heap[i], heap[2*i])) goto err;
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}
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else
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{
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if (BN_is_zero(heap[2*i]))
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{
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if (!BN_copy(heap[i], heap[2*i + 1])) goto err;
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}
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else
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{
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if (!group->meth->field_mul(group, heap[i],
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heap[2*i], heap[2*i + 1], ctx)) goto err;
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}
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}
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}
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prod_Z[i] = BN_new();
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if (prod_Z[i] == NULL) goto err;
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}
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/* invert heap[1] */
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if (!BN_is_zero(heap[1]))
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{
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if (!BN_mod_inverse(heap[1], heap[1], &group->field, ctx))
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{
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ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
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goto err;
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}
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}
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if (group->meth->field_encode != 0)
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{
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/* in the Montgomery case, we just turned R*H (representing H)
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* into 1/(R*H), but we need R*(1/H) (representing 1/H);
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* i.e. we have need to multiply by the Montgomery factor twice */
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if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
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if (!group->meth->field_encode(group, heap[1], heap[1], ctx)) goto err;
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}
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/* Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z,
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* skipping any zero-valued inputs (pretend that they're 1). */
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/* set other heap[i]'s to their inverses */
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for (i = 2; i < pow2/2 + num; i += 2)
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if (!BN_is_zero(&points[0]->Z))
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{
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/* i is even */
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if ((heap[i + 1] != NULL) && !BN_is_zero(heap[i + 1]))
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if (!BN_copy(prod_Z[0], &points[0]->Z)) goto err;
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}
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else
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{
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if (group->meth->field_set_to_one != 0)
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{
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if (!group->meth->field_mul(group, tmp0, heap[i/2], heap[i + 1], ctx)) goto err;
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if (!group->meth->field_mul(group, tmp1, heap[i/2], heap[i], ctx)) goto err;
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if (!BN_copy(heap[i], tmp0)) goto err;
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if (!BN_copy(heap[i + 1], tmp1)) goto err;
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if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) goto err;
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}
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else
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{
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if (!BN_copy(heap[i], heap[i/2])) goto err;
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if (!BN_one(prod_Z[0])) goto err;
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}
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}
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/* we have replaced all non-zero Z's by their inverses, now fix up all the points */
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for (i = 1; i < num; i++)
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{
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if (!BN_is_zero(&points[i]->Z))
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{
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if (!group->meth->field_mul(group, prod_Z[i], prod_Z[i - 1], &points[i]->Z, ctx)) goto err;
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}
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else
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{
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if (!BN_copy(prod_Z[i], prod_Z[i - 1])) goto err;
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}
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}
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/* Now use a single explicit inversion to replace every
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* non-zero points[i]->Z by its inverse. */
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if (!BN_mod_inverse(tmp, prod_Z[num - 1], &group->field, ctx))
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{
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ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB);
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goto err;
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}
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if (group->meth->field_encode != 0)
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{
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/* In the Montgomery case, we just turned R*H (representing H)
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* into 1/(R*H), but we need R*(1/H) (representing 1/H);
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* i.e. we need to multiply by the Montgomery factor twice. */
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if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
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if (!group->meth->field_encode(group, tmp, tmp, ctx)) goto err;
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}
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for (i = num - 1; i > 0; --i)
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{
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/* Loop invariant: tmp is the product of the inverses of
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* points[0]->Z .. points[i]->Z (zero-valued inputs skipped). */
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if (!BN_is_zero(&points[i]->Z))
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{
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/* Set tmp_Z to the inverse of points[i]->Z (as product
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* of Z inverses 0 .. i, Z values 0 .. i - 1). */
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if (!group->meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) goto err;
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/* Update tmp to satisfy the loop invariant for i - 1. */
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if (!group->meth->field_mul(group, tmp, tmp, &points[i]->Z, ctx)) goto err;
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/* Replace points[i]->Z by its inverse. */
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if (!BN_copy(&points[i]->Z, tmp_Z)) goto err;
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}
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}
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if (!BN_is_zero(&points[0]->Z))
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{
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/* Replace points[0]->Z by its inverse. */
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if (!BN_copy(&points[0]->Z, tmp)) goto err;
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}
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/* Finally, fix up the X and Y coordinates for all points. */
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for (i = 0; i < num; i++)
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{
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EC_POINT *p = points[i];
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if (!BN_is_zero(&p->Z))
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{
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/* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */
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if (!group->meth->field_sqr(group, tmp1, &p->Z, ctx)) goto err;
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if (!group->meth->field_mul(group, &p->X, &p->X, tmp1, ctx)) goto err;
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if (!group->meth->field_sqr(group, tmp, &p->Z, ctx)) goto err;
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if (!group->meth->field_mul(group, &p->X, &p->X, tmp, ctx)) goto err;
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if (!group->meth->field_mul(group, tmp, tmp, &p->Z, ctx)) goto err;
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if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp, ctx)) goto err;
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if (!group->meth->field_mul(group, tmp1, tmp1, &p->Z, ctx)) goto err;
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if (!group->meth->field_mul(group, &p->Y, &p->Y, tmp1, ctx)) goto err;
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if (group->meth->field_set_to_one != 0)
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{
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if (!group->meth->field_set_to_one(group, &p->Z, ctx)) goto err;
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@ -1323,20 +1302,19 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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if (new_ctx != NULL)
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BN_CTX_free(new_ctx);
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if (heap != NULL)
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if (prod_Z != NULL)
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{
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/* heap[pow2/2] .. heap[pow2-1] have not been allocated locally! */
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for (i = pow2/2 - 1; i > 0; i--)
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for (i = 0; i < num; i++)
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{
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if (heap[i] != NULL)
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BN_clear_free(heap[i]);
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if (prod_Z[i] != NULL)
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BN_clear_free(prod_Z[i]);
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}
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OPENSSL_free(heap);
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OPENSSL_free(prod_Z);
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}
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return ret;
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}
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@ -199,6 +199,7 @@ static void group_order_tests(EC_GROUP *group)
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EC_POINT *P = EC_POINT_new(group);
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EC_POINT *Q = EC_POINT_new(group);
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BN_CTX *ctx = BN_CTX_new();
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int i;
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n1 = BN_new(); n2 = BN_new(); order = BN_new();
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fprintf(stdout, "verify group order ...");
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@ -212,21 +213,55 @@ static void group_order_tests(EC_GROUP *group)
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if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
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if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
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fprintf(stdout, " ok\n");
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fprintf(stdout, "long/negative scalar tests ... ");
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if (!BN_one(n1)) ABORT;
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/* n1 = 1 - order */
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if (!BN_sub(n1, n1, order)) ABORT;
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if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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/* n2 = 1 + order */
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if (!BN_add(n2, order, BN_value_one())) ABORT;
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if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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/* n2 = (1 - order) * (1 + order) */
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if (!BN_mul(n2, n1, n2, ctx)) ABORT;
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if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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fprintf(stdout, "long/negative scalar tests ");
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for (i = 1; i <= 2; i++)
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{
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const BIGNUM *scalars[6];
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const EC_POINT *points[6];
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fprintf(stdout, i == 1 ?
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"allowing precomputation ... " :
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"without precomputation ... ");
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if (!BN_set_word(n1, i)) ABORT;
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/* If i == 1, P will be the predefined generator for which
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* EC_GROUP_precompute_mult has set up precomputation. */
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if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) ABORT;
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if (!BN_one(n1)) ABORT;
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/* n1 = 1 - order */
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if (!BN_sub(n1, n1, order)) ABORT;
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if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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/* n2 = 1 + order */
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if (!BN_add(n2, order, BN_value_one())) ABORT;
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if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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/* n2 = (1 - order) * (1 + order) = 1 - order^2 */
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if (!BN_mul(n2, n1, n2, ctx)) ABORT;
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if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
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if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
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/* n2 = order^2 - 1 */
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BN_set_negative(n2, 0);
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if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
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/* Add P to verify the result. */
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if (!EC_POINT_add(group, Q, Q, P, ctx)) ABORT;
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if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
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/* Exercise EC_POINTs_mul, including corner cases. */
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scalars[0] = n1; points[0] = Q; /* => infinity */
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scalars[1] = n2; points[1] = P; /* => -P */
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scalars[2] = n1; points[2] = Q; /* => infinity */
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scalars[3] = n2; points[3] = Q; /* => infinity */
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scalars[4] = n1; points[4] = P; /* => P */
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scalars[5] = n2; points[5] = Q; /* => infinity */
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if (!EC_POINTs_mul(group, Q, NULL, 5, points, scalars, ctx)) ABORT;
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if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
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}
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fprintf(stdout, "ok\n");
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EC_POINT_free(P);
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EC_POINT_free(Q);
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BN_free(n1);
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