From 281720c2a38653035cf6cd6f424ded2913d4c931 Mon Sep 17 00:00:00 2001 From: Bodo Moeller Date: Fri, 1 Aug 2014 17:18:14 +0200 Subject: [PATCH] Simplify and fix ec_GFp_simple_points_make_affine (which didn't always handle value 0 correctly). Reviewed-by: emilia@openssl.org Conflicts: CHANGES --- CHANGES | 5 +- crypto/ec/ecp_smpl.c | 174 +++++++++++++++++++------------------------ crypto/ec/ectest.c | 63 ++++++++++++---- 3 files changed, 129 insertions(+), 113 deletions(-) diff --git a/CHANGES b/CHANGES index 53b6c6f01f..0740ac9b43 100644 --- a/CHANGES +++ b/CHANGES @@ -4,7 +4,10 @@ Changes between 1.0.1h and 1.0.1i [xx XXX xxxx] - *) + *) Fix ec_GFp_simple_points_make_affine (thus, EC_POINTs_mul etc.) + for corner cases. (Certain input points at infinity could lead to + bogus results, with non-infinity inputs mapped to infinity too.) + [Bodo Moeller] Changes between 1.0.1g and 1.0.1h [5 Jun 2014] diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index 7cbb321f9a..ef5285477a 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -1181,9 +1181,8 @@ int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ct 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; @@ -1198,124 +1197,104 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT } 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; @@ -1329,20 +1308,19 @@ int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, EC_POINT } 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) + BN_clear_free(prod_Z[i]); } - OPENSSL_free(heap); + OPENSSL_free(prod_Z); } return ret; } diff --git a/crypto/ec/ectest.c b/crypto/ec/ectest.c index 102eaa9b23..82c8c8bfb1 100644 --- a/crypto/ec/ectest.c +++ b/crypto/ec/ectest.c @@ -199,6 +199,7 @@ static void group_order_tests(EC_GROUP *group) EC_POINT *P = EC_POINT_new(group); EC_POINT *Q = EC_POINT_new(group); BN_CTX *ctx = BN_CTX_new(); + int i; n1 = BN_new(); n2 = BN_new(); order = BN_new(); fprintf(stdout, "verify group order ..."); @@ -212,21 +213,55 @@ static void group_order_tests(EC_GROUP *group) if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; if (!EC_POINT_is_at_infinity(group, Q)) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "long/negative scalar tests ... "); - if (!BN_one(n1)) ABORT; - /* n1 = 1 - order */ - if (!BN_sub(n1, n1, order)) ABORT; - if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; - if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; - /* n2 = 1 + order */ - if (!BN_add(n2, order, BN_value_one())) ABORT; - if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; - if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; - /* n2 = (1 - order) * (1 + order) */ - if (!BN_mul(n2, n1, n2, ctx)) ABORT; - if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; - if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + fprintf(stdout, "long/negative scalar tests "); + for (i = 1; i <= 2; i++) + { + const BIGNUM *scalars[6]; + const EC_POINT *points[6]; + + fprintf(stdout, i == 1 ? + "allowing precomputation ... " : + "without precomputation ... "); + if (!BN_set_word(n1, i)) ABORT; + /* If i == 1, P will be the predefined generator for which + * EC_GROUP_precompute_mult has set up precomputation. */ + if (!EC_POINT_mul(group, P, n1, NULL, NULL, ctx)) ABORT; + + if (!BN_one(n1)) ABORT; + /* n1 = 1 - order */ + if (!BN_sub(n1, n1, order)) ABORT; + if (!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + + /* n2 = 1 + order */ + if (!BN_add(n2, order, BN_value_one())) ABORT; + if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + + /* n2 = (1 - order) * (1 + order) = 1 - order^2 */ + if (!BN_mul(n2, n1, n2, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + + /* n2 = order^2 - 1 */ + BN_set_negative(n2, 0); + if (!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + /* Add P to verify the result. */ + if (!EC_POINT_add(group, Q, Q, P, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + + /* Exercise EC_POINTs_mul, including corner cases. */ + scalars[0] = n1; points[0] = Q; /* => infinity */ + scalars[1] = n2; points[1] = P; /* => -P */ + scalars[2] = n1; points[2] = Q; /* => infinity */ + scalars[3] = n2; points[3] = Q; /* => infinity */ + scalars[4] = n1; points[4] = P; /* => P */ + scalars[5] = n2; points[5] = Q; /* => infinity */ + if (!EC_POINTs_mul(group, Q, NULL, 5, points, scalars, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + } fprintf(stdout, "ok\n"); + EC_POINT_free(P); EC_POINT_free(Q); BN_free(n1); -- 2.25.1