Simplify and fix ec_GFp_simple_points_make_affine
authorBodo Moeller <bodo@openssl.org>
Fri, 1 Aug 2014 15:18:14 +0000 (17:18 +0200)
committerBodo Moeller <bodo@openssl.org>
Fri, 1 Aug 2014 15:18:14 +0000 (17:18 +0200)
(which didn't always handle value 0 correctly).

Reviewed-by: emilia@openssl.org
CHANGES
crypto/ec/ecp_smpl.c
crypto/ec/ectest.c

diff --git a/CHANGES b/CHANGES
index 10d3eb2..9f444d3 100644 (file)
--- a/CHANGES
+++ b/CHANGES
 
  Changes between 1.0.1e and 1.0.2 [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]
+
   *) Initial support for PowerISA 2.0.7, first implemented in POWER8.
      This covers AES, SHA256/512 and GHASH. "Initial" means that most
      common cases are optimized and there still is room for further
index 16371e3..f2cd6f7 100644 (file)
@@ -1175,9 +1175,8 @@ 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;
 
@@ -1192,124 +1191,104 @@ 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;
@@ -1323,20 +1302,19 @@ 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;
        }
index 102eaa9..82c8c8b 100644 (file)
@@ -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);