[test] ECC: check the bounds for auto computing cofactor

Reviewed-by: NMatt Caswell <matt@openssl.org>
Reviewed-by: NNicola Tuveri <nic.tuv@gmail.com>
(Merged from https://github.com/openssl/openssl/pull/9821)

test/ectest.c

@@ -2121,6 +2121,96 @@ err:
     return r;
 }
 
+/*-
+ * random 256-bit explicit parameters curve, cofactor absent
+ * order:    0x0c38d96a9f892b88772ec2e39614a82f4f (132 bit)
+ * cofactor:   0x12bc94785251297abfafddf1565100da (125 bit)
+ */
+static const unsigned char params_cf_pass[] = {
+    0x30, 0x81, 0xcd, 0x02, 0x01, 0x01, 0x30, 0x2c, 0x06, 0x07, 0x2a, 0x86,
+    0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x21, 0x00, 0xe5, 0x00, 0x1f, 0xc5,
+    0xca, 0x71, 0x9d, 0x8e, 0xf7, 0x07, 0x4b, 0x48, 0x37, 0xf9, 0x33, 0x2d,
+    0x71, 0xbf, 0x79, 0xe7, 0xdc, 0x91, 0xc2, 0xff, 0xb6, 0x7b, 0xc3, 0x93,
+    0x44, 0x88, 0xe6, 0x91, 0x30, 0x44, 0x04, 0x20, 0xe5, 0x00, 0x1f, 0xc5,
+    0xca, 0x71, 0x9d, 0x8e, 0xf7, 0x07, 0x4b, 0x48, 0x37, 0xf9, 0x33, 0x2d,
+    0x71, 0xbf, 0x79, 0xe7, 0xdc, 0x91, 0xc2, 0xff, 0xb6, 0x7b, 0xc3, 0x93,
+    0x44, 0x88, 0xe6, 0x8e, 0x04, 0x20, 0x18, 0x8c, 0x59, 0x57, 0xc4, 0xbc,
+    0x85, 0x57, 0xc3, 0x66, 0x9f, 0x89, 0xd5, 0x92, 0x0d, 0x7e, 0x42, 0x27,
+    0x07, 0x64, 0xaa, 0x26, 0xed, 0x89, 0xc4, 0x09, 0x05, 0x4d, 0xc7, 0x23,
+    0x47, 0xda, 0x04, 0x41, 0x04, 0x1b, 0x6b, 0x41, 0x0b, 0xf9, 0xfb, 0x77,
+    0xfd, 0x50, 0xb7, 0x3e, 0x23, 0xa3, 0xec, 0x9a, 0x3b, 0x09, 0x31, 0x6b,
+    0xfa, 0xf6, 0xce, 0x1f, 0xff, 0xeb, 0x57, 0x93, 0x24, 0x70, 0xf3, 0xf4,
+    0xba, 0x7e, 0xfa, 0x86, 0x6e, 0x19, 0x89, 0xe3, 0x55, 0x6d, 0x5a, 0xe9,
+    0xc0, 0x3d, 0xbc, 0xfb, 0xaf, 0xad, 0xd4, 0x7e, 0xa6, 0xe5, 0xfa, 0x1a,
+    0x58, 0x07, 0x9e, 0x8f, 0x0d, 0x3b, 0xf7, 0x38, 0xca, 0x02, 0x11, 0x0c,
+    0x38, 0xd9, 0x6a, 0x9f, 0x89, 0x2b, 0x88, 0x77, 0x2e, 0xc2, 0xe3, 0x96,
+    0x14, 0xa8, 0x2f, 0x4f
+};
+
+/*-
+ * random 256-bit explicit parameters curve, cofactor absent
+ * order:    0x045a75c0c17228ebd9b169a10e34a22101 (131 bit)
+ * cofactor:   0x2e134b4ede82649f67a2e559d361e5fe (126 bit)
+ */
+static const unsigned char params_cf_fail[] = {
+    0x30, 0x81, 0xcd, 0x02, 0x01, 0x01, 0x30, 0x2c, 0x06, 0x07, 0x2a, 0x86,
+    0x48, 0xce, 0x3d, 0x01, 0x01, 0x02, 0x21, 0x00, 0xc8, 0x95, 0x27, 0x37,
+    0xe8, 0xe1, 0xfd, 0xcc, 0xf9, 0x6e, 0x0c, 0xa6, 0x21, 0xc1, 0x7d, 0x6b,
+    0x9d, 0x44, 0x42, 0xea, 0x73, 0x4e, 0x04, 0xb6, 0xac, 0x62, 0x50, 0xd0,
+    0x33, 0xc2, 0xea, 0x13, 0x30, 0x44, 0x04, 0x20, 0xc8, 0x95, 0x27, 0x37,
+    0xe8, 0xe1, 0xfd, 0xcc, 0xf9, 0x6e, 0x0c, 0xa6, 0x21, 0xc1, 0x7d, 0x6b,
+    0x9d, 0x44, 0x42, 0xea, 0x73, 0x4e, 0x04, 0xb6, 0xac, 0x62, 0x50, 0xd0,
+    0x33, 0xc2, 0xea, 0x10, 0x04, 0x20, 0xbf, 0xa6, 0xa8, 0x05, 0x1d, 0x09,
+    0xac, 0x70, 0x39, 0xbb, 0x4d, 0xb2, 0x90, 0x8a, 0x15, 0x41, 0x14, 0x1d,
+    0x11, 0x86, 0x9f, 0x13, 0xa2, 0x63, 0x1a, 0xda, 0x95, 0x22, 0x4d, 0x02,
+    0x15, 0x0a, 0x04, 0x41, 0x04, 0xaf, 0x16, 0x71, 0xf9, 0xc4, 0xc8, 0x59,
+    0x1d, 0xa3, 0x6f, 0xe7, 0xc3, 0x57, 0xa1, 0xfa, 0x9f, 0x49, 0x7c, 0x11,
+    0x27, 0x05, 0xa0, 0x7f, 0xff, 0xf9, 0xe0, 0xe7, 0x92, 0xdd, 0x9c, 0x24,
+    0x8e, 0xc7, 0xb9, 0x52, 0x71, 0x3f, 0xbc, 0x7f, 0x6a, 0x9f, 0x35, 0x70,
+    0xe1, 0x27, 0xd5, 0x35, 0x8a, 0x13, 0xfa, 0xa8, 0x33, 0x3e, 0xd4, 0x73,
+    0x1c, 0x14, 0x58, 0x9e, 0xc7, 0x0a, 0x87, 0x65, 0x8d, 0x02, 0x11, 0x04,
+    0x5a, 0x75, 0xc0, 0xc1, 0x72, 0x28, 0xeb, 0xd9, 0xb1, 0x69, 0xa1, 0x0e,
+    0x34, 0xa2, 0x21, 0x01
+};
+
+/*-
+ * Test two random 256-bit explicit parameters curves with absent cofactor.
+ * The two curves are chosen to roughly straddle the bounds at which the lib
+ * can compute the cofactor automatically, roughly 4*sqrt(p). So test that:
+ *
+ * - params_cf_pass: order is sufficiently close to p to compute cofactor
+ * - params_cf_fail: order is too far away from p to compute cofactor
+ *
+ * For standards-compliant curves, cofactor is chosen as small as possible.
+ * So you can see neither of these curves are fit for cryptographic use.
+ *
+ * Some standards even mandate an upper bound on the cofactor, e.g. SECG1 v2:
+ * h <= 2**(t/8) where t is the security level of the curve, for which the lib
+ * will always succeed in computing the cofactor. Neither of these curves
+ * conform to that -- this is just robustness testing.
+ */
+static int cofactor_range_test(void)
+{
+    EC_GROUP *group = NULL;
+    BIGNUM *cf = NULL;
+    int ret = 0;
+    const unsigned char *b1 = (const unsigned char *)params_cf_fail;
+    const unsigned char *b2 = (const unsigned char *)params_cf_pass;
+
+    if (!TEST_ptr(group = d2i_ECPKParameters(NULL, &b1, sizeof(params_cf_fail)))
+        || !TEST_BN_eq_zero(EC_GROUP_get0_cofactor(group))
+        || !TEST_ptr(group = d2i_ECPKParameters(&group, &b2,
+                                                sizeof(params_cf_pass)))
+        || !TEST_int_gt(BN_hex2bn(&cf, "12bc94785251297abfafddf1565100da"), 0)
+        || !TEST_BN_eq(cf, EC_GROUP_get0_cofactor(group)))
+        goto err;
+    ret = 1;
+ err:
+    BN_free(cf);
+    EC_GROUP_free(group);
+    return ret;
+}
+
 /*-
  * For named curves, test that:
  * - the lib correctly computes the cofactor if passed a NULL or zero cofactor
@@ -2269,6 +2359,7 @@ int setup_tests(void)
         return 0;
 
     ADD_TEST(parameter_test);
+    ADD_TEST(cofactor_range_test);
     ADD_ALL_TESTS(cardinality_test, crv_len);
     ADD_TEST(prime_field_tests);
 # ifndef OPENSSL_NO_EC2M