[crypto/ec] for ECC parameters with NULL or zero cofactor, compute it

The cofactor argument to EC_GROUP_set_generator is optional, and SCA
mitigations for ECC currently use it. So the library currently falls
back to very old SCA-vulnerable code if the cofactor is not present.

This PR allows EC_GROUP_set_generator to compute the cofactor for all
curves of cryptographic interest. Steering scalar multiplication to more
SCA-robust code.

This issue affects persisted private keys in explicit parameter form,
where the (optional) cofactor field is zero or absent.

It also affects curves not built-in to the library, but constructed
programatically with explicit parameters, then calling
EC_GROUP_set_generator with a nonsensical value (NULL, zero).

The very old scalar multiplication code is known to be vulnerable to
local uarch attacks, outside of the OpenSSL threat model. New results
suggest the code path is also vulnerable to traditional wall clock
timing attacks.

CVE-2019-1547

Reviewed-by: Nicola Tuveri <nic.tuv@gmail.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #9799)

Author: bbbrumley

CHANGES

@@ -9,6 +9,13 @@
 
  Changes between 1.0.2s and 1.0.2t [xx XXX xxxx]
 
+  *) Compute ECC cofactors if not provided during EC_GROUP construction. Before
+     this change, EC_GROUP_set_generator would accept order and/or cofactor as
+     NULL. After this change, only the cofactor parameter can be NULL. It also
+     does some minimal sanity checks on the passed order.
+     (CVE-2019-1547)
+     [Billy Bob Brumley]
+
   *) Document issue with installation paths in diverse Windows builds
 
      '/usr/local/ssl' is an unsafe prefix for location to install OpenSSL

crypto/ec/ec.h

@@ -1073,6 +1073,7 @@ int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
  * The following lines are auto generated by the script mkerr.pl. Any changes
  * made after this point may be overwritten when the script is next run.
  */
+
 void ERR_load_EC_strings(void);
 
 /* Error codes for the EC functions. */
@@ -1270,13 +1271,14 @@ void ERR_load_EC_strings(void);
 # define EC_R_SLOT_FULL                                   108
 # define EC_R_UNDEFINED_GENERATOR                         113
 # define EC_R_UNDEFINED_ORDER                             128
+# define EC_R_UNKNOWN_COFACTOR                            152
 # define EC_R_UNKNOWN_GROUP                               129
 # define EC_R_UNKNOWN_ORDER                               114
 # define EC_R_UNSUPPORTED_FIELD                           131
 # define EC_R_WRONG_CURVE_PARAMETERS                      145
 # define EC_R_WRONG_ORDER                                 130
 
-#ifdef  __cplusplus
+# ifdef  __cplusplus
 }
-#endif
+# endif
 #endif

crypto/ec/ec_err.c

@@ -1,6 +1,6 @@
 /* crypto/ec/ec_err.c */
 /* ====================================================================
- * Copyright (c) 1999-2015 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1999-2019 The OpenSSL Project.  All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
@@ -310,6 +310,7 @@ static ERR_STRING_DATA EC_str_reasons[] = {
     {ERR_REASON(EC_R_SLOT_FULL), "slot full"},
     {ERR_REASON(EC_R_UNDEFINED_GENERATOR), "undefined generator"},
     {ERR_REASON(EC_R_UNDEFINED_ORDER), "undefined order"},
+    {ERR_REASON(EC_R_UNKNOWN_COFACTOR), "unknown cofactor"},
     {ERR_REASON(EC_R_UNKNOWN_GROUP), "unknown group"},
     {ERR_REASON(EC_R_UNKNOWN_ORDER), "unknown order"},
     {ERR_REASON(EC_R_UNSUPPORTED_FIELD), "unsupported field"},

crypto/ec/ec_lib.c

@@ -294,6 +294,67 @@ int EC_METHOD_get_field_type(const EC_METHOD *meth)
     return meth->field_type;
 }
 
+/*-
+ * Try computing cofactor from the generator order (n) and field cardinality (q).
+ * This works for all curves of cryptographic interest.
+ *
+ * Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
+ * h_min = (q + 1 - 2*sqrt(q))/n
+ * h_max = (q + 1 + 2*sqrt(q))/n
+ * h_max - h_min = 4*sqrt(q)/n
+ * So if n > 4*sqrt(q) holds, there is only one possible value for h:
+ * h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
+ *
+ * Otherwise, zero cofactor and return success.
+ */
+static int ec_guess_cofactor(EC_GROUP *group) {
+    int ret = 0;
+    BN_CTX *ctx = NULL;
+    BIGNUM *q = NULL;
+
+    /*-
+     * If the cofactor is too large, we cannot guess it.
+     * The RHS of below is a strict overestimate of lg(4 * sqrt(q))
+     */
+    if (BN_num_bits(&group->order) <= (BN_num_bits(&group->field) + 1) / 2 + 3) {
+        /* default to 0 */
+        BN_zero(&group->cofactor);
+        /* return success */
+        return 1;
+    }
+
+    if ((ctx = BN_CTX_new()) == NULL)
+        return 0;
+
+    BN_CTX_start(ctx);
+    if ((q = BN_CTX_get(ctx)) == NULL)
+        goto err;
+
+    /* set q = 2**m for binary fields; q = p otherwise */
+    if (group->meth->field_type == NID_X9_62_characteristic_two_field) {
+        BN_zero(q);
+        if (!BN_set_bit(q, BN_num_bits(&group->field) - 1))
+            goto err;
+    } else {
+        if (!BN_copy(q, &group->field))
+            goto err;
+    }
+
+    /* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
+    if (!BN_rshift1(&group->cofactor, &group->order) /* n/2 */
+        || !BN_add(&group->cofactor, &group->cofactor, q) /* q + n/2 */
+        /* q + 1 + n/2 */
+        || !BN_add(&group->cofactor, &group->cofactor, BN_value_one())
+        /* (q + 1 + n/2)/n */
+        || !BN_div(&group->cofactor, NULL, &group->cofactor, &group->order, ctx))
+        goto err;
+    ret = 1;
+ err:
+    BN_CTX_end(ctx);
+    BN_CTX_free(ctx);
+    return ret;
+}
+
 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                            const BIGNUM *order, const BIGNUM *cofactor)
 {
@@ -302,6 +363,33 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
         return 0;
     }
 
+    /* require group->field >= 1 */
+    if (BN_is_zero(&group->field) || BN_is_negative(&group->field)) {
+        ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_FIELD);
+        return 0;
+    }
+
+    /*-
+     * - require order >= 1
+     * - enforce upper bound due to Hasse thm: order can be no more than one bit
+     *   longer than field cardinality
+     */
+    if (order == NULL || BN_is_zero(order) || BN_is_negative(order)
+        || BN_num_bits(order) > BN_num_bits(&group->field) + 1) {
+        ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_GROUP_ORDER);
+        return 0;
+    }
+
+    /*-
+     * Unfortunately the cofactor is an optional field in many standards.
+     * Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
+     * So accept cofactor == NULL or cofactor >= 0.
+     */
+    if (cofactor != NULL && BN_is_negative(cofactor)) {
+        ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_UNKNOWN_COFACTOR);
+        return 0;
+    }
+
     if (group->generator == NULL) {
         group->generator = EC_POINT_new(group);
         if (group->generator == NULL)
@@ -310,17 +398,17 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
     if (!EC_POINT_copy(group->generator, generator))
         return 0;
 
-    if (order != NULL) {
-        if (!BN_copy(&group->order, order))
-            return 0;
-    } else
-        BN_zero(&group->order);
+    if (!BN_copy(&group->order, order))
+        return 0;
 
-    if (cofactor != NULL) {
+    /* Either take the provided positive cofactor, or try to compute it */
+    if (cofactor != NULL && !BN_is_zero(cofactor)) {
         if (!BN_copy(&group->cofactor, cofactor))
             return 0;
-    } else
+    } else if (!ec_guess_cofactor(group)) {
         BN_zero(&group->cofactor);
+        return 0;
+    }
 
     /*-
      * Access to the `mont_data` field of an EC_GROUP struct should always be