[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 #9795)
openssl · Sep 7, 2019 · 7c1709c · 7c1709c
1 parent 207a564
commit 7c1709c
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diff --git a/CHANGES b/CHANGES
@@ -9,14 +9,20 @@
 
  Changes between 1.1.0k and 1.1.0l [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]
+
   *) Use Windows installation paths in the mingw builds
 
      Mingw isn't a POSIX environment per se, which means that Windows
      paths should be used for installation.
      (CVE-2019-1552)
      [Richard Levitte]
 
-
  Changes between 1.1.0j and 1.1.0k [28 May 2019]
 
   *) Change the default RSA, DSA and DH size to 2048 bit instead of 1024.

diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c
@@ -273,6 +273,7 @@ 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"},

diff --git a/crypto/ec/ec_lib.c b/crypto/ec/ec_lib.c
@@ -257,6 +257,67 @@ 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)
 {
@@ -265,6 +326,34 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
         return 0;
     }
 
+    /* require group->field >= 1 */
+    if (group->field == NULL || 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)
@@ -273,17 +362,17 @@ 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;
+    }
 
     /*
      * Some groups have an order with

diff --git a/include/openssl/ec.h b/include/openssl/ec.h
@@ -1568,6 +1568,7 @@ int 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                            164
 # define EC_R_UNKNOWN_GROUP                               129
 # define EC_R_UNKNOWN_ORDER                               114
 # define EC_R_UNSUPPORTED_FIELD                           131