Add blinding to an ECDSA signature

Keegan Ryan (NCC Group) has demonstrated a side channel attack on an
ECDSA signature operation. During signing the signer calculates:

s:= k^-1 * (m + r * priv_key) mod order

The addition operation above provides a sufficient signal for a
flush+reload attack to derive the private key given sufficient signature
operations.

As a mitigation (based on a suggestion from Keegan) we add blinding to
the operation so that:

s := k^-1 * blind^-1 (blind * m + blind * r * priv_key) mod order

Since this attack is a localhost side channel only no CVE is assigned.

Reviewed-by: Rich Salz <[email protected]>

CHANGES

@@ -8,6 +8,10 @@
  release branch.
 
  Changes between 1.1.0h and 1.1.1 [xx XXX xxxx]
+  *) Add blinding to an ECDSA signature to protect against side channel attacks
+     discovered by Keegan Ryan (NCC Group).
+     [Matt Caswell]
+
   *) Enforce checking in the pkeyutl command line app to ensure that the input
      length does not exceed the maximum supported digest length when performing
      a sign, verify or verifyrecover operation.

crypto/ec/ecdsa_ossl.c

@@ -196,7 +196,8 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
                                EC_KEY *eckey)
 {
     int ok = 0, i;
-    BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL;
+    BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL, *blind = NULL;
+    BIGNUM *blindm = NULL;
     const BIGNUM *order, *ckinv;
     BN_CTX *ctx = NULL;
     const EC_GROUP *group;
@@ -229,8 +230,18 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
     }
     s = ret->s;
 
-    if ((ctx = BN_CTX_new()) == NULL ||
-        (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) {
+    ctx = BN_CTX_secure_new();
+    if (ctx == NULL) {
+        ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
+        goto err;
+    }
+
+    BN_CTX_start(ctx);
+    tmp = BN_CTX_get(ctx);
+    m = BN_CTX_get(ctx);
+    blind = BN_CTX_get(ctx);
+    blindm = BN_CTX_get(ctx);
+    if (blindm == NULL) {
         ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE);
         goto err;
     }
@@ -270,18 +281,64 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
             }
         }
 
-        if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) {
+        /*
+         * The normal signature calculation is:
+         *
+         *   s := k^-1 * (m + r * priv_key) mod order
+         *
+         * We will blind this to protect against side channel attacks
+         *
+         *   s := k^-1 * blind^-1 * (blind * m + blind * r * priv_key) mod order
+         */
+
+        /* Generate a blinding value */
+        do {
+            if (!BN_priv_rand(blind, BN_num_bits(order) - 1,
+                              BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY))
+                goto err;
+        } while (BN_is_zero(blind));
+        BN_set_flags(blind, BN_FLG_CONSTTIME);
+        BN_set_flags(blindm, BN_FLG_CONSTTIME);
+        BN_set_flags(tmp, BN_FLG_CONSTTIME);
+
+        /* tmp := blind * priv_key * r mod order */
+        if (!BN_mod_mul(tmp, blind, priv_key, order, ctx)) {
             ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
             goto err;
         }
-        if (!BN_mod_add_quick(s, tmp, m, order)) {
+        if (!BN_mod_mul(tmp, tmp, ret->r, order, ctx)) {
             ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
             goto err;
         }
+
+        /* blindm := blind * m mod order */
+        if (!BN_mod_mul(blindm, blind, m, order, ctx)) {
+            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
+            goto err;
+        }
+
+        /* s : = (blind * priv_key * r) + (blind * m) mod order */
+        if (!BN_mod_add_quick(s, tmp, blindm, order)) {
+            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
+            goto err;
+        }
+
+        /* s:= s * blind^-1 mod order */
+        if (BN_mod_inverse(blind, blind, order, ctx) == NULL) {
+            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
+            goto err;
+        }
+        if (!BN_mod_mul(s, s, blind, order, ctx)) {
+            ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
+            goto err;
+        }
+
+        /* s := s * k^-1 mod order */
         if (!BN_mod_mul(s, s, ckinv, order, ctx)) {
             ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB);
             goto err;
         }
+
         if (BN_is_zero(s)) {
             /*
              * if kinv and r have been supplied by the caller, don't
@@ -303,9 +360,8 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
         ECDSA_SIG_free(ret);
         ret = NULL;
     }
+    BN_CTX_end(ctx);
     BN_CTX_free(ctx);
-    BN_clear_free(m);
-    BN_clear_free(tmp);
     BN_clear_free(kinv);
     return ret;
 }