ec/ecdsa_ossl.c: revert blinding in ECDSA signature.

Originally suggested solution for "Return Of the Hidden Number Problem"
is arguably too expensive. While it has marginal impact on slower
curves, none to ~6%, optimized implementations suffer real penalties.
Most notably sign with P-256 went more than 2 times[!] slower. Instead,
just implement constant-time BN_mod_add_quick.

Reviewed-by: Rich Salz <rsalz@openssl.org>
Reviewed-by: David Benjamin <davidben@google.com>
(Merged from https://github.com/openssl/openssl/pull/6664)

crypto/bn/bn_mod.c

@@ -35,16 +35,70 @@ int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
 
 /*
  * BN_mod_add variant that may be used if both a and b are non-negative and
- * less than m
+ * less than m. The original algorithm was
+ *
+ *    if (!BN_uadd(r, a, b))
+ *       return 0;
+ *    if (BN_ucmp(r, m) >= 0)
+ *       return BN_usub(r, r, m);
+ *
+ * which is replaced with addition, subtracting modulus, and conditional
+ * move depending on whether or not subtraction borrowed.
  */
+int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+                         const BIGNUM *m)
+{
+    size_t i, ai, bi, mtop = m->top;
+    BN_ULONG storage[1024 / BN_BITS2];
+    BN_ULONG carry, temp, mask, *rp, *tp = storage;
+    const BN_ULONG *ap, *bp;
+
+    if (bn_wexpand(r, mtop) == NULL)
+        return 0;
+
+    if (mtop > sizeof(storage) / sizeof(storage[0])
+        && (tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG))) == NULL)
+	return 0;
+
+    ap = a->d != NULL ? a->d : tp;
+    bp = b->d != NULL ? b->d : tp;
+
+    for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
+        mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
+        temp = ((ap[ai] & mask) + carry) & BN_MASK2;
+        carry = (temp < carry);
+
+        mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
+        tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
+        carry += (tp[i] < temp);
+
+        i++;
+        ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
+        bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
+    }
+    rp = r->d;
+    carry -= bn_sub_words(rp, tp, m->d, mtop);
+    for (i = 0; i < mtop; i++) {
+        rp[i] = (carry & tp[i]) | (~carry & rp[i]);
+        ((volatile BN_ULONG *)tp)[i] = 0;
+    }
+    r->top = mtop;
+
+    if (tp != storage)
+        OPENSSL_free(tp);
+
+    return 1;
+}
+
 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                      const BIGNUM *m)
 {
-    if (!BN_uadd(r, a, b))
+    int ret = bn_mod_add_fixed_top(r, a, b, m);
-        return 0;
+
-    if (BN_ucmp(r, m) >= 0)
+    if (ret)
-        return BN_usub(r, r, m);
+        bn_correct_top(r);
-    return 1;
+
+    return ret;
 }
 
 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,

crypto/ec/ecdsa_ossl.c

@@ -172,8 +172,7 @@ 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, *blind = NULL;
+    BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL;
-    BIGNUM *blindm = NULL;
     const BIGNUM *order, *ckinv;
     BN_CTX *ctx = NULL;
     const EC_GROUP *group;
@@ -206,18 +205,8 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
     }
     s = ret->s;
 
-    ctx = BN_CTX_secure_new();
+    if ((ctx = BN_CTX_new()) == NULL ||
-    if (ctx == NULL) {
+        (tmp = BN_new()) == NULL || (m = BN_new()) == 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;
     }
@@ -257,64 +246,18 @@ 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 := blind^-1 * k^-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_mul(tmp, tmp, ret->r, order, ctx)) {
+        if (!BN_mod_add_quick(s, tmp, m, order)) {
             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 * 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;
         }
-
-        /* 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;
-        }
-
         if (BN_is_zero(s)) {
             /*
              * if kinv and r have been supplied by the caller, don't
@@ -336,9 +279,9 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
         ECDSA_SIG_free(ret);
         ret = NULL;
     }
-    if (ctx != NULL)
-        BN_CTX_end(ctx);
     BN_CTX_free(ctx);
+    BN_clear_free(m);
+    BN_clear_free(tmp);
     BN_clear_free(kinv);
     return ret;
 }

crypto/include/internal/bn_int.h

@@ -71,5 +71,7 @@ int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                           BN_MONT_CTX *mont, BN_CTX *ctx);
 int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
                          BN_CTX *ctx);
+int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+                         const BIGNUM *m);
 
 #endif