diff --git a/CHANGES b/CHANGES
index a4beda66dd..4dc065923c 100644
--- a/CHANGES
+++ b/CHANGES
@@ -13,8 +13,8 @@
      chosen point SCA attacks.
      [Sohaib ul Hassan, Nicola Tuveri, Billy Bob Brumley]
 
-  *) Add blinding to an ECDSA signature to protect against side channel attacks
-     discovered by Keegan Ryan (NCC Group).
+  *) Add blinding to ECDSA and DSA signatures 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
diff --git a/crypto/dsa/dsa_ossl.c b/crypto/dsa/dsa_ossl.c
index d78c5f00cb..5237794d8f 100644
--- a/crypto/dsa/dsa_ossl.c
+++ b/crypto/dsa/dsa_ossl.c
@@ -59,19 +59,13 @@ const DSA_METHOD *DSA_OpenSSL(void)
 static DSA_SIG *dsa_do_sign(const unsigned char *dgst, int dlen, DSA *dsa)
 {
     BIGNUM *kinv = NULL;
-    BIGNUM *m;
-    BIGNUM *xr;
+    BIGNUM *m, *blind, *blindm, *tmp;
     BN_CTX *ctx = NULL;
     int reason = ERR_R_BN_LIB;
     DSA_SIG *ret = NULL;
     int rv = 0;
 
-    m = BN_new();
-    xr = BN_new();
-    if (m == NULL || xr == NULL)
-        goto err;
-
-    if (!dsa->p || !dsa->q || !dsa->g) {
+    if (dsa->p == NULL || dsa->q == NULL || dsa->g == NULL) {
         reason = DSA_R_MISSING_PARAMETERS;
         goto err;
     }
@@ -87,6 +81,13 @@ static DSA_SIG *dsa_do_sign(const unsigned char *dgst, int dlen, DSA *dsa)
     ctx = BN_CTX_new();
     if (ctx == NULL)
         goto err;
+    m = BN_CTX_get(ctx);
+    blind = BN_CTX_get(ctx);
+    blindm = BN_CTX_get(ctx);
+    tmp = BN_CTX_get(ctx);
+    if (tmp == NULL)
+        goto err;
+
  redo:
     if (!dsa_sign_setup(dsa, ctx, &kinv, &ret->r, dgst, dlen))
         goto err;
@@ -101,17 +102,50 @@ static DSA_SIG *dsa_do_sign(const unsigned char *dgst, int dlen, DSA *dsa)
     if (BN_bin2bn(dgst, dlen, m) == NULL)
         goto err;
 
-    /* Compute  s = inv(k) (m + xr) mod q */
-    if (!BN_mod_mul(xr, dsa->priv_key, ret->r, dsa->q, ctx))
-        goto err;               /* s = xr */
-    if (!BN_add(ret->s, xr, m))
-        goto err;               /* s = m + xr */
-    if (BN_cmp(ret->s, dsa->q) > 0)
-        if (!BN_sub(ret->s, ret->s, dsa->q))
+    /*
+     * The normal signature calculation is:
+     *
+     *   s := k^-1 * (m + r * priv_key) mod q
+     *
+     * We will blind this to protect against side channel attacks
+     *
+     *   s := blind^-1 * k^-1 * (blind * m + blind * r * priv_key) mod q
+     */
+
+    /* Generate a blinding value */
+    do {
+        if (!BN_priv_rand(blind, BN_num_bits(dsa->q) - 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 q */
+    if (!BN_mod_mul(tmp, blind, dsa->priv_key, dsa->q, ctx))
+        goto err;
+    if (!BN_mod_mul(tmp, tmp, ret->r, dsa->q, ctx))
+        goto err;
+
+    /* blindm := blind * m mod q */
+    if (!BN_mod_mul(blindm, blind, m, dsa->q, ctx))
+        goto err;
+
+    /* s : = (blind * priv_key * r) + (blind * m) mod q */
+    if (!BN_mod_add_quick(ret->s, tmp, blindm, dsa->q))
+        goto err;
+
+    /* s := s * k^-1 mod q */
     if (!BN_mod_mul(ret->s, ret->s, kinv, dsa->q, ctx))
         goto err;
 
+    /* s:= s * blind^-1 mod q */
+    if (BN_mod_inverse(blind, blind, dsa->q, ctx) == NULL)
+        goto err;
+    if (!BN_mod_mul(ret->s, ret->s, blind, dsa->q, ctx))
+        goto err;
+
     /*
      * Redo if r or s is zero as required by FIPS 186-3: this is very
      * unlikely.
@@ -128,8 +162,6 @@ static DSA_SIG *dsa_do_sign(const unsigned char *dgst, int dlen, DSA *dsa)
         ret = NULL;
     }
     BN_CTX_free(ctx);
-    BN_clear_free(m);
-    BN_clear_free(xr);
     BN_clear_free(kinv);
     return ret;
 }
diff --git a/crypto/ec/ecdsa_ossl.c b/crypto/ec/ecdsa_ossl.c
index 640593bc2d..cdd0cf0228 100644
--- a/crypto/ec/ecdsa_ossl.c
+++ b/crypto/ec/ecdsa_ossl.c
@@ -288,7 +288,7 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
          *
          * We will blind this to protect against side channel attacks
          *
-         *   s := k^-1 * blind^-1 * (blind * m + blind * r * priv_key) mod order
+         *   s := blind^-1 * k^-1 * (blind * m + blind * r * priv_key) mod order
          */
 
         /* Generate a blinding value */
@@ -323,6 +323,12 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
             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);
@@ -333,12 +339,6 @@ ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len,
             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