diff --git a/deps/openssl/openssl/crypto/dsa/dsa_ossl.c b/deps/openssl/openssl/crypto/dsa/dsa_ossl.c
index 4aa49f554af3b8..3b657d5d3d13f4 100644
--- a/deps/openssl/openssl/crypto/dsa/dsa_ossl.c
+++ b/deps/openssl/openssl/crypto/dsa/dsa_ossl.c
@@ -25,6 +25,8 @@ static int dsa_do_verify(const unsigned char *dgst, int dgst_len,
                          DSA_SIG *sig, DSA *dsa);
 static int dsa_init(DSA *dsa);
 static int dsa_finish(DSA *dsa);
+static BIGNUM *dsa_mod_inverse_fermat(const BIGNUM *k, const BIGNUM *q,
+                                      BN_CTX *ctx);
 
 static DSA_METHOD openssl_dsa_meth = {
     "OpenSSL DSA method",
@@ -261,7 +263,7 @@ static int dsa_sign_setup(DSA *dsa, BN_CTX *ctx_in,
         goto err;
 
     /* Compute  part of 's = inv(k) (m + xr) mod q' */
-    if ((kinv = BN_mod_inverse(NULL, k, dsa->q, ctx)) == NULL)
+    if ((kinv = dsa_mod_inverse_fermat(k, dsa->q, ctx)) == NULL)
         goto err;
 
     BN_clear_free(*kinvp);
@@ -395,3 +397,31 @@ static int dsa_finish(DSA *dsa)
     BN_MONT_CTX_free(dsa->method_mont_p);
     return (1);
 }
+
+/*
+ * Compute the inverse of k modulo q.
+ * Since q is prime, Fermat's Little Theorem applies, which reduces this to
+ * mod-exp operation.  Both the exponent and modulus are public information
+ * so a mod-exp that doesn't leak the base is sufficient.  A newly allocated
+ * BIGNUM is returned which the caller must free.
+ */
+static BIGNUM *dsa_mod_inverse_fermat(const BIGNUM *k, const BIGNUM *q,
+                                      BN_CTX *ctx)
+{
+    BIGNUM *res = NULL;
+    BIGNUM *r, *e;
+
+    if ((r = BN_new()) == NULL)
+        return NULL;
+
+    BN_CTX_start(ctx);
+    if ((e = BN_CTX_get(ctx)) != NULL
+            && BN_set_word(r, 2)
+            && BN_sub(e, q, r)
+            && BN_mod_exp_mont(r, k, e, q, ctx, NULL))
+        res = r;
+    else
+        BN_free(r);
+    BN_CTX_end(ctx);
+    return res;
+}