diff --git a/net/third_party/nss/ssl/ssl3con.c b/net/third_party/nss/ssl/ssl3con.c
index 06992e0..cf7ef32 100644
--- a/net/third_party/nss/ssl/ssl3con.c
+++ b/net/third_party/nss/ssl/ssl3con.c
@@ -6973,14 +6973,27 @@ no_memory:	/* no-memory error has already been set. */
 
 
 /*
- * Returns true if the client authentication key is an RSA or DSA key that
- * may be able to sign only SHA-1 hashes.
+ * Returns the TLS signature algorithm for the client authentication key and
+ * whether it is an RSA or DSA key that may be able to sign only SHA-1 hashes.
  */
-static PRBool
-ssl3_ClientKeyPrefersSHA1(sslSocket *ss)
+static SECStatus
+ssl3_ExtractClientKeyInfo(sslSocket *ss,
+			  TLSSignatureAlgorithm *sigAlg,
+			  PRBool *preferSha1)
 {
+    SECStatus rv = SECSuccess;
     SECKEYPublicKey *pubk;
-    PRBool prefer_sha1 = PR_FALSE;
+
+    pubk = CERT_ExtractPublicKey(ss->ssl3.clientCertificate);
+    if (pubk == NULL) {
+	rv = SECFailure;
+	goto done;
+    }
+
+    rv = ssl3_TLSSignatureAlgorithmForKeyType(pubk->keyType, sigAlg);
+    if (rv != SECSuccess) {
+	goto done;
+    }
 
 #if defined(NSS_PLATFORM_CLIENT_AUTH) && defined(_WIN32)
     /* If the key is in CAPI, assume conservatively that the CAPI service
@@ -6989,7 +7002,8 @@ ssl3_ClientKeyPrefersSHA1(sslSocket *ss)
     if (ss->ssl3.platformClientKey->dwKeySpec != CERT_NCRYPT_KEY_SPEC) {
 	/* CAPI only supports RSA and DSA signatures, so we don't need to
 	 * check the key type. */
-	return PR_TRUE;
+	*preferSha1 = PR_TRUE;
+	goto done;
     }
 #endif  /* NSS_PLATFORM_CLIENT_AUTH && _WIN32 */
 
@@ -6999,38 +7013,61 @@ ssl3_ClientKeyPrefersSHA1(sslSocket *ss)
      * older, DSA key size is at most 1024 bits and the hash function must
      * be SHA-1.
      */
-    pubk = CERT_ExtractPublicKey(ss->ssl3.clientCertificate);
-    if (pubk == NULL) {
-	return PR_FALSE;
-    }
     if (pubk->keyType == rsaKey || pubk->keyType == dsaKey) {
-	prefer_sha1 = SECKEY_PublicKeyStrength(pubk) <= 128;
+	*preferSha1 = SECKEY_PublicKeyStrength(pubk) <= 128;
+    } else {
+	*preferSha1 = PR_FALSE;
     }
-    SECKEY_DestroyPublicKey(pubk);
-    return prefer_sha1;
+
+  done:
+    if (pubk)
+	SECKEY_DestroyPublicKey(pubk);
+    return rv;
 }
 
-/* Destroys the backup handshake hash context if we don't need it. */
+/* Destroys the backup handshake hash context if we don't need it. Note that
+ * this function selects the hash algorithm for client authentication
+ * signatures; ssl3_SendCertificateVerify uses the presence of the backup hash
+ * to determine whether to use SHA-1 or SHA-256. */
 static void
 ssl3_DestroyBackupHandshakeHashIfNotNeeded(sslSocket *ss,
 					   const SECItem *algorithms)
 {
-    PRBool need_backup_hash = PR_FALSE;
+    SECStatus rv;
+    TLSSignatureAlgorithm sigAlg;
+    PRBool preferSha1;
+    PRBool supportsSha1 = PR_FALSE;
+    PRBool supportsSha256 = PR_FALSE;
+    PRBool needBackupHash = PR_FALSE;
     unsigned int i;
 
     PORT_Assert(ss->ssl3.hs.md5);
-    if (ssl3_ClientKeyPrefersSHA1(ss)) {
-	/* Use SHA-1 if the server supports it. */
-	for (i = 0; i < algorithms->len; i += 2) {
-	    if (algorithms->data[i] == tls_hash_sha1 &&
-		(algorithms->data[i+1] == tls_sig_rsa ||
-		 algorithms->data[i+1] == tls_sig_dsa)) {
-		need_backup_hash = PR_TRUE;
-		break;
+
+    /* Determine the key's signature algorithm and whether it prefers SHA-1. */
+    rv = ssl3_ExtractClientKeyInfo(ss, &sigAlg, &preferSha1);
+    if (rv != SECSuccess) {
+	goto done;
+    }
+
+    /* Determine the server's hash support for that signature algorithm. */
+    for (i = 0; i < algorithms->len; i += 2) {
+	if (algorithms->data[i+1] == sigAlg) {
+	    if (algorithms->data[i] == tls_hash_sha1) {
+		supportsSha1 = PR_TRUE;
+	    } else if (algorithms->data[i] == tls_hash_sha256) {
+		supportsSha256 = PR_TRUE;
 	    }
 	}
     }
-    if (!need_backup_hash) {
+
+    /* If either the server does not support SHA-256 or the client key prefers
+     * SHA-1, leave the backup hash. */
+    if (supportsSha1 && (preferSha1 || !supportsSha256)) {
+	needBackupHash = PR_TRUE;
+    }
+
+done:
+    if (!needBackupHash) {
 	PK11_DestroyContext(ss->ssl3.hs.md5, PR_TRUE);
 	ss->ssl3.hs.md5 = NULL;
     }