diff --git a/src/crypto/tls/handshake_client.go b/src/crypto/tls/handshake_client.go
index 63d86b9f3a7ef..0ef87d4d775aa 100644
--- a/src/crypto/tls/handshake_client.go
+++ b/src/crypto/tls/handshake_client.go
@@ -857,6 +857,10 @@ func (hs *clientHandshakeState) sendFinished(out []byte) error {
 	return nil
 }
 
+// maxRSAKeySize is the maximum RSA key size in bits that we are willing
+// to verify the signatures of during a TLS handshake.
+const maxRSAKeySize = 8192
+
 // verifyServerCertificate parses and verifies the provided chain, setting
 // c.verifiedChains and c.peerCertificates or sending the appropriate alert.
 func (c *Conn) verifyServerCertificate(certificates [][]byte) error {
@@ -868,6 +872,10 @@ func (c *Conn) verifyServerCertificate(certificates [][]byte) error {
 			c.sendAlert(alertBadCertificate)
 			return errors.New("tls: failed to parse certificate from server: " + err.Error())
 		}
+		if cert.cert.PublicKeyAlgorithm == x509.RSA && cert.cert.PublicKey.(*rsa.PublicKey).N.BitLen() > maxRSAKeySize {
+			c.sendAlert(alertBadCertificate)
+			return fmt.Errorf("tls: server sent certificate containing RSA key larger than %d bits", maxRSAKeySize)
+		}
 		activeHandles[i] = cert
 		certs[i] = cert.cert
 	}
diff --git a/src/crypto/tls/handshake_client_test.go b/src/crypto/tls/handshake_client_test.go
index 22be38faff468..6b5b61aed503b 100644
--- a/src/crypto/tls/handshake_client_test.go
+++ b/src/crypto/tls/handshake_client_test.go
@@ -2616,3 +2616,81 @@ func TestClientHandshakeContextCancellation(t *testing.T) {
 		t.Error("Client connection was not closed when the context was canceled")
 	}
 }
+
+// discardConn wraps a net.Conn but discards all writes, but reports that they happened.
+type discardConn struct {
+	net.Conn
+}
+
+func (dc *discardConn) Write(data []byte) (int, error) {
+	return len(data), nil
+}
+
+// largeRSAKeyCertPEM contains a 8193 bit RSA key
+const largeRSAKeyCertPEM = `-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----`
+
+func TestHandshakeRSATooBig(t *testing.T) {
+	testCert, _ := pem.Decode([]byte(largeRSAKeyCertPEM))
+
+	c := &Conn{conn: &discardConn{}, config: testConfig.Clone()}
+
+	expectedErr := "tls: server sent certificate containing RSA key larger than 8192 bits"
+	err := c.verifyServerCertificate([][]byte{testCert.Bytes})
+	if err == nil || err.Error() != expectedErr {
+		t.Errorf("Conn.verifyServerCertificate unexpected error: want %q, got %q", expectedErr, err)
+	}
+
+	expectedErr = "tls: client sent certificate containing RSA key larger than 8192 bits"
+	err = c.processCertsFromClient(Certificate{Certificate: [][]byte{testCert.Bytes}})
+	if err == nil || err.Error() != expectedErr {
+		t.Errorf("Conn.processCertsFromClient unexpected error: want %q, got %q", expectedErr, err)
+	}
+}
diff --git a/src/crypto/tls/handshake_server.go b/src/crypto/tls/handshake_server.go
index e22f284cfb428..9def927314815 100644
--- a/src/crypto/tls/handshake_server.go
+++ b/src/crypto/tls/handshake_server.go
@@ -818,6 +818,10 @@ func (c *Conn) processCertsFromClient(certificate Certificate) error {
 			c.sendAlert(alertBadCertificate)
 			return errors.New("tls: failed to parse client certificate: " + err.Error())
 		}
+		if certs[i].PublicKeyAlgorithm == x509.RSA && certs[i].PublicKey.(*rsa.PublicKey).N.BitLen() > maxRSAKeySize {
+			c.sendAlert(alertBadCertificate)
+			return fmt.Errorf("tls: client sent certificate containing RSA key larger than %d bits", maxRSAKeySize)
+		}
 	}
 
 	if len(certs) == 0 && requiresClientCert(c.config.ClientAuth) {