diff --git a/handshake_client.go b/handshake_client.go
index 57e622f..c35e8ee 100644
--- a/handshake_client.go
+++ b/handshake_client.go
@@ -936,6 +936,10 @@ 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 {
@@ -947,6 +951,10 @@ 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/handshake_server.go b/handshake_server.go
index 1c3d74a..5915e31 100644
--- a/handshake_server.go
+++ b/handshake_server.go
@@ -864,6 +864,10 @@ 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) {