diff --git a/key.go b/key.go
index 7bd10f7..cc17f5f 100644
--- a/key.go
+++ b/key.go
@@ -390,7 +390,11 @@ func LoadPublicKeyFromDER(der_block []byte) (PublicKey, error) {
 
 // GenerateRSAKey generates a new RSA private key with an exponent of 3.
 func GenerateRSAKey(bits int) (PrivateKey, error) {
-	exponent := 3
+	return GenerateRSAKeyWithExponent(bits, 3)
+}
+
+// GenerateRSAKeyWithExponent generates a new RSA private key.
+func GenerateRSAKeyWithExponent(bits int, exponent int) (PrivateKey, error) {
 	rsa := C.RSA_generate_key(C.int(bits), C.ulong(exponent), nil, nil)
 	if rsa == nil {
 		return nil, errors.New("failed to generate RSA key")
diff --git a/key_test.go b/key_test.go
index e7b5add..0af9012 100644
--- a/key_test.go
+++ b/key_test.go
@@ -152,6 +152,10 @@ func TestGenerate(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
+	_, err = GenerateRSAKeyWithExponent(1024, 65537)
+	if err != nil {
+		t.Fatal(err)
+	}
 }
 
 func TestSign(t *testing.T) {