diff --git a/tls.go b/tls.go
index b33301e..20cddba 100644
--- a/tls.go
+++ b/tls.go
@@ -27,7 +27,6 @@ package reality
 // https://www.imperialviolet.org/2013/02/04/luckythirteen.html.
 
 import (
-	"bytes"
 	"context"
 	"crypto"
 	"crypto/aes"
@@ -799,7 +798,7 @@ func X509KeyPair(certPEMBlock, keyPEMBlock []byte) (Certificate, error) {
 		if !ok {
 			return fail(errors.New("tls: private key type does not match public key type"))
 		}
-		if pub.N.Cmp(priv.N) != 0 {
+		if !priv.PublicKey.Equal(pub) {
 			return fail(errors.New("tls: private key does not match public key"))
 		}
 	case *ecdsa.PublicKey:
@@ -807,7 +806,7 @@ func X509KeyPair(certPEMBlock, keyPEMBlock []byte) (Certificate, error) {
 		if !ok {
 			return fail(errors.New("tls: private key type does not match public key type"))
 		}
-		if pub.X.Cmp(priv.X) != 0 || pub.Y.Cmp(priv.Y) != 0 {
+		if !priv.PublicKey.Equal(pub) {
 			return fail(errors.New("tls: private key does not match public key"))
 		}
 	case ed25519.PublicKey:
@@ -815,7 +814,7 @@ func X509KeyPair(certPEMBlock, keyPEMBlock []byte) (Certificate, error) {
 		if !ok {
 			return fail(errors.New("tls: private key type does not match public key type"))
 		}
-		if !bytes.Equal(priv.Public().(ed25519.PublicKey), pub) {
+		if !priv.Public().(ed25519.PublicKey).Equal(pub) {
 			return fail(errors.New("tls: private key does not match public key"))
 		}
 	default: