diff --git a/ssh/cipher.go b/ssh/cipher.go
index 1c380f4607..951812ff9b 100644
--- a/ssh/cipher.go
+++ b/ssh/cipher.go
@@ -114,7 +114,8 @@ var cipherModes = map[string]*cipherMode{
 	"arcfour": {16, 0, streamCipherMode(0, newRC4)},
 
 	// AEAD ciphers
-	gcmCipherID:        {16, 12, newGCMCipher},
+	gcm128CipherID:     {16, 12, newGCMCipher},
+	gcm256CipherID:     {32, 12, newGCMCipher},
 	chacha20Poly1305ID: {64, 0, newChaCha20Cipher},
 
 	// CBC mode is insecure and so is not included in the default config.
diff --git a/ssh/cipher_test.go b/ssh/cipher_test.go
index bfb059d032..8e9bd6366b 100644
--- a/ssh/cipher_test.go
+++ b/ssh/cipher_test.go
@@ -141,7 +141,7 @@ func TestCVE202143565(t *testing.T) {
 		constructPacket func(packetCipher) io.Reader
 	}{
 		{
-			cipher: gcmCipherID,
+			cipher: gcm128CipherID,
 			constructPacket: func(client packetCipher) io.Reader {
 				internalCipher := client.(*gcmCipher)
 				b := &bytes.Buffer{}
diff --git a/ssh/common.go b/ssh/common.go
index c7964275de..e6a77f26a0 100644
--- a/ssh/common.go
+++ b/ssh/common.go
@@ -28,7 +28,7 @@ const (
 // supportedCiphers lists ciphers we support but might not recommend.
 var supportedCiphers = []string{
 	"aes128-ctr", "aes192-ctr", "aes256-ctr",
-	"aes128-gcm@openssh.com",
+	"aes128-gcm@openssh.com", gcm256CipherID,
 	chacha20Poly1305ID,
 	"arcfour256", "arcfour128", "arcfour",
 	aes128cbcID,
@@ -37,7 +37,7 @@ var supportedCiphers = []string{
 
 // preferredCiphers specifies the default preference for ciphers.
 var preferredCiphers = []string{
-	"aes128-gcm@openssh.com",
+	"aes128-gcm@openssh.com", gcm256CipherID,
 	chacha20Poly1305ID,
 	"aes128-ctr", "aes192-ctr", "aes256-ctr",
 }
@@ -168,7 +168,7 @@ func (a *directionAlgorithms) rekeyBytes() int64 {
 	// 2^(BLOCKSIZE/4) blocks. For all AES flavors BLOCKSIZE is
 	// 128.
 	switch a.Cipher {
-	case "aes128-ctr", "aes192-ctr", "aes256-ctr", gcmCipherID, aes128cbcID:
+	case "aes128-ctr", "aes192-ctr", "aes256-ctr", gcm128CipherID, gcm256CipherID, aes128cbcID:
 		return 16 * (1 << 32)
 
 	}
@@ -178,7 +178,8 @@ func (a *directionAlgorithms) rekeyBytes() int64 {
 }
 
 var aeadCiphers = map[string]bool{
-	gcmCipherID:        true,
+	gcm128CipherID:     true,
+	gcm256CipherID:     true,
 	chacha20Poly1305ID: true,
 }
 
diff --git a/ssh/handshake_test.go b/ssh/handshake_test.go
index b05aab30c7..3d0ab5044c 100644
--- a/ssh/handshake_test.go
+++ b/ssh/handshake_test.go
@@ -562,7 +562,7 @@ func TestHandshakeRekeyDefault(t *testing.T) {
 }
 
 func TestHandshakeAEADCipherNoMAC(t *testing.T) {
-	for _, cipher := range []string{chacha20Poly1305ID, gcmCipherID} {
+	for _, cipher := range []string{chacha20Poly1305ID, gcm128CipherID} {
 		checker := &syncChecker{
 			called: make(chan int, 1),
 		}
diff --git a/ssh/transport.go b/ssh/transport.go
index acf5a21bbb..da015801ea 100644
--- a/ssh/transport.go
+++ b/ssh/transport.go
@@ -17,7 +17,8 @@ import (
 const debugTransport = false
 
 const (
-	gcmCipherID    = "aes128-gcm@openssh.com"
+	gcm128CipherID = "aes128-gcm@openssh.com"
+	gcm256CipherID = "aes256-gcm@openssh.com"
 	aes128cbcID    = "aes128-cbc"
 	tripledescbcID = "3des-cbc"
 )