diff --git a/ssh/keys.go b/ssh/keys.go
index 3482c4d..78f0963 100644
--- a/ssh/keys.go
+++ b/ssh/keys.go
@@ -1635,10 +1635,28 @@ func parseOpenSSHPrivateKey(key []byte, decrypt openSSHDecryptFunc) (crypto.Priv
 			return nil, err
 		}
 
+		// Mirror the validation done in parseRSA for public keys: cap the
+		// modulus at the same limit enforced by crypto/tls, reject oversized
+		// or invalid exponents, and additionally bound the prime factors to
+		// avoid the expensive CRT coefficient recomputation in pk.Precompute.
+		if key.N.BitLen() > 8192 {
+			return nil, errors.New("ssh: rsa modulus too large")
+		}
+		if key.P.BitLen() > 4096 || key.Q.BitLen() > 4096 {
+			return nil, errors.New("ssh: rsa prime too large")
+		}
+		if key.E.BitLen() > 24 {
+			return nil, errors.New("ssh: exponent too large")
+		}
+		e := key.E.Int64()
+		if e < 3 || e&1 == 0 {
+			return nil, errors.New("ssh: incorrect exponent")
+		}
+
 		pk := &rsa.PrivateKey{
 			PublicKey: rsa.PublicKey{
 				N: key.N,
-				E: int(key.E.Int64()),
+				E: int(e),
 			},
 			D:      key.D,
 			Primes: []*big.Int{key.P, key.Q},
diff --git a/ssh/keys_test.go b/ssh/keys_test.go
index 93a0a13..c973c8c 100644
--- a/ssh/keys_test.go
+++ b/ssh/keys_test.go
@@ -232,6 +232,200 @@ func TestParseRSAModulusTooLarge(t *testing.T) {
 	}
 }
 
+func TestParsePrivateKeyRSAModulusTooLarge(t *testing.T) {
+	rsa16384 := []byte(`-----BEGIN OPENSSH PRIVATE KEY-----
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+-----END OPENSSH PRIVATE KEY-----
+`)
+	_, err := ParseRawPrivateKey(rsa16384)
+	if err == nil {
+		t.Fatal("ParseRawPrivateKey accepted a 16384-bit modulus; expected it to be rejected")
+	}
+
+	expectedError := "rsa modulus too large"
+	if !strings.Contains(err.Error(), expectedError) {
+		t.Errorf("unexpected error message: got %q, want substring %q", err.Error(), expectedError)
+	}
+}
+
 func TestParseECPrivateKey(t *testing.T) {
 	key := testPrivateKeys["ecdsa"]