diff --git a/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php b/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
index 4364324d..4f1db684 100644
--- a/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
+++ b/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
@@ -523,11 +523,13 @@ abstract class PKCS8 extends PKCS
         $key = [
             'version' => 'v1',
             'privateKeyAlgorithm' => [
-                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid,
-                'parameters' => $params
+                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid
              ],
             'privateKey' => $key
         ];
+        if ($oid != 'id-Ed25519' && $oid != 'id-Ed448') {
+            $key['privateKeyAlgorithm']['parameters'] = $params;
+        }
         if (!empty($attr)) {
             $key['attributes'] = $attr;
         }
diff --git a/phpseclib/Crypt/EC/Formats/Keys/PKCS8.php b/phpseclib/Crypt/EC/Formats/Keys/PKCS8.php
index a2d0ff28..346c8117 100644
--- a/phpseclib/Crypt/EC/Formats/Keys/PKCS8.php
+++ b/phpseclib/Crypt/EC/Formats/Keys/PKCS8.php
@@ -226,8 +226,7 @@ abstract class PKCS8 extends Progenitor
                 [],
                 null,
                 $password,
-                $curve instanceof Ed25519 ? 'id-Ed25519' : 'id-Ed448',
-                "\0" . $curve->encodePoint($publicKey)
+                $curve instanceof Ed25519 ? 'id-Ed25519' : 'id-Ed448'
             );
         }
 
diff --git a/tests/Unit/Crypt/EC/KeyTest.php b/tests/Unit/Crypt/EC/KeyTest.php
index db3651a3..cbe96a09 100644
--- a/tests/Unit/Crypt/EC/KeyTest.php
+++ b/tests/Unit/Crypt/EC/KeyTest.php
@@ -271,9 +271,11 @@ MCwwBwYDK2VwBQADIQAZv0QJaYTN/oVBusFn3DuWyFCGqjC2tssMXDitcDFm4Q==
     public function testEd25519PrivateKey()
     {
         // without public key (public key should be derived)
-        $key = PublicKeyLoader::load('-----BEGIN PRIVATE KEY-----
+        $expected = '-----BEGIN PRIVATE KEY-----
 MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
------END PRIVATE KEY-----');
+-----END PRIVATE KEY-----';
+        $key = PublicKeyLoader::load($expected);
+        $this->assertSameNL($expected, $key->toString('PKCS8'));
         $this->assertSameNL('Ed25519', $key->getCurve());
         $this->assertSameNL('Ed25519', $key->getPublicKey()->getCurve());
 
@@ -289,14 +291,10 @@ Z9w7lshQhqowtrbLDFw4rXAxZuE=
         // the above key not only omits NULL - it also includes a
         // unstructuredName attribute with a value of "Curdle Chairs"
         // that the following key does not have
-        $expected = '-----BEGIN PRIVATE KEY-----
+        $key = PublicKeyLoader::load('-----BEGIN PRIVATE KEY-----
 MFMCAQEwBwYDK2VwBQAEIgQg1O5y2/kTWErVttjx92n4rTr+fCjL8dT74Jeoj0R1
 WEKBIQAZv0QJaYTN/oVBusFn3DuWyFCGqjC2tssMXDitcDFm4Q==
------END PRIVATE KEY-----';
-        $this->assertSameNL($expected, $key->toString('PKCS8'));
-
-        $expected = EC::createKey('Ed25519')->toString('PKCS8');
-        $key = PublicKeyLoader::load($expected);
+-----END PRIVATE KEY-----');
         $this->assertSameNL('Ed25519', $key->getCurve());
         $this->assertSameNL('Ed25519', $key->getPublicKey()->getCurve());
     }