diff --git a/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php b/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
index d5a9db4e..b11325a9 100644
--- a/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
+++ b/phpseclib/Crypt/Common/Formats/Keys/PKCS8.php
@@ -600,12 +600,15 @@ abstract class PKCS8 extends PKCS
 
         $key = [
             'publicKeyAlgorithm' => [
-                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid,
-                'parameters' => $params
+                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid
             ],
             'publicKey' => "\0" . $key
         ];
 
+        if ($oid != 'id-Ed25519' && $oid != 'id-Ed448') {
+            $key['publicKeyAlgorithm']['parameters'] = $params;
+        }
+
         $key = ASN1::encodeDER($key, Maps\PublicKeyInfo::MAP);
 
         return "-----BEGIN PUBLIC KEY-----\r\n" .
diff --git a/tests/Unit/Crypt/EC/KeyTest.php b/tests/Unit/Crypt/EC/KeyTest.php
index 103e4dce..56c54c22 100644
--- a/tests/Unit/Crypt/EC/KeyTest.php
+++ b/tests/Unit/Crypt/EC/KeyTest.php
@@ -258,18 +258,11 @@ BjoJZJZQztmlj7Qep/sf1l8=
     // from https://tools.ietf.org/html/draft-ietf-curdle-pkix-07#section-10.1
     public function testEd25519PublicKey(): void
     {
-        $key = PublicKeyLoader::load('-----BEGIN PUBLIC KEY-----
-MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE=
------END PUBLIC KEY-----');
-        $this->assertSameNL('Ed25519', $key->getCurve());
-
-        // in the above key AlgorithmIdentifier has a single "child". in the
-        // following key it has two. The second one is ("optional") NULL.
-        // https://security.stackexchange.com/q/110330/15922 elaborates on
-        // why phpseclib is encoding the NULL as opposed to omitting it.
         $expected = '-----BEGIN PUBLIC KEY-----
-MCwwBwYDK2VwBQADIQAZv0QJaYTN/oVBusFn3DuWyFCGqjC2tssMXDitcDFm4Q==
+MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE=
 -----END PUBLIC KEY-----';
+        $key = PublicKeyLoader::load($expected);
+        $this->assertSameNL('Ed25519', $key->getCurve());
         $this->assertSameNL($expected, $key->toString('PKCS8'));
     }