diff --git a/phpseclib/File/X509.php b/phpseclib/File/X509.php
index 8e700bee..de777775 100644
--- a/phpseclib/File/X509.php
+++ b/phpseclib/File/X509.php
@@ -1120,7 +1120,8 @@ class X509
                         $subjectKeyID = $this->getExtension('id-ce-subjectKeyIdentifier');
                         switch (true) {
                             case !is_array($authorityKey):
-                            case is_array($authorityKey) && isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
+                            case !$subjectKeyID:
+                            case isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
                                 $signingCert = $this->currentCert; // working cert
                         }
                 }
@@ -1137,7 +1138,11 @@ class X509
                                 $subjectKeyID = $this->getExtension('id-ce-subjectKeyIdentifier', $ca);
                                 switch (true) {
                                     case !is_array($authorityKey):
-                                    case is_array($authorityKey) && isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
+                                    case !$subjectKeyID:
+                                    case isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
+                                        if (is_array($authorityKey) && isset($authorityKey['authorityCertSerialNumber']) && !$authorityKey['authorityCertSerialNumber']->equals($ca['tbsCertificate']['serialNumber'])) {
+                                            break 2; // serial mismatch - check other ca
+                                        }
                                         $signingCert = $ca; // working cert
                                         break 3;
                                 }
@@ -1183,7 +1188,11 @@ class X509
                                 $subjectKeyID = $this->getExtension('id-ce-subjectKeyIdentifier', $ca);
                                 switch (true) {
                                     case !is_array($authorityKey):
-                                    case is_array($authorityKey) && isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
+                                    case !$subjectKeyID:
+                                    case isset($authorityKey['keyIdentifier']) && $authorityKey['keyIdentifier'] === $subjectKeyID:
+                                        if (is_array($authorityKey) && isset($authorityKey['authorityCertSerialNumber']) && !$authorityKey['authorityCertSerialNumber']->equals($ca['tbsCertificate']['serialNumber'])) {
+                                            break 2; // serial mismatch - check other ca
+                                        }
                                         $signingCert = $ca; // working cert
                                         break 3;
                                 }
diff --git a/tests/Unit/File/X509/X509Test.php b/tests/Unit/File/X509/X509Test.php
index ddfcae6e..6be74535 100644
--- a/tests/Unit/File/X509/X509Test.php
+++ b/tests/Unit/File/X509/X509Test.php
@@ -380,81 +380,6 @@ Mj93S
         $this->assertFalse($x509->validateSignature());
     }
 
-    public function testLooseComparison()
-    {
-        if (!extension_loaded('runkit')) {
-            return false;
-        }
-
-        define('FILE_X509_IGNORE_TYPE', true);
-
-        $x509 = new X509();
-        $x509->loadCA('-----BEGIN CERTIFICATE-----
-MIIEbDCCA1SgAwIBAgIUJguKOMpJm/yRMDlMOW04NV0YPXowDQYJKoZIhvcNAQEF
-BQAwYTELMAkGA1UEBhMCUEwxNzA1BgNVBAoTLkNaaUMgQ2VudHJhc3QgU0EgdyBp
-bWllbml1IE1pbmlzdHJhIEdvc3BvZGFya2kxGTAXBgNVBAMTEENaaUMgQ2VudHJh
-c3QgU0EwHhcNMDkwNDI5MTE1MzIxWhcNMTMxMjEzMjM1OTU5WjBzMQswCQYDVQQG
-EwJQTDEoMCYGA1UEChMfS3Jham93YSBJemJhIFJvemxpY3plbmlvd2EgUy5BLjEk
-MCIGA1UEAxMbQ09QRSBTWkFGSVIgLSBLd2FsaWZpa293YW55MRQwEgYDVQQFEwtO
-ciB3cGlzdTogNjCCASIwDQYJKoZIhvcNAQEBBQADggEPADCCAQoCggEBAIjNy3EL
-oK0uKTqAJokiP8VIxER/0OfwhY4DBhJGW38W6Pfema8iUs4net0NgoIeDpMQ8IHj
-FDSKkSaRkyL5f7PgvqBwzKe0HD1Duf9G/Lr2lu/J4QUMF3rqKaMRipXKkkEoKrub
-Qe41/mPiPXeClNswNQUEyInqWpfWNncU8AIs2GKIFTfSNqK4PgWOY1kG9MYfoNVr
-74dhejv7yHexEw9eAIcM1fIkEEq0vWIOjRtBXBAuWtUyD8iSeBs4nIN+614pHIjv
-ncHxG7xTDbmOAVZFgGZ8Hk5CUseAtTpazQNdU66XRUuCj4km01L4wsfZ1X8tfYQA
-6msMRYj+F7hLtoECAwEAAaOCAQgwggEEMA8GA1UdEwEB/wQFMAMBAf8wgY4GA1Ud
-IwSBhjCBg4AU2a7r85Cp1iJNW0Ca1LR6VG3996ShZaRjMGExCzAJBgNVBAYTAlBM
-MTcwNQYDVQQKEy5DWmlDIENlbnRyYXN0IFNBIHcgaW1pZW5pdSBNaW5pc3RyYSBH
-b3Nwb2RhcmtpMRkwFwYDVQQDExBDWmlDIENlbnRyYXN0IFNBggQ9/0sQMDEGA1Ud
-IAEB/wQnMCUwIwYEVR0gADAbMBkGCCsGAQUFBwIBFg13d3cubmNjZXJ0LnBsMA4G
-A1UdDwEB/wQEAwIBBjAdBgNVHQ4EFgQU3TGldJXipN4oGS3ZYmnBDMFs8gIwDQYJ
-KoZIhvcNAQEFBQADggEBAJrkn3XycfimT5C6D+lYvQNB4/X44KZRhxhnplMOdr/V
-3O13oJA/G2SkVaRZS1Rqy01vC9H3YSFfYnjFXJTOXldzodwszHEcGLHF/3JazHI9
-BTpP1F4oFyd0Un/wkp1usGU4e1riU5RAlSp8YcMX3q+nOqyCh0JsxnP7LjauHkE3
-KZ1RuBDZYbsYOwkAKjHax8srKugdWtq4sMNcqpxGFUah/4uLQn6hD4jeRpP4VGDv
-HZDmxaIoJdmCxfn9XeIS5PcZR+mHHkUOIhYLnfdUp/T3Yxxo+XrrTckC6AjtsL5/
-OA0vBLngVqqeuzVf0tUhcrCwPKQo5rKoakbApeXrows=
------END CERTIFICATE-----');
-
-        $x509->loadX509('-----BEGIN CERTIFICATE-----
-MIIFzzCCBLegAwIBAgIDAfdlMA0GCSqGSIb3DQEBBQUAMHMxCzAJBgNVBAYTAlBM
-MSgwJgYDVQQKDB9LcmFqb3dhIEl6YmEgUm96bGljemVuaW93YSBTLkEuMSQwIgYD
-VQQDDBtDT1BFIFNaQUZJUiAtIEt3YWxpZmlrb3dhbnkxFDASBgNVBAUTC05yIHdw
-aXN1OiA2MB4XDTExMTEwOTA2MDAwMFoXDTEzMTEwOTA2MDAwMFowgdkxCzAJBgNV
-BAYTAlBMMRwwGgYDVQQKDBNVcnrEhWQgTWlhc3RhIEdkeW5pMRswGQYDVQQFExJQ
-RVNFTDogNjEwNjA2MDMxMTgxGTAXBgNVBAMMEEplcnp5IFByemV3b3Jza2kxTzBN
-BgNVBBAwRgwiQWwuIE1hcnN6YcWCa2EgUGnFgnN1ZHNraWVnbyA1Mi81NAwNODEt
-MzgyIEdkeW5pYQwGUG9sc2thDAlwb21vcnNraWUxDjAMBgNVBCoMBUplcnp5MRMw
-EQYDVQQEDApQcnpld29yc2tpMIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCM
-m5vjGqHPthJCMqKpqssSISRos0PYDTcEQzyyurfX67EJWKtZj6HNwuDMEGJ02iBN
-ZfjUl7r8dIi28bSKhNlsfycXZKYRcIjp0+r5RqtR2auo9GQ6veKb61DEAGIqaR+u
-LLcJVTHCu0w9oXLGbRlGth5eNoj03CxXVAH2IfhbNwIDAQABo4IChzCCAoMwDAYD
-VR0TAQH/BAIwADCCAUgGA1UdIAEB/wSCATwwggE4MIIBNAYJKoRoAYb3IwEBMIIB
-JTCB3QYIKwYBBQUHAgIwgdAMgc1EZWtsYXJhY2phIHRhIGplc3Qgb8Wbd2lhZGN6
-ZW5pZW0gd3lkYXdjeSwgxbxlIHRlbiBjZXJ0eWZpa2F0IHpvc3RhxYIgd3lkYW55
-IGpha28gY2VydHlmaWthdCBrd2FsaWZpa293YW55IHpnb2RuaWUgeiB3eW1hZ2Fu
-aWFtaSB1c3Rhd3kgbyBwb2RwaXNpZSBlbGVrdHJvbmljem55bSBvcmF6IHRvd2Fy
-enlzesSFY3ltaSBqZWogcm96cG9yesSFZHplbmlhbWkuMEMGCCsGAQUFBwIBFjdo
-dHRwOi8vd3d3Lmtpci5jb20ucGwvY2VydHlmaWthY2phX2tsdWN6eS9wb2xpdHlr
-YS5odG1sMAkGA1UdCQQCMAAwIQYDVR0RBBowGIEWai5wcnpld29yc2tpQGdkeW5p
-YS5wbDAOBgNVHQ8BAf8EBAMCBkAwgZ4GA1UdIwSBljCBk4AU3TGldJXipN4oGS3Z
-YmnBDMFs8gKhd6R1MHMxCzAJBgNVBAYTAlBMMSgwJgYDVQQKDB9LcmFqb3dhIEl6
-YmEgUm96bGljemVuaW93YSBTLkEuMSQwIgYDVQQDDBtDT1BFIFNaQUZJUiAtIEt3
-YWxpZmlrb3dhbnkxFDASBgNVBAUTC05yIHdwaXN1OiA2ggJb9jBIBgNVHR8EQTA/
-MD2gO6A5hjdodHRwOi8vd3d3Lmtpci5jb20ucGwvY2VydHlmaWthY2phX2tsdWN6
-eS9DUkxfT1pLMzIuY3JsMA0GCSqGSIb3DQEBBQUAA4IBAQBYPIqnAreyeql7/opJ
-jcar/qWZy9ruhB2q0lZFsJOhwgMnbQXzp/4vv93YJqcHGAXdHP6EO8FQX47mjo2Z
-KQmi+cIHJHLONdX/3Im+M17V0iNAh7Z1lOSfTRT+iiwe/F8phcEaD5q2RmvYusR7
-zXZq/cLL0If0hXoPZ/EHQxjN8pxzxiUx6bJAgturnIMEfRNesxwghdr1dkUjOhGL
-f3kHVzgM6j3VAM7oFmMUb5y5s96Bzl10DodWitjOEH0vvnIcsppSxH1C1dCAi0o9
-f/1y2XuLNhBNHMAyTqpYPX8Yvav1c+Z50OMaSXHAnTa20zv8UtiHbaAhwlifCelU
-Mj93S
------END CERTIFICATE-----');
-        $this->assertTrue($x509->validateSignature());
-
-        runkit_constant_remove('FILE_X509_IGNORE_TYPE');
-    }
-
     // fixed by #1104
     public function testMultipleDomainNames()
     {
@@ -551,4 +476,84 @@ C47x9g==
 
         $this->assertTrue($x509->validateURL('https://www.google.com'));
     }
+
+    public function testValidateSignatureWithoutKeyIdentifier()
+    {
+        $x509 = new X509();
+        $x509->loadX509('-----BEGIN CERTIFICATE-----
+MIIDATCCAmqgAwIBAgICApowDQYJKoZIhvcNAQEFBQAwdzELMAkGA1UEBhMCVUsx
+DzANBgNVBAgMBkxvbmRvbjEPMA0GA1UEBwwGTG9uZG9uMQwwCgYDVQQKDANNUFMx
+DDAKBgNVBAsMA0RldjENMAsGA1UEAwwEdGVzdDEbMBkGCSqGSIb3DQEJARYMZGVr
+aUBtcHMuY29tMB4XDTE3MTEyNDE4MzE0MFoXDTE4MTEyNDE4MzE0MFowYTELMAkG
+A1UEBhMCVUsxDzANBgNVBAgMBkxvbmRvbjEPMA0GA1UEBwwGTG9uZG9uMQwwCgYD
+VQQKDANNUFMxETAPBgNVBAsMCERldi90ZXN0MQ8wDQYDVQQDDAZ0ZXN0MDEwgZ8w
+DQYJKoZIhvcNAQEBBQADgY0AMIGJAoGBAJ6+ydLXtjwbKhUBIodrm9Zq5yhhfMUM
+IDhpcEZ2PAWWUiwKZOo9eyXGAv4LnpvDcX5GzThqI1g3/rcPjgBMOB8bcuQA6RE0
+I9Jcf3YHbg/ednp7Q2X/zqUW+QUd01VfG8OJiRvO/4WKJTdQMU7/DKAv5WScIa4c
+0b11X4iiLUVvAgMBAAGjgbEwga4wgZMGA1UdIwSBizCBiKF7pHkwdzELMAkGA1UE
+BhMCVUsxDzANBgNVBAgMBkxvbmRvbjEPMA0GA1UEBwwGTG9uZG9uMQwwCgYDVQQK
+DANNUFMxDDAKBgNVBAsMA0RldjENMAsGA1UEAwwEdGVzdDEbMBkGCSqGSIb3DQEJ
+ARYMZGVraUBtcHMuY29tggkA+Fj4n7pGuRMwCQYDVR0TBAIwADALBgNVHQ8EBAMC
+BPAwDQYJKoZIhvcNAQEFBQADgYEAK0s83KbLM0OSj93/aly7UZHKGY3R/XhBNcsQ
+3fcxzX6VX8naJpqfK9kM5Ry9IBnqu6LwCnk18kqt6V6PSjqQ3gj9S3x8znTMdus1
+xraMNBOqRrn9quWCGEQt/iBrXHZ8zCdb4a+Eb5Jhz6/qK00KVufxw67fhuvhsjjv
+nnA8of4=
+-----END CERTIFICATE-----');
+
+        $authorityKeyIdentifier = $x509->getExtension('id-ce-authorityKeyIdentifier');
+        $this->assertNotNull($authorityKeyIdentifier);
+        $this->assertFalse(isset($authorityKeyIdentifier['keyIdentifier']));
+
+        $x509->loadCA('-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----');
+
+        $this->assertTrue($x509->validateSignature());
+    }
+
+    public function testValidateSignatureSelfSignedWithoutKeyIdentifier()
+    {
+        $x509 = new X509();
+        $x509->loadX509('-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----');
+
+        $authorityKeyIdentifier = $x509->getExtension('id-ce-authorityKeyIdentifier');
+        $this->assertNotNull($authorityKeyIdentifier);
+        $this->assertFalse(isset($authorityKeyIdentifier['keyIdentifier']));
+
+        $this->assertTrue($x509->validateSignature(false));
+    }
 }