diff --git a/src/Crypto/CoseKey.php b/src/Crypto/CoseKey.php
index f591b75..4478da0 100644
--- a/src/Crypto/CoseKey.php
+++ b/src/Crypto/CoseKey.php
@@ -74,12 +74,23 @@ public function toString(): string
 
     public static function parseCbor(ByteBuffer $buffer, int $offset = 0, int &$endOffset = null): CoseKey
     {
+        // Fix incorrect EdDSA keys
+        $isIncorrectKey = $buffer->getBytes($offset, 17) == "\xa3\x01\x63\x4f\x4b\x50\x03\x27\x20\x67\x45\x64\x32\x35\x35\x31\x39";
+        if ($isIncorrectKey) {
+            $buffer = new ByteBuffer($buffer->getBytes(0, $offset) . "\xa4" . $buffer->getBytes($offset + 1, $buffer->getLength() - $offset - 1));
+        }
         $data = CborDecoder::decodeInPlace($buffer, $offset, $endOffset);
 
         if (!$data instanceof CborMap) {
             throw new DataValidationException('Failed to decode CBOR encoded COSE key'); // TODO: change exceptions
         }
 
+        // Replace textual kty's with their numeric counterparts
+        if ($data->get(self::COSE_KEY_PARAM_KTY) === 'OKP')
+            $data->set(self::COSE_KEY_PARAM_KTY, 1);
+        elseif ($data->get(self::COSE_KEY_PARAM_KTY) === 'EC2')
+            $data->set(self::COSE_KEY_PARAM_KTY, 2);
+
         DataValidator::checkMap(
             $data,
             [
@@ -88,6 +99,11 @@ public static function parseCbor(ByteBuffer $buffer, int $offset = 0, int &$endO
             false
         );
 
+        // Fix incorrect EdDSA keys, part 2: x coordinate should be bstr, not array
+        if ($isIncorrectKey && $data->has(-2) && is_array($data->get(-2))) {
+            $data->set(-2, new ByteBuffer(implode(array_map('chr', $data->get(-2)))));
+        }
+
         $keyType = $data->get(self::COSE_KEY_PARAM_KTY);
         return self::createKey($keyType, $data);
     }
diff --git a/src/Crypto/OkpKey.php b/src/Crypto/OkpKey.php
index 9aa4271..5a41afe 100644
--- a/src/Crypto/OkpKey.php
+++ b/src/Crypto/OkpKey.php
@@ -113,6 +113,16 @@ public function asDer(): string
 
     public static function fromCborData(CborMap $data): OkpKey
     {
+        // Translate literal curves to their numeric constant
+        if ($data->get(self::KTP_CRV) === 'X25519')
+            $data->set(self::KTP_CRV, 4);
+        elseif ($data->get(self::KTP_CRV) === 'X448')
+            $data->set(self::KTP_CRV, 5);
+        elseif ($data->get(self::KTP_CRV) === 'Ed25519')
+            $data->set(self::KTP_CRV, 6);
+        elseif ($data->get(self::KTP_CRV) === 'Ed448')
+            $data->set(self::KTP_CRV, 7);
+
         // Note: leading zeroes in X and Y coordinates are preserved in CBOR
         // See RFC8152 13.1.1. Double Coordinate Curves
         DataValidator::checkMap(