diff --git a/phpseclib/Crypt/RSA.php b/phpseclib/Crypt/RSA.php
index fec68958..7f5df1d5 100644
--- a/phpseclib/Crypt/RSA.php
+++ b/phpseclib/Crypt/RSA.php
@@ -1396,9 +1396,14 @@ class RSA
                 $this->components = array();
 
                 $xml = xml_parser_create('UTF-8');
-                xml_set_object($xml, $this);
-                xml_set_element_handler($xml, '_start_element_handler', '_stop_element_handler');
-                xml_set_character_data_handler($xml, '_data_handler');
+                if (version_compare(PHP_VERSION, '8.4.0', '>=')) {
+                    xml_set_element_handler($xml, array($this, '_start_element_handler'), array($this, '_stop_element_handler'));
+                    xml_set_character_data_handler($xml, array($this, '_data_handler'));
+                } else {
+                    xml_set_object($xml, $this);
+                    xml_set_element_handler($xml, '_start_element_handler', '_stop_element_handler');
+                    xml_set_character_data_handler($xml, '_data_handler');
+                }
                 // add <xml></xml> to account for "dangling" tags like <BitStrength>...</BitStrength> that are sometimes added
                 if (!xml_parse($xml, '<xml>' . $key . '</xml>')) {
                     xml_parser_free($xml);
diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php
index 7747a95b..74b54a26 100644
--- a/phpseclib/Math/BigInteger.php
+++ b/phpseclib/Math/BigInteger.php
@@ -252,7 +252,8 @@ class BigInteger
     {
         if (!defined('MATH_BIGINTEGER_MODE')) {
             switch (true) {
-                case extension_loaded('gmp'):
+                // PHP 8.4.0 and 8.4.1 don't work with GMP per https://github.com/php/php-src/issues/16870
+                case extension_loaded('gmp') && !(version_compare(PHP_VERSION, '8.4.0', '>=') && version_compare(PHP_VERSION, '8.4.1', '<=')):
                     define('MATH_BIGINTEGER_MODE', self::MODE_GMP);
                     break;
                 case extension_loaded('bcmath'):