diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php
index a9b6c675..6bc11261 100644
--- a/phpseclib/Math/BigInteger.php
+++ b/phpseclib/Math/BigInteger.php
@@ -39,7 +39,7 @@ use phpseclib3\Exception\BadConfigurationException;
  * @author  Jim Wigginton <terrafrost@php.net>
  * @access  public
  */
-class BigInteger implements \Serializable
+class BigInteger
 {
     /**
      * Main Engine
@@ -69,6 +69,24 @@ class BigInteger implements \Serializable
      */
     private $value;
 
+    /**
+     * Mode independent value used for serialization.
+     *
+     * @see self::__sleep()
+     * @see self::__wakeup()
+     * @var string
+     */
+    private $hex;
+
+    /**
+     * Precision (used only for serialization)
+     *
+     * @see self::__sleep()
+     * @see self::__wakeup()
+     * @var int
+     */
+    private $precision;
+
     /**
      * Sets engine type.
      *
@@ -390,39 +408,38 @@ class BigInteger implements \Serializable
      *
      * Will be called, automatically, when serialize() is called on a BigInteger object.
      *
-     * phpseclib 1.0 serialized strings look like this:
-     * O:15:"Math_BigInteger":1:{s:3:"hex";s:18:"00ab54a98ceb1f0ad2";}
+     * __sleep() / __wakeup() have been around since PHP 4.0
      *
-     * phpseclib 3.0 serialized strings look like this:
-     * C:25:"phpseclib\Math\BigInteger":42:{a:1:{s:3:"hex";s:18:"00ab54a98ceb1f0ad2";}}
+     * \Serializable was introduced in PHP 5.1 and deprecated in PHP 8.1:
+     * https://wiki.php.net/rfc/phase_out_serializable
+     *
+     * __serialize() / __unserialize() were introduced in PHP 7.4:
+     * https://wiki.php.net/rfc/custom_object_serialization
      *
      * @return string
      */
-    public function serialize()
+    public function __sleep()
     {
-        $val = ['hex' => $this->toHex(true)];
-        $precision = $this->value->getPrecision();
-        if ($precision > 0) {
-            $val['precision'] = $precision;
+        $this->hex = $this->toHex(true);
+        $vars = ['hex'];
+        if ($this->getPrecision() > 0) {
+            $vars[] = 'precision';
         }
-        return serialize($val);
+        return $vars;
     }
 
     /**
      * Serialize
      *
      * Will be called, automatically, when unserialize() is called on a BigInteger object.
-     *
-     * @param string $serialized
      */
-    public function unserialize($serialized)
+    public function __wakeup()
     {
-        $r = unserialize($serialized);
-        $temp = new static($r['hex'], -16);
+        $temp = new static($this->hex, -16);
         $this->value = $temp->value;
-        if (isset($r['precision'])) {
+        if ($this->precision > 0) {
             // recalculate $this->bitmask
-            $this->setPrecision($r['precision']);
+            $this->setPrecision($this->precision);
         }
     }
 
diff --git a/phpseclib/Math/BigInteger/Engines/Engine.php b/phpseclib/Math/BigInteger/Engines/Engine.php
index 10dd994b..17b1996c 100644
--- a/phpseclib/Math/BigInteger/Engines/Engine.php
+++ b/phpseclib/Math/BigInteger/Engines/Engine.php
@@ -28,7 +28,7 @@ use phpseclib3\Common\Functions\Strings;
  * @author  Jim Wigginton <terrafrost@php.net>
  * @access  public
  */
-abstract class Engine implements \Serializable
+abstract class Engine
 {
     /**
      * Holds the BigInteger's value
@@ -65,6 +65,15 @@ abstract class Engine implements \Serializable
      */
     protected $reduce;
 
+    /**
+     * Mode independent value used for serialization.
+     *
+     * @see self::__sleep()
+     * @see self::__wakeup()
+     * @var string
+     */
+    protected $hex;
+
     /**
      * Default constructor
      *
@@ -295,31 +304,29 @@ abstract class Engine implements \Serializable
      *
      * @return string
      */
-    public function serialize()
+    public function __sleep()
     {
-        $val = ['hex' => $this->toHex(true)];
+        $this->hex = $this->toHex(true);
+        $vars = ['hex'];
         if ($this->precision > 0) {
-            $val['precision'] = $this->precision;
+            $vars[] = 'precision';
         }
-        return serialize($val);
+        return $vars;
     }
 
     /**
      * Serialize
      *
      * Will be called, automatically, when unserialize() is called on a BigInteger object.
-     *
-     * @param string $serialized
      */
-    public function unserialize($serialized)
+    public function __wakeup()
     {
-        $r = unserialize($serialized);
-        $temp = new static($r['hex'], -16);
+        $temp = new static($this->hex, -16);
         $this->value = $temp->value;
         $this->is_negative = $temp->is_negative;
-        if (isset($r['precision'])) {
+        if ($this->precision > 0) {
             // recalculate $this->bitmask
-            $this->setPrecision($r['precision']);
+            $this->setPrecision($this->precision);
         }
     }