diff --git a/IPython/kernel/zmq/session.py b/IPython/kernel/zmq/session.py
index d4b8b13..a85988e 100644
--- a/IPython/kernel/zmq/session.py
+++ b/IPython/kernel/zmq/session.py
@@ -28,6 +28,7 @@ import hmac
 import logging
 import os
 import pprint
+import random
 import uuid
 from datetime import datetime
 
@@ -310,8 +311,16 @@ class Session(Configurable):
             self.auth = hmac.HMAC(new)
         else:
             self.auth = None
+    
     auth = Instance(hmac.HMAC)
+    
     digest_history = Set()
+    digest_history_size = Integer(2**16, config=True,
+        help="""The maximum number of digests to remember.
+        
+        The digest history will be culled when it exceeds this value.
+        """
+    )
 
     keyfile = Unicode('', config=True,
         help="""path to file containing execution key.""")
@@ -699,6 +708,30 @@ class Session(Configurable):
             idents, msg_list = msg_list[:idx], msg_list[idx+1:]
             return [m.bytes for m in idents], msg_list
 
+    def _add_digest(self, signature):
+        """add a digest to history to protect against replay attacks"""
+        if self.digest_history_size == 0:
+            # no history, never add digests
+            return
+        
+        self.digest_history.add(signature)
+        if len(self.digest_history) > self.digest_history_size:
+            # threshold reached, cull 10%
+            self._cull_digest_history()
+    
+    def _cull_digest_history(self):
+        """cull the digest history
+        
+        Removes a randomly selected 10% of the digest history
+        """
+        current = len(self.digest_history)
+        n_to_cull = max(int(current // 10), current - self.digest_history_size)
+        if n_to_cull >= current:
+            self.digest_history = set()
+            return
+        to_cull = random.sample(self.digest_history, n_to_cull)
+        self.digest_history.difference_update(to_cull)
+    
     def unserialize(self, msg_list, content=True, copy=True):
         """Unserialize a msg_list to a nested message dict.
 
@@ -734,8 +767,8 @@ class Session(Configurable):
             if not signature:
                 raise ValueError("Unsigned Message")
             if signature in self.digest_history:
-                raise ValueError("Duplicate Signature: %r"%signature)
-            self.digest_history.add(signature)
+                raise ValueError("Duplicate Signature: %r" % signature)
+            self._add_digest(signature)
             check = self.sign(msg_list[1:5])
             if not signature == check:
                 raise ValueError("Invalid Signature: %r" % signature)
diff --git a/IPython/kernel/zmq/tests/test_session.py b/IPython/kernel/zmq/tests/test_session.py
index d039462..df7b77b 100644
--- a/IPython/kernel/zmq/tests/test_session.py
+++ b/IPython/kernel/zmq/tests/test_session.py
@@ -204,4 +204,22 @@ class TestSession(SessionTestCase):
         self.assertEqual(session.bsession, session.session.encode('ascii'))
         self.assertEqual(b'stuff', session.bsession)
 
+    def test_zero_digest_history(self):
+        session = ss.Session(digest_history_size=0)
+        for i in range(11):
+            session._add_digest(uuid.uuid4().bytes)
+        self.assertEqual(len(session.digest_history), 0)
+
+    def test_cull_digest_history(self):
+        session = ss.Session(digest_history_size=100)
+        for i in range(100):
+            session._add_digest(uuid.uuid4().bytes)
+        self.assertTrue(len(session.digest_history) == 100)
+        session._add_digest(uuid.uuid4().bytes)
+        self.assertTrue(len(session.digest_history) == 91)
+        for i in range(9):
+            session._add_digest(uuid.uuid4().bytes)
+        self.assertTrue(len(session.digest_history) == 100)
+        session._add_digest(uuid.uuid4().bytes)
+        self.assertTrue(len(session.digest_history) == 91)