diff --git a/aux/ristretto/ristretto.sage b/aux/ristretto/ristretto.sage
index 0f217a6..68682da 100644
--- a/aux/ristretto/ristretto.sage
+++ b/aux/ristretto/ristretto.sage
@@ -529,11 +529,26 @@ def test(cls,n):
     Q = cls()
     for i in xrange(n):
         #print binascii.hexlify(Q.encode())
-        QQ = cls.decode(Q.encode())
+        QE = Q.encode()
+        QQ = cls.decode(QE)
         if QQ != Q: raise TestFailedException("Round trip %s != %s" % (str(QQ),str(Q)))
+    
+        # Testing s -> 1/s: encodes -point on cofactor 
+        s = cls.bytesToGf(QE)
+        if s != 0:
+            ss = cls.gfToBytes(1/s,mustBePositive=True)
+            try:
+                QN = cls.decode(ss)
+                if cls.cofactor == 8:
+                    raise TestFailedException("1/s shouldnt work for cofactor 8")
+                if QN != -Q:
+                    raise TestFailedException("s -> 1/s should negate point for cofactor 4")
+            except InvalidEncodingException as e:
+                # Should be raised iff cofactor==8
+                if cls.cofactor == 4:
+                    raise TestFailedException("s -> 1/s should work for cofactor 4")
         
         QT = Q
-        QE = Q.encode()
         for h in xrange(cls.cofactor):
             QT = QT.torque()
             if QT.encode() != QE: