A new class of RC4 colliding key pairs with greater hamming distance

Abstract

In this paper, we discovered a new class of colliding key pairs of RC4, namely, two different secret keys generate the same internal state after RC4's key scheduling algorithm. This is to our knowledge the first discovery of RC4 colliding keys with hamming distance greater than one, that is, the colliding key pairs we found can differ from each other at three different positions, and the value difference between these positions needs not be fixed. We analyzed the transition pattern and evaluated the probability of the existence of this new class of colliding key pairs. Our result shows that RC4 key collision could be achieved by two keys with greater hamming distance than the ones found in [1] and [2]. And this newly discovered class of colliding key pairs reveals the weakness that RC4's key scheduling algorithm could generate even more colliding keys. We also proposed an algorithm for searching colliding key pairs within this new class. Some concrete colliding key pairs are demonstrated in this paper, among which 55-byte colliding key pair is the shortest one we found by using our algorithm within one hour time. © Springer-Verlag Berlin Heidelberg 2010.