Generalized RC4 Key Collisions and Hash Collisions

In this paper, we discovered that RC4 can generate colliding key pairs with various hamming distances, other than those found by Matsui (with hamming distance one), and by Chen and Miyaji (with hamming distance three). We formalized RC4 colliding key pairs into two large patterns, namely, Transitional pattern and Self-Absorbing pattern, according to the behavior during KSA. The colliding key pairs found in the previous researches can be seen as either subsets of the Transitional pattern or of the Self-Absorbing pattern. We analyzed both patterns and clarified the relations among the probability of key collision, key length and hamming distances which yield the colliding key pairs. Also we show how to make use of the RC4 key collision patterns to find collisions of RC4-Hash function which was proposed in INDOCRYPT 2006. Some concrete experimental results (RC4-Hash collision and RC4 colliding key pairs) are also given in this paper.