Refined Glimpse Correlations of RC4

Abstract

RC4 stream cipher, designed by Rivest in 1987, is widely used in various standard protocols and commercial applications. After the disclosure of RC4 algorithm in 1994, many cryptanalytic results on RC4 have been reported. In 1996, Jenkins discovered correlations between a keystream byte and an internal state variable. This is known as the Glimpse theorem. In 2013, Maitra and Sen Gupta proved the Glimpse theorem and showed other correlations between two consecutive keystream bytes and an internal state variable. This is called the long-term Glimpse. These correlations provide only cases with positive biases, and hold generally on any round. In this paper, we refine known Glimpse correlations from two aspects. One is to find new positive or negative biases on all values in addition to a known value. The other is to provide precise biases on specific rounds. As a result, we can discover 6 cases with several new biases, and prove these cases theoretically. From the first refinement, combining our new biases with known one, the long-term Glimpse with positive biases is integrated into a whole. From the second refinement, we can successfully find that two correlations on specific rounds become an impossible condition.