Paper 2020/068

Further Clarification on Mantin's Digraph Repetition Bias in RC4

Pranab Chakraborty and Subhamoy Maitra

Abstract

In this paper we provide a theoretical argument towards an unsolved question related to Mantin's ``Digraph Repetition Bias" (Eurocrypt 2005) that is observed in the key-stream of RC4. The open question, that depends on the observation that arrival of four consecutive same bytes (of the form $AAAA$) in RC4 key-stream is slightly negatively biased, was posed by Bricout et al [Des. Codes Cryptogr. (2018) 86:743-770] in 2016. Moreover, for the first time, we consider the ``Reverse Digraph Repetition Bias" and show that there is significant negative bias in arrival of $ABBA$ ($A, B$ two distinct bytes) in RC4 key-stream.

Note: Added a new section on Reverse Digraph Repetition Bias.