Convergence in Differential Distributions

Abstract

Differential cryptanalysis is a general attack based on the notion of differences. The success of the attack is derived from the proba- bility of a differential. While it has been observed that the distribution of differentials can be modeled as a Markov chain, there have been few anal- yses that take advantage of this observation because of the prohibitive computations involved. In this paper we apply the Markov approach to the differentially 2-uniform mappings, and show that they converge ex- ponentially fast with high probability.