Construction of Differential Characteristics in ARX Designs Application to Skein

In this paper, we study differential attacks against ARX schemes. We build upon the generalized characteristics of de Cannière and Rechberger and the multi-bit constraints of Leurent. We describe a more efficient way to propagate multi-bit constraints, that allows us to use the complete set of 2 2.5-bit constraints, instead of the reduced sets used by Leurent. As a result, we are able to build complex non-linear differential characteristics for reduced versions of the hash function Skein. We present several characteristics for use in various attack scenarios; this results in attacks with a relatively low complexity, in relatively strong settings. In particular, we show practical free-start and semi-free-start collision attacks for 20 rounds and 12 rounds of Skein-256, respectively. To the best of our knowledge, these are the first examples of complex differential trails built for pure ARX designs. We believe this is an important work to assess the security of ARX designs against differential cryptanalysis. Our improved tools will be publicly available with the final version of this paper.