A Strategy for Constructing Fast Round Functions with Practical Security Against Differential and Linear Cryptanalysis

摘要

In this paper, we study a strategy for constructing fast and practically secure round functions that yield sufficiently small values of the maximum differential and linear probabilities p, q. We consider mn-bit round functions with 2-round SPN structure for Feistel ciphers. In this strategy, we regard a linear transformation layer as an n x n matrix P over {0,1}. We describe the relationship between the matrix representation and the actual construction of the linear transformation layer. We propose a search algorithm for constructing the optimal linear transformation layer by using the matrix representation in order to minimize probabilities p, q as much possible. Furthermore, by this algorithm, we determine the optimal linear transformation layer that provides p ≤ p_s~5, q ≤ q_s~5 in the case of n = 8, where p_e, q_s denote the maximum differential and linear probabilities of s-box.