A strategy for constructing fast round functions with practical security against differential and linear cryptanalysis

Abstract

In this paper, we study a strategy for constructing fast and practically secure round functions that yield suffciently 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× 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≤ p5s; q≤ q5s in the case of n = 8, where p s; q sdenote the maximum differential and linear probabilities of s-box.