An equivalent condition on the switching construction of differentially 4-uniform permutations on from the inverse function. Issue 6 (3rd June 2017) - Chen, Xi; Deng, Yazhi; Zhu, Min; Qu, Longjiang
ABSTRACT: Differentially 4-uniform permutations onF 2 2 k with high nonlinearity are often chosen as substitution boxes in block ciphers. Recently, Qu et al. used the powerful switching method to construct permutations with low differential uniformity from the inverse function [Qu et al., Constructing differentially 4-uniform permutations overF 2 2 k via the switching method, IEEE Trans. Inform. Theory 59(7) (2013), pp. 4675–4686, Qu et al., More constructions of differentially 4-uniform permutations onF 2 2 k, Des. Codes Cryptogr. DOI 10.1007/s10623-014-0006-x] and proposed a sufficient but not necessary condition for these permutations to be differentially 4-uniform. In this paper, a sufficient and necessary condition is presented. We also give a compact estimation for the number of constructed differentially 4-uniform permutations. Comparing with those constructions in [11, 12 ], the number of functions constructed here is much bigger. As an application, a new class of differentially 4-uniform permutations is constructed. The obtained functions in this paper may provide more choices for the design of substitution boxes.