IACR News item: 27 August 2014
Xi Chen, Yazhi Deng, Min Zhu, Longjiang Qu
ePrint Reportwhere f is a Boolean function. They proved that if f is a preferred Boolean function (PBF), then G is a permutation polynomial over $\\gf_{2^n}$ whose differential uniformity is at most 4. However, as pointed out in [9],f is a PBF is a sufficient but not necessary condition. In this paper, a sufficient and necessary condition for G to be a differentially 4-uniform permutation is presented. We also show that G can not be an almost perfect nonlinear (APN) function. As an application, a new class of differentially 4-uniform permutations where f are not PBFs are constructed. By comparing this family with previous constructions, the number of permutations here is much bigger. The obtained functions in this paper may provide more choices for the design of Substitution boxes.
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