Generating binary diffusion layers with maximum/high branch numbers and low search complexity

Abstract

In this paper, we propose a new method to generate n × n binary matrices (for n = k·2t where k and t are positive integers) with a maximum/high of branch numbers and a minimum number of fixed points by using 2t×2t Hadamard (almost) maximum distance separable matrices and k × k cyclic binary matrix groups. By using the proposed method, we generate n × n (for n = 6, 8, 12, 16, and 32) binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m × m circulant matrices to generate n × n(for n = k·m) binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 × 16, 48 × 48, and 64 × 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright © 2016 John Wiley & Sons, Ltd.