Abstract
In this paper, we investigate the Bracken-Leander power function F(x)=x22k+2k+1 over F24k where k is an odd positive integer, and first give a much shorter proof on the binary representation of its inverse based on the Chinese Remainder Theorem. Besides, based on a known connection between the differential spectrum and Fourier spectrum of a function, we also give another shorter proof to determine the differential spectrum of F(x). These two results are solved recently with quite involved skills by Kölsch (2020) [7], Xiong and Yan (2017) [10], respectively. We hope that our work is helpful to have a better understanding of this function because of its importance in the construction of S-boxes in block ciphers.
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