On cryptographic properties of ( n + 1)-bit S-boxes constructed by known n -bit S-boxes
Yu Zhou, Daoguang Mu, Xinfeng Dong · Journal of Mathematical Cryptology · 2020
Abstract S-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for ( n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of ( n + 1)-bit S-boxes, and one necessary and sufficient conditions of ( n + 1)-bit S-boxes satisfying m -order resilient. Meanwhile, we also give one characterization of ( n + 1)-bit S-boxes satisfying t -order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n -bit S-box S 0 and the ( n + 1)-bit S-box S (which is constructed by S 0 ).