The nonhomomorphicity of S-boxes

Abstract. In this paper, we introduce the concept of kth-order nonhomomorphicity of mappings or S-boxes as an alternative indicator that forecasts nonlinearity characteristics of an S-box, where k 4 is even. Main results of this paper include: (1) we show that nonhomomorphicity, especially the 4th order nonhomomorphicity, can be precisely expressed by using other important nonlinear indicators of an S-box. (2) we establish tight lower and upper bounds on the nonhomomorphicity of S-boxes, (3) we identify the mean of nonhomomorphicity over all the S-boxes with the same size and the relative nonhomomorphicity of an S-box, both of which are useful in estimating, statistically, the nonhomomorphicity of an S-box. Key Words Sequences, Boolean Functions, S-boxes, Cryptanalysis, Cryptography, Nonhomomorphicity. 1 Motivation of this Research The so-called S-boxes, which are functionally identical to mappings or tuples of Boolean functions, are of critical importance to the strength of a block ci...

• Type: Conference
• Year: 1998
• Where: ICISC
• Authors: Yuliang Zheng, Xian-Mo Zhang
• Keywords: Boolean Functions, ICISC 1998, ICISC 2007, Important Nonlinear Indicators, Key Words Sequences