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The Kth-Order Nonhomomorphicity Of S-Boxes, Yuliang Zheng, Xian-Mo Zhang

Faculty of Engineering and Information Sciences - Papers: Part A

Nonhomomorphicity is a new nonlinearity criterion of a mapping or S-box used in a private key encryption algorithm. An important advantage of nonhomomorphicity over other nonlinearity criteria is that the value of nonhomomorphicity is easy to estimate by the use of a fast statistical method. Due to the Law of Large Numbers, such a statistical method is highly reliable. Major contributions of this paper are (1) to explicitly express the nonhomomorphicity by other nonlinear characteristics, (2) to identify tight upper and lower bounds on nonhomomorphicity, and (3) to find the mean of nonhomomorphicity over all the S-boxes with the same …