Relating Differential Distribution Tables to Other Properties of of Substitution Boxes |
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| Authors: | Xian-Mo Zhang Yuliang Zheng Hideki Imai |
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| Affiliation: | (1) School of Information Technology and Computer Science, University of Wollongong, Wollongong, NSW 2522, Australia;(2) School of Computing and Information Technology, Monash University, Frankston, Melbourne, VIC 3199, Australia;(3) The Third Department, Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo, 106-8558, Japan |
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| Abstract: | Due to the success of differential and linear attacks on a large number of encryption algorithms, it is important to investigate relationships among various cryptographic, including differential and linear, characteristics of an S-box (substitution box). After discussing a precise relationship among three tables, namely the difference, auto-correlation and correlation immunity distribution tables, of an S-box, we develop a number of results on various properties of S-boxes. More specifically, we show (1) close connections among three indicators of S-boxes, (2) a tight lower bound on the sum of elements in the leftmost column of its differential distribution table, (3) a non-trivial and tight lower bound on the differential uniformity of an S-box, and (4) two upper bounds on the nonlinearity of S-boxes (one for a general, not necessarily regular, S-box and the other for a regular S-box). |
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| Keywords: | Boolean Functions cryptography differential attack linear attack nonlinearity S-boxes |
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