Go home now Header Background Image
Submission Procedure
share: |
Follow us
Volume 6 / Issue 8

available in:   PDF (276 kB) PS (102 kB)
Similar Docs BibTeX   Write a comment
Links into Future
DOI:   10.3217/jucs-006-08-0830


The kth-Order Nonhomomorphicity of S-Boxes

Yuliang Zheng (School of Network Computing, Monash University, Australia)

Xian-Mo Zhang (School of Information Technology and Computer Science, University of Wollongong, Australia)

Abstract: 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 size. It is hoped that these results on nonhomomorphicity facilitate the analysis and design of S-boxes.

Keywords: Boolean Functions, S-boxes, cryptanalysis, cryptography, nonhomomorphicity

Categories: E.3