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More New Classes of Differentially 4Uniform Permutations with Good Cryptographic Properties
Jie PENG Chik How TAN Qichun WANG Jianhua GAO Haibin KAN
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.6
pp.945952 Publication Date: 2018/06/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.945
Type of Manuscript: PAPER Category: Cryptography and Information Security Keyword: permutation polynomial, differentially 4uniform, algebraic degree, nonlinearity, CCZequivalence,
Full Text: PDF(1.6MB)>>
Summary:
Research on permutation polynomials over the finite field F_{22k} with significant cryptographical properties such as possibly low differential uniformity, possibly high nonlinearity and algebraic degree has attracted a lot of attention and made considerable progress in recent years. Once used as the substitution boxes (Sboxes) in the block ciphers with Substitution Permutation Network (SPN) structure, this kind of polynomials can have a good performance against the classical cryptographic analysis such as linear attacks, differential attacks and the higher order differential attacks. In this paper we put forward a new construction of differentially 4uniformity permutations over F_{22k} by modifying the inverse function on some specific subsets of the finite field. Compared with the previous similar works, there are several advantages of our new construction. One is that it can provide a very large number of CarletCharpinZinoviev equivalent classes of functions (increasing exponentially). Another advantage is that all the functions are explicitly constructed, and the polynomial forms are obtained for three subclasses. The third advantage is that the chosen subsets are very large, hence all the new functions are not close to the inverse function. Therefore, our construction may provide more choices for designing of Sboxes. Moreover, it has been checked by a software programm for k=3 that except for one special function, all the other functions in our construction are CarletCharpinZinoviev equivalent to the existing ones.

