Abstract
The aim of this paper is to construct S-boxes of different sizes with good cryptographic properties. An algebraic construction for bijective S-boxes is described. It uses quasi-cyclic representations of the binary simplex code. Good S-boxes of sizes 4, 6, 8, 9, 10, 11, 12, 14, 15, 16 and 18 are obtained.
Highlights
S-boxes are among the most common and essential components of the block ciphers
The popular techniques for constructing S-boxes can be classified into three categories: algebraic structures, pseudo-random generation and different heuristic approaches
In the case of bijective S-box, instead of a generator matrix we can consider a (2n − 1) × 2n matrix whose rows are all nonzero codewords of the given extended simplex code
Summary
S-boxes are among the most common and essential components of the block ciphers. They provide block ciphers with resistance to known and potential cryptanalytic attacks. Significant research effort has been made in developing methods for constructing S-boxes with optimal parameters and desirable cryptographic properties. Properties as well as various techniques and methods for constructing good S-boxes have been investigated. The aim of this paper is the constructions of bijective S-boxes of different sizes with good cryptographic properties. The bijective S-boxes of size n = 4 have been extensively studied, classifications have been made, criteria of optimality are defined [12, 16, 17]. A general classification of all optimal S-boxes of size n = 4 is given in the work of Leander and Poschmann [12] in 2007, where the authors make a comprehensive analysis and find all classes of affine equivalent S-boxes for which they explore linearity, differential uniformity, and algebraic degree.
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