Design of S-boxes by concatenation of rotation-symmetric S-boxes

Date

2016

Author

Baloğlu, Sevdenur

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In most of the block cipher cryptosystems, the substitution boxes, or so-called S-boxes, are the only nonlinear components, and hence the strength of these cryptosystems depends heavily on the cryptographic properties of the S-boxes. In this thesis, it is aimed to design S-boxes which are on one hand strong in terms of traditional cryptographic properties such as nonlinearity, differential uniformity, absolute indicator and algebraic degree, and on the other hand resistant to side-channel attacks such as differential power analysis (DPA). In the direction of this aim, an efficient exhaustive search algorithm is proposed to generate 6x6 bijective S-boxes situated in a class of symmetric S-boxes under the permutation tau(x)=(x0, x2, x3, x4, x5, x1), where x=(x0, x1,..., x5). Due to the symmetry property of tau(S(x))=S( tau(x)) for all x, any S-box S in this class can be considered as a construction obtained by the concatenation of 5x5 rotation-symmetric S-boxes (RSSBs). In this algorithm, using the combinatorial properties of RSSBs and eliminating the affine equivalent concatenations, the search space of this class is reduced from 2^(61,28) to 2^(48,47). At the end of this search, it is found that in this class there exist 2^(37,56) S-boxes having the best known nonlinearity 24 and among them the number of differentially 4-uniform ones is 2^(33,99), which indicates that the concatenation method provides a rich class in terms of high nonlinearity and low differential uniformity.

Subject Keywords

Ciphers., Cryptography., Algebra, Boolean., Computer algorithms.

URI

http://etd.lib.metu.edu.tr/upload/12620505/index.pdf
https://hdl.handle.net/11511/25980

Collections

Graduate School of Applied Mathematics, Thesis

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Citation Formats

S. Baloğlu, “Design of S-boxes by concatenation of rotation-symmetric S-boxes,” M.S. - Master of Science, Middle East Technical University, 2016.