Some Studies on CCZ-Equivalence of the Inverse Function

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2021-9-28

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Fidan, Mehtap

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Most cryptographic systems, like block ciphers, depend heavily on vectorial Boolean functions. A function with good cryptological properties should have low differential uniformity which is invariant under some equivalence classes. The more general one of these is CCZ-equivalence which is introduced by Carlet, Charpin and Zinoviev in 1998. In cryptography, CCZ-equivalence gained an interest since it preserves many significant properties like differential uniformity. Looking for permutations within the CCZ-class of a function for the construction of S-boxes used in block ciphers is also intriguing. In this thesis, we presented a detailed description on the results of Kölsch's paper about nonexistence of permutation polynomials in the form $L_m(x^{-1})+L_{m'}(x)$ over binary finite field. This proves that every permutation CCZ-equivalent to the inverse function is also affine equivalent to it. We also gave a criterian to be a permutation polynomial which is verified by using Kloosterman sums.

Subject Keywords

CCZ-equivalence, kloosterman sum, permutation polynomial, inverse function

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https://hdl.handle.net/11511/92890

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

M. Fidan, “Some Studies on CCZ-Equivalence of the Inverse Function,” M.S. - Master of Science, Middle East Technical University, 2021.