Abstract
An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. In addition, we show that our proof techniques allow us to treat in a unified fashion all quadratic permutations, regardless of the underlying construction methods. This greatly simplifies the proofs for a number of known results on nonlinearity characteristics of quadratic permutations. As a by-product, we obtain a negative answer to an open problem regarding the existence of differentially 2-uniform quadratic permutations on an even dimensional vector space.
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Seberry, J., Zhang, XM., Zheng, Y. (1995). Relationships among nonlinearity criteria. In: De Santis, A. (eds) Advances in Cryptology — EUROCRYPT'94. EUROCRYPT 1994. Lecture Notes in Computer Science, vol 950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053452
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DOI: https://doi.org/10.1007/BFb0053452
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