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Constructing differentially 4-uniform permutations over \(\mathrm{GF}(2^{2m})\) from quadratic APN permutations over \(\mathrm{GF}(2^{2m+1})\). (English) Zbl 1319.94077
Summary: In this paper, by means of the idea proposed by C. Carlet [ACISP 2011, Lect. Notes Comput. Sci. 6812, 1–15 (2011; Zbl 1279.94060)], differentially 4-uniform permutations with the best known nonlinearity over \(\mathbb{F}_{2^{2m}}\) are constructed using quadratic APN permutations over \(\mathbb{F}_{2^{2m+1}}\). Special constructions are given using the Gold functions. The algebraic degree of the constructions and their compositional inverses is also investigated. One construction and its compositional inverse both have algebraic degree \(m+1\) over \(\mathbb{F}_2^{2m}\).

MSC:
94A60 Cryptography
06E30 Boolean functions
11T06 Polynomials over finite fields
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