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Constructing differentially 4-uniform permutations over GF(22m) from quadratic APN permutations over GF(22m+1)

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Abstract

In this paper, by means of the idea proposed by Carlet (ACISP 1-15, 2011), 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 \({\mathbb{F}_2^{2m}}\) .

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Authors and Affiliations

  1. The State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Yongqiang Li & Mingsheng Wang

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  1. Yongqiang Li
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  2. Mingsheng Wang
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Correspondence to Mingsheng Wang.

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Communicated by C. Carlet.

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Li, Y., Wang, M. Constructing differentially 4-uniform permutations over GF(22m) from quadratic APN permutations over GF(22m+1). Des. Codes Cryptogr. 72, 249–264 (2014). https://doi.org/10.1007/s10623-012-9760-9

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  • DOI: https://doi.org/10.1007/s10623-012-9760-9

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