New secondary constructions of differentially 4-uniform permutations over

ABSTRACT

In this paper, we generalize the switching method and present a method to construct new differentially 4-uniform permutations from two known ones by determining the corresponding cycle sets. As for applications, by determining all the cycle sets of $(x+1{)}^{-1}+1$ and $(x+1{)}^{-1}+\omega$ related to the inverse functions, respectively, we present two efficient constructions of differentially 4-uniform permutations. Moreover, it has been checked by the Magma software for small n that, both constructions give many new Carlet–Charpin–Zinoviev (CCZ)-inequivalent classes of functions that are not CCZ-equivalent to the known functions.

KEYWORDS:

• S-box
• differentially 4-uniform permutation
• cycle set
• algebraic degree
• nonlinearity

2010 AMS SUBJECT CLASSIFICATIONS:

• 94A60
• 11T71
• 14G50
• 68P25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partly supported by the National Natural Science Foundation of China under Grants [61202471] and [61572189], and partly supported by Shanghai Key Laboratory of Intelligent Information Processing under Grant [IIPL-2014-005].