Further constructions and characterizations of generalized almost perfect nonlinear functions

Sălăgean, Ana and Özbudak, Ferruh (2023) Further constructions and characterizations of generalized almost perfect nonlinear functions. Cryptography and Communications . ISSN 1936-2447 (Print) 1936-2455 (Online) Published Online First https://dx.doi.org/10.1007/s12095-023-00647-1

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APN (almost perfect nonlinear) functions over finite fields of even characteristic are interesting and have many applications to the design of symmetric ciphers resistant to differential attacks. This notion was generalized to GAPN (generalized APN) for arbitrary characteristic p by Kuroda and Tsujie. In this paper, we completely classify GAPN monomial functions xd for the case when the exponent d has exactly two non-zero digits when represented in base p; these functions can be viewed as generalizations of the APN Gold functions. In particular, we characterise all the monomial GAPN functions over Fp2 . We also obtain a new characterization for certain GAPN functions over Fpn of algebraic degree p using the multivariate algebraic normal form; this allows us to explicitly construct a family of GAPN functions of algebraic degree p for n= 3 and arbitrary prime p≥ 3 .
Item Type: Article
Uncontrolled Keywords: Algebraic degree; APN function; Discrete derivative; GAPN function
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ferruh Özbudak
Date Deposited: 06 Aug 2023 22:03
Last Modified: 06 Aug 2023 22:03
URI: https://research.sabanciuniv.edu/id/eprint/47358

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