On CCZ-inequivalence of some families of almost perfect nonlinear functions to permutations

2021 ◽  
Author(s):  
Faruk Göloğlu ◽  
Jiří Pavlu̇
Keyword(s):  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Almost Perfect Nonlinear Functions

scholarly journals Monomial Generalized Almost Perfect Nonlinear Functions

2020 ◽  
Vol 31 (03) ◽  
pp. 411-419
Author(s):  
Masamichi Kuroda
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Algebraic Degree ◽  
Apn Functions ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Basic Properties ◽  
Almost Perfect Nonlinear Functions

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In particular, on finite fields of even characteristic, GAPN functions coincide with APN functions. In this paper, we study monomial GAPN functions for odd characteristic. We give monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic. Moreover, we define a generalization of exceptional APN functions and give typical examples.

scholarly journals NON-BOOLEAN ALMOST PERFECT NONLINEAR FUNCTIONS ON NON-ABELIAN GROUPS

2011 ◽  
Vol 22 (06) ◽  
pp. 1351-1367 ◽  
Author(s):  
LAURENT POINSOT ◽  
ALEXANDER POTT
Keyword(s):  
Finite Group ◽  
Boolean Functions ◽  
Abelian Groups ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Almost Perfect Nonlinear Functions ◽  
A Finite Group

The purpose of this paper is to present extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.

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