scholarly journals Kim-type APN functions are affine equivalent to Gold functions

2021 ◽  
Author(s):  
Benjamin Chase ◽  
Petr Lisoněk
Keyword(s):  
Apn Functions

On equivalence between known polynomial APN functions and power APN functions

2021 ◽  
Vol 71 ◽  
pp. 101762
Author(s):  
Qianhong Wan ◽  
Longjiang Qu ◽  
Chao Li
Keyword(s):  
Apn Functions

scholarly journals Partially APN functions with APN-like polynomial representations

2020 ◽  
Vol 88 (6) ◽  
pp. 1159-1177
Author(s):  
Lilya Budaghyan ◽  
Nikolay Kaleyski ◽  
Constanza Riera ◽  
Pantelimon Stănică
Keyword(s):  
Apn Functions ◽  
Polynomial Representations

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.

Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Ulrich Dempwolff ◽  
Yves Edel
Keyword(s):  
Apn Functions ◽  
Dimensional Dual Hyperovals

AbstractIn [J. Algebraic Combin. 39 (2014), 457–496] an extension construction of (

scholarly journals Correction to: Algebraic Construction of Near-Bent and APN Functions

2020 ◽  
Vol 30 (2) ◽  
Author(s):  
Prasanna Poojary ◽  
Harikrishnan Panackal ◽  
Vadiraja G. R. Bhatta
Keyword(s):  
Apn Functions ◽  
Algebraic Construction

Constructing New Piecewise Differentially 4-Uniform Permutations from Known APN Functions

2015 ◽  
Vol 26 (05) ◽  
pp. 599-609
Author(s):  
Guangkui Xu ◽  
Xiwang Cao
Keyword(s):  
Apn Functions

A method for constructing piecewise differentially 4-uniform permutations has been recently introduced by Zha, Hu and Sun. By using this method, we provide two new infinite families of differentially 4-uniform permutations from the known APN functions. The CCZ inequivalence between these constructed functions and the known differentially 4-uniform permutations are also investigated by computation.

scholarly journals New semifields, PN and APN functions

2009 ◽  
Vol 54 (3) ◽  
pp. 189-200 ◽  
Author(s):  
Jürgen Bierbrauer
Keyword(s):  
Apn Functions
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