scholarly journals Determining the Walsh spectra of Taniguchi's and related APN-functions

2019 ◽  
Vol 60 ◽  
pp. 101577
Author(s):  
Nurdagül Anbar ◽  
Tekgül Kalaycı ◽  
Wilfried Meidl
Keyword(s):  
Apn Functions ◽  
Walsh Spectra

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 Two Boolean Functions with Five-Valued Walsh Spectra and High Nonlinearity

2015 ◽  
Vol 26 (05) ◽  
pp. 537-556 ◽  
Author(s):  
Xiwang Cao ◽  
Lei Hu
Keyword(s):  
Finite Fields ◽  
Boolean Functions ◽  
Exponential Sums ◽  
New Method ◽  
High Nonlinearity ◽  
Walsh Spectra ◽  
And Diffusion ◽  
Confusion And Diffusion

For cryptographic systems the method of confusion and diffusion is used as a fundamental technique to achieve security. Confusion is reflected in nonlinearity of certain Boolean functions describing the cryptographic transformation. In this paper, we present two Boolean functions which have low Walsh spectra and high nonlinearity. In the proof of the nonlinearity, a new method for evaluating some exponential sums over finite fields is provided.

Quantum algorithms for learning Walsh spectra of multi-output Boolean functions

2019 ◽  
Vol 18 (6) ◽  
Author(s):  
Jingyi Cui ◽  
Jiansheng Guo ◽  
Linhong Xu ◽  
Mingming Li
Keyword(s):  
Boolean Functions ◽  
Quantum Algorithms ◽  
Walsh Spectra
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