English

An Infinite Family of Quadratic Quadrinomial APN Functions

General Mathematics 2007-07-10 v1
Authors: Carl Bracken , Eimear Byrne , Nadya Markin , Gary McGuire
View on arXiv ↗ PDF ↗

Abstract

We present an infinite family of quadratic APN functions on a finite field of dimension over GF(2) divisible by 3.

Keywords

APN functions quadratic functions quadrinomials finite fields GF(2) infinite family cryptography

Cite

@article{arxiv.0707.1223,
  title  = {An Infinite Family of Quadratic Quadrinomial APN Functions},
  author = {Carl Bracken and Eimear Byrne and Nadya Markin and Gary McGuire},
  journal= {arXiv preprint arXiv:0707.1223},
  year   = {2007}
}

Comments

7pgs

Related papers

View all related →
Information Theory · Computer Science
A Few More Quadratic APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin, Gary McGuire
2008-05-01
Information Theory · Computer Science
On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
Carl Bracken, Zhengbang Zha
2008-12-01
Combinatorics · Mathematics
On the infiniteness of a family of APN functions
Daniele Bartoli, Marco Calderini, Olga Polverino, Ferdinando Zullo
2021-07-21
Information Theory · Computer Science
On a Class of Quadratic Polynomials with no Zeros and its Application to APN Functions
Carl Bracken, Chik How Tan, Tan Yin
2011-10-17
Cryptography and Security · Computer Science
On Some Properties of Quadratic APN Functions of a Special Form
Irene Villa
2017-10-25
Number Theory · Mathematics
Quadratic Binomial APN Functions and Absolutely Irreducible Polynomials
E. Byrne, G. McGuire
2008-10-27
Information Theory · Computer Science
Two new infinite classes of APN functions
Kangquan Li, Yue Zhou, Chunlei Li, Longjiang Qu
2021-05-19
Information Theory · Computer Science
Two new families of bivariate APN functions
Marco Calderini, Kangquan Li, Irene Villa
2022-04-27
Information Theory · Computer Science
Constructing new APN functions through relative trace functions
Lijing Zheng, Haibin Kan, Yanjun Li, Jie Peng +1
2021-01-28
Information Theory · Computer Science
Trims and Extensions of Quadratic APN Functions
Christof Beierle, Gregor Leander, Léo Perrin
2022-03-29
Combinatorics · Mathematics
A new APN function which is not equivalent to a power mapping
Yves Edel, Gohar Kyureghyan, Alexander Pott
2016-11-17
Combinatorics · Mathematics
Triprojective almost perfect nonlinear permutations and functions
Faruk Göloğlu, Lukas Kölsch
2026-05-19
Combinatorics · Mathematics
On the Equivalence of Quadratic APN Functions
Eimear Byrne, Carl Bracken, Gary McGuire, Gabriele Nebe
2011-01-10
Information Theory · Computer Science
New Instances of Quadratic APN Functions
Christof Beierle, Gregor Leander
2021-12-24
Information Theory · Computer Science
Several classes of bent, near-bent and 2-plateaued functions over finite fields of odd characteristic
Guangkui Xu, Xiwang Cao
2015-08-17
Information Theory · Computer Science
New construction of APN quaratic
Zahid Mounir
2011-07-20
Number Theory · Mathematics
Functions of degree 4e that are not APN infinitely often
François Rodier
2016-02-03
Cryptography and Security · Computer Science
On Equivalence of Known Families of APN Functions in Small Dimensions
Bo Sun
2017-09-25
Number Theory · Mathematics
Irreducible polynomials over a finite field with restricted coefficients
Sam Porritt
2019-08-15
Number Theory · Mathematics
On $k$-PN Functions over Finite Fields
Marco Pizzato
2013-12-25
Number Theory · Mathematics
On planar functions over $\mathbb{F}_{q^3}$
João Paulo Guardieiro, Adler Marques, Luciane Quoos, Guilherme Tizziotti
2026-05-27
Information Theory · Computer Science
Gold Functions and Switched Cube Functions Are Not 0-Extendable in Dimension $n > 5$
Christof Beierle, Claude Carlet
2023-02-28
Combinatorics · Mathematics
Millions of inequivalent quadratic APN functions in eight variables
Christof Beierle, Philippe Langevin, Gregor Leander, Alexandr Polujan +1
2025-08-07
Information Theory · Computer Science
A complete characterization of the APN property of a class of quadrinomials
Kangquan Li, Chunlei Li, Tor Helleseth, Longjiang Qu
2020-07-09
Combinatorics · Mathematics
A lower bound on the number of inequivalent APN functions
Christian Kaspers, Yue Zhou
2020-02-05