7 citations · 20 across the 12 of their papers we have counts for
12 papers
On a Class of Quadratic Polynomials with no Zeros and its Application to APN Functions
Carl Bracken, Chik How Tan, Tan Yin
We show that the there exists an infinite family of APN functions of the form , over $\gf…
On the Equivalence of Quadratic APN Functions
Eimear Byrne, Carl Bracken, Gary McGuire +1
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions i…
Triple-Error-Correcting BCH-Like Codes
Carl Bracken, Tor Helleseth
The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance 7 with generator polynomial having zeros , and where is a primitive ro…
A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree
Carl Bracken, Gregor Leander
Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption…
On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
Carl Bracken, Zhengbang Zha
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case…
A Few More Quadratic APN Functions
Carl Bracken, Eimear Byrne, Nadya Markin +1
We present two infinite families of APN functions where the degree of the field is divisible by 3 but not 9. Our families contain two already known families as special cases. We al…