Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions

Authors

  • Stefka Bouyuklieva Faculty of Mathematics and Informatics Veliko Tarnovo University Veliko Tarnovo, Bulgaria
  • Iliya Bouyukliev Institute of Mathematics and Informatics Bulgarian Academy of Sciences P. O. Box 323 Veliko Tarnovo, Bulgaria

DOI:

https://doi.org/10.55630/sjc.2016.10.245-262

Keywords:

Boolean Function, Walsh Transform, S-Box, Linearity, Algorithms

Abstract

In this article, we study two representations of a Boolean function
which are very important in the context of cryptography. We describe
Möbius and Walsh Transforms for Boolean functions in details and present
effective algorithms for their implementation. We combine these algorithms
with the Gray code to compute the linearity, nonlinearity and algebraic degree
of a vectorial Boolean function. Such a detailed consideration will be
very helpful for students studying the design of block ciphers, including PhD
students in the beginning of their research.

ACM Computing Classification System (1998): F.2.1, F.2.2.

Downloads

Published

2017-11-03

Issue

Section

Articles