Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions

Bouyuklieva, Stefka, and Bouyukliev, Iliya. "Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions." Serdica Journal of Computing 10.3-4 (2016): 245-262. <http://eudml.org/doc/289534>.

@article{Bouyuklieva2016,
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.},
author = {Bouyuklieva, Stefka, Bouyukliev, Iliya},
journal = {Serdica Journal of Computing},
keywords = {Boolean Function; Walsh Transform; S-Box; Linearity; Algorithms},
language = {eng},
number = {3-4},
pages = {245-262},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions},
url = {http://eudml.org/doc/289534},
volume = {10},
year = {2016},
}

TY - JOUR
AU - Bouyuklieva, Stefka
AU - Bouyukliev, Iliya
TI - Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions
JO - Serdica Journal of Computing
PY - 2016
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 3-4
SP - 245
EP - 262
AB - 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.
LA - eng
KW - Boolean Function; Walsh Transform; S-Box; Linearity; Algorithms
UR - http://eudml.org/doc/289534
ER -