Geodesic
Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions
Serdica Journal of Computing, Tome 10 (2016) no. 3-4, pp. 245-262.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Boolean Function, Walsh Transform, S-Box, Linearity, Algorithms 
@article{SJC_2016_10_3-4_a3,
     author = {Bouyuklieva, Stefka and Bouyukliev, Iliya},
     title = {Algorithms for {Computing} the {Linearity} and {Degree} of {Vectorial} {Boolean} {Functions}},
     journal = {Serdica Journal of Computing},
     pages = {245--262},
     publisher = {mathdoc},
     volume = {10},
     number = {3-4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2016_10_3-4_a3/}
}
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
SP  - 245
EP  - 262
VL  - 10
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2016_10_3-4_a3/
LA  - en
ID  - SJC_2016_10_3-4_a3
ER  - 
%0 Journal Article
%A Bouyuklieva, Stefka
%A Bouyukliev, Iliya
%T Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions
%J Serdica Journal of Computing
%D 2016
%P 245-262
%V 10
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2016_10_3-4_a3/
%G en
%F SJC_2016_10_3-4_a3
Bouyuklieva, Stefka; Bouyukliev, Iliya. Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions. Serdica Journal of Computing, Tome 10 (2016) no. 3-4, pp. 245-262. http://geodesic.mathdoc.fr/item/SJC_2016_10_3-4_a3/