In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8107-1-2016,
author = {Huaning Liu and Min Zhang},
title = {A large family of Boolean functions},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {251-262},
zbl = {06545350},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8107-1-2016}
}
Huaning Liu; Min Zhang. A large family of Boolean functions. Acta Arithmetica, Tome 172 (2016) pp. 251-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8107-1-2016/