International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Maria Fedorova

Publications

Year
Venue
Title
2001
EPRINT
On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
Maria Fedorova Yuriy Tarannikov
In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound ${1\over\log_2(\sqrt{5}+1)}=0.5902...$ for the important ratio ${t\over t+k}$ of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of its parameters is equal to lower bound. By means of these matrices we construct $m$-resilient $n$-variable functions with maximum possible nonlinearity $2^{n-1}-2^{m+1}$ for $m=0.5902...n+O(\log_2 n)$. This result supersedes the previous record.

Coauthors

Yuriy Tarannikov (1)