Welcome to the resource topic for 2001/083
Title:
On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
Authors: Maria Fedorova, Yuriy Tarannikov
Abstract: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.
ePrint: https://eprint.iacr.org/2001/083
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