Paper 2001/083 Original: eprint.iacr.org/2001/083 ↗
On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices
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.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2001-10-05: last updated
- 2001-10-05: published
- Short URL
- https://ia.cr/2001/083
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2001/083,
author = {Maria Fedorova and Yuriy Tarannikov},
title = {On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices},
howpublished = {Cryptology {ePrint} Archive, Paper 2001/083},
year = {2001},
url = {https://eprint.iacr.org/2001/083}
}