On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices

Maria Fedorova; Yuriy Tarannikov

Paper 2001/083

On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices

Maria Fedorova and 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 $\frac{1}{\log_{2} (\sqrt{5} + 1)} = 0.5902 . . .$ for the important ratio $\frac{t}{t + k}$ 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 -resilient -variable functions with maximum possible nonlinearity for . This result supersedes the previous record.

Metadata

Available format(s): PS
Category: Secret-key cryptography
Publication info: Published elsewhere. a slightly shortened version will be published in Proceedings of Indocrypt 2001 in LNCS, Springer-Verlag.
Keywords: stream cipher Boolean function nonlinear combining function correlation-immunity resiliency nonlinearity special matrices.
Contact author(s): yutaran @ mech math msu su
History: 2001-10-05: received
Short URL: https://ia.cr/2001/083
License: CC BY

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}
}