The constructing of $3$-resilient Boolean functions of $9$ variables with nonlinearity $240$.

Andrey Khalyavin

Paper 2007/212

The constructing of $3$ -resilient Boolean functions of $9$ variables with nonlinearity $240$ .

Andrey Khalyavin

Abstract

In this work we present a new way to construct $3$ -resilient Boolean functions of $9$ variables with nonlinearity $240$ . Such function have been discovered very recently by heuristic search. We find these functions by exhaustive search in the class of functions symmetric under cyclic shifts of the first seven variables. The exhaustive search was reduced significantly by using of special techniques and algorithms which can be helpful in other similar problems. Also we construct some new functions that attain the upper bound on nonlinearity of higher number of variables.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: secret-key cryptography Boolean functions resiliency nonlinearity fast algorithms.
Contact author(s): halyavin @ gmail com
History: 2007-06-15: revised; 2007-06-05: received; See all versions
Short URL: https://ia.cr/2007/212
License: CC BY

BibTeX

@misc{cryptoeprint:2007/212,
      author = {Andrey Khalyavin},
      title = {The constructing of $3$-resilient Boolean functions of $9$ variables with nonlinearity $240$.},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/212},
      year = {2007},
      url = {https://eprint.iacr.org/2007/212}
}

Paper 2007/212

The constructing of 3-resilient Boolean functions of 9 variables with nonlinearity 240.

Abstract

Metadata

The constructing of $3$ -resilient Boolean functions of $9$ variables with nonlinearity $240$ .