International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

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

Authors:
Andrey Khalyavin
Download:
URL: http://eprint.iacr.org/2007/212
Search ePrint
Search Google
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.
BibTeX
@misc{eprint-2007-13493,
  title={The constructing of $3$-resilient Boolean functions of $9$ variables with nonlinearity $240$},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / secret-key cryptography, Boolean functions, resiliency,  nonlinearity, fast algorithms.},
  url={http://eprint.iacr.org/2007/212},
  note={ halyavin@gmail.com 13679 received 4 Jun 2007, last revised 15 Jun 2007},
  author={Andrey Khalyavin},
  year=2007
}