Cryptology ePrint Archive: Report 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.

Category / Keywords: secret-key cryptography / secret-key cryptography, Boolean functions, resiliency, nonlinearity, fast algorithms.

Date: received 4 Jun 2007, last revised 15 Jun 2007

Contact author: halyavin at gmail com

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Version: 20070615:152613 (All versions of this report)

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