Cryptology ePrint Archive: Report 2007/212
The constructing of $3$-resilient Boolean functions of $9$ variables with nonlinearity $240$.
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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