## Cryptology ePrint Archive: Report 2000/069

New constructions of resilient Boolean functions with maximal nonlinearity

Yuriy Tarannikov

Abstract: In this paper we develop a technique that allows to obtain new effective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound $2^{n-1}-2^{m+1}$ on nonlinearity of m-resilient n-variable Boolean functions is achieved for $0.6n-1\le m\le n-2$.

Category / Keywords: secret-key cryptography / stream cipher, Boolean function, nonlinear combining function, correlation-immunity, resiliency, nonlinearity