Highly nonlinear 0-1 balanced boolean functions satisfying strict avalanche criterion

Abstract

Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0- 1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearity 22k-2k and satisfying SAC, (ii) 0-1 balanced boolean functions on V2k (k ≥ 2) having nonlinearity 22k-1-2k and satisfying SAC. We demonstrate that the above non hnearities are very high not only for the 0-1 balanced functions satisfying SAC but also for all 0-1 balanced functions.