Hybrid classes of balanced Boolean functions with good cryptographic properties

Cryptographically strong Boolean functions play an imperative role in the design of almost every modern symmetric cipher. In this context, the cryptographic properties of Boolean functions, such as non-linearity, algebraic degree, correlation immunity and propagation criteria, are critically considered in the process of designing these ciphers. More recently, with the emergence of algebraic and fast algebraic attacks, algebraic immunity has also been included as an integral property to be considered. As a result, several constructions of Boolean functions with high non-linearity, maximal algebraic degree and optimal algebraic immunity have been devised since then. This paper focuses on some of these constructions and presents two hybrid classes of Boolean functions. The functions constructed within these classes possess maximal algebraic degree for balanced functions, optimal algebraic immunity, high non-linearity and good resistance to algebraic and fast algebraic attacks. A hybrid class of 1-resilient functions has also been proposed that also possesses high algebraic degree, optimal algebraic immunity, high non-linearity and good resistance to algebraic and fast algebraic attacks. (c) 2014 Elsevier Inc. All rights reserved.