Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
In this paper, we concentrate on the design of 1-resilient Boolean functions with desirable cryptographic properties. Firstly, we put forward a novel secondary construction to obtain 1-resilient functions. Next, we present the relationships between the properties of these constructed 1-resilient functions and that of the initial functions. Based on the construction and a class of bent functions on n variables, we can obtain a class of (n+3)-variable 1-resilient non-separable cryptographic functions with a high algebraic immunity, whose nonlinearity is equal to the bent concatenation bound 2(n+2)-2((n+2)/2). Furthermore, we propose a set of 1-resilient non-separable functions on odd number of variables with an optimal algebraic degree, a high algebraic immunity, and a high nonlinearity. Copyright (c) 2011 John Wiley & Sons, Ltd.
boolean functions nonlinearity 1-resilient functions bent functions algebraic immunity stream ciphers block ciphers