New Constructions for Resilient and Highly Nonlinear Boolean Functions

Abstract. We explore three applications of geometric sequences in constructing cryptographic Boolean functions. First, we construct 1-resilient functions of n Boolean variables with nonlinearity 2n−1 −2(n−1)/2 , n odd. The Hadamard transform of these functions is 3-valued, which limits the efficiency of certain stream cipher attacks. From the case for n odd, we construct highly nonlinear 1-resilient functions which disprove a conjecture of Pasalic and Johansson for n even. Our constructions do not have a potential weakness shared by resilient functions which are formed from concatenation of linear functions. Second, we give a new construction for balanced Boolean functions with high nonlinearity, exceeding 2n−1 −2(n−1)/2 , which is not based on the direct sum construction. Moreover, these functions have high algebraic degree and large linear span. Third, we construct balanced vectorial Boolean functions with nonlinearity 2n−1 − 2(n−1)/2 and low maximum correlation. Th...

• Type: Conference
• Year: 2003
• Where: ACISP
• Authors: Khoongming Khoo, Guang Gong
• Keywords: 1-resilient Functions, ACISP 2003, Boolean Functions, Cryptographic Boolean Functions, Security Privacy