Nonlinearity Bounds and Constructions of Resilient Boolean Functions

In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known XiaoMassey characterization. As a consequence, a nontrivial upper bound on the nonlinearity of resilient functions is obtained. This result coupled with Siegenthaler’s inequality leads to the notion of best possible tradeoff among the parameters: number of variables, order of resiliency, nonlinearity and algebraic degree. We further show that functions achieving the best possible trade-off can be constructed by the Maiorana-McFarland like technique. Also we provide constructions of some previously unknown functions.

• Type: Conference
• Year: 2000
• Where: CRYPTO
• Authors: Palash Sarkar, Subhamoy Maitra
• Keywords: CRYPTO 2000, Cryptology, Nonlinearity, Nontrivial Upper Bound, Resilient Functions