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CRYPTO
2000
Springer

Nonlinearity Bounds and Constructions of Resilient Boolean Functions

8 years 7 months ago
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.
Palash Sarkar, Subhamoy Maitra
Added 02 Aug 2010
Updated 02 Aug 2010
Type Conference
Year 2000
Where CRYPTO
Authors Palash Sarkar, Subhamoy Maitra
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