Welcome to the resource topic for 2000/009
Title:
New Directions in Design of Resilient Boolean Functions
Authors: Palash Sarkar, Subhamoy Maitra
Abstract:There has been a recent upsurge of research in the design of resilient
Boolean functions for use in stream cipher systems. The existing
research concentrates on maximum degree resilient functions and tries
to obtain as high nonlinearity as possible. In sharp contrast to this
approach we identify the class of functions with {\em provably best}
possible trade-off among the parameters: number of variables,
resiliency, nonlinearity and algebraic degree. We first prove a
sharper version of McEliece theorem for Reed-Muller codes as applied
to resilient functions, which also generalizes the well known
Xiao-Massey characterization. As a consequence a nontrivial upper
bound on the nonlinearity of resilient functions is obtained. This
result coupled with Siegenthaler’s inequality naturally leads to
the notion of provably best resilient functions. We further show that
such best functions can be constructed by the Maiorana-McFarland
like technique. In cases where this method fails, we provide new ideas
to construct best functions. We also briefly discuss efficient
implementation of these functions in hardware.
ePrint: https://eprint.iacr.org/2000/009
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