Efficient computation of algebraic immunity of symmetric boolean functions

Authors:
Feng Liu;Keqin Feng
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing, China;Department of Mathematical Sciences, Tsinghua University, Beijing, China
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

The computation on algebraic immunity (AI) of symmetric boolean functions includes: determining the AI of a given symmetric function and searching all symmetric functions with AI = d or AI ≥ d, where d ≤ ⌈n/2⌉. In this paper we firstly showed a necessary and sufficient condition of AI of symmetric boolean functions and then proposed several efficient algorithms on computation of algebraic immunity of symmetric boolean functions. By these algorithms we could assess the vulnerability of symmetric boolean functions against algebraic/fast algebraic attacks efficiently, and find all symmetric functions having a given algebraic immunity AIn(f) = d, for some 0 ≤ d ≤ n.