Abstract

DALAI, Deepak Kumar  and  MAITRA, Subhamoy. Algebraic Immunity of Boolean Functions - Analysis and Construction. Comp. y Sist. [online]. 2009, vol.12, n.3, pp.297-321. ISSN 2007-9737.

In this paper, we first analyse the method of finding algebraic immunity of a Boolean function. Given a Boolean function f on n-variables, we identify a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators of f at a specific degree. Moreover, we analyse how an affine transformation on the input variables of f can be exploited to achieve further reduction in the set of homogeneous linear equations. Next, from the design point of view, we construct balanced Boolean functions with maximum possible AI with an additional property which is necessary to resist the fast algebraic attack.

Keywords : Algebraic Attacks; Algebraic Normal Form; Annihilators; Boolean Functions; Fast Algebraic Attacks; Homogeneous Linear Equations.

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