[Resource Topic] 2006/434: Balanced Boolean Functions with (more than) Maximum Algebraic Immunity

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Balanced Boolean Functions with (more than) Maximum Algebraic Immunity

Authors: Deepak Kumar Dalai, Subhamoy Maitra


In this correspondence, construction of balanced Boolean functions with maximum possible algebraic (annihilator) immunity (AI) is studied with an additional property which is necessary to resist fast algebraic attack. The additional property considered here is, given an n-variable (n even) balanced function f with maximum possible AI \frac{n}{2}, and given two n-variable Boolean functions g, h such that fg = h, if \deg(h) = \frac{n}{2}, then \deg(g) must be greater than or equal to \frac{n}{2}. Our results can also be used to present theoretical construction of resilient Boolean functions having maximum possible AI.

ePrint: https://eprint.iacr.org/2006/434

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