Balanced Boolean Functions with (more than) Maximum Algebraic Immunity.
Deepak Kumar Dalai, Subhamoy Maitra · IACR Cryptology ePrint Archive · 2006
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 n2 , and given two n-variable Boolean functions g, h such that fg = h, if deg(h) = n2 , then deg(g) must be greater than or equal to n 2 . Our results can also be used to present theoretical construction of resilient Boolean functions having maximum possible AI.