## Cryptology ePrint Archive: Report 2006/434

Balanced Boolean Functions with (more than) Maximum Algebraic Immunity

Deepak Kumar Dalai and Subhamoy Maitra

Abstract: 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.

Category / Keywords: secret-key cryptography / Algebraic Attacks, Annihilators, Boolean Functions, Fast Algebraic Attacks.