A note on linear codes and algebraic immunity of Boolean functions

Since 2003, Algebraic Attacks have received a lot of attention in the cryptography literature. In this context, algebraic immunity quantifies the resistance of a Boolean function to the standard algebraic attack of the pseudo-random generators using it as a nonlinear Boolean function. A high value of algebraic immunity is now an absolutely necessary cryptographic criterion for a resistance to algebraic attacks but is not sufficient, because of a more general kind of attacks socalled Fast Algebraic Attacks. In view of these attacks, the study of the set of annihilators of a Boolean function has become very important. We show that studying the annihilators of a Boolean function can be translated into studying the codewords of a linear code. We then explain how to exploit that connection to evaluate or estimate the algebraic immunity of a cryptographic function. keywords: Boolean functions, Algebraic immunity, Cyclic code.