On the fast algebraic immunity of even-variable rotation symmetric Boolean functions

An AAR (algebraic attack resistant) Boolean function is considered having good capability against both classical and fast algebraic attacks. However, AAR is too hard to achieve. This paper studies the protection against fast algebraic attacks on rotation symmetric Boolean functions by discussing their fast algebraic immunity. The result shows that all the even n-variable rotation symmetric Boolean functions of degree (n-1) are not AAR because their fast algebraic immunity is at most (n-1). Furthermore, we find that some of the even n-variable rotation symmetric Boolean functions of degree n or (n-2) have fast algebraic immunity at most (n-1), too.