International Association
for Cryptologic Research

A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two. Also the Carlet-Feng function on $2^s+1$ variables and the modified Carlet-Feng function on $2^s$ variables are shown to be perfect algebraic immune functions. Furthermore, it is shown that a perfect algebraic immune function behaves good against probabilistic algebraic attacks as well.