Use of simple arithmetic operations to construct efficiently implementable Boolean functions possessing high nonlinearity and good resistance to algebraic attacks

Abstract

We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\le 20$, we show that there are functions in the family achieving a combination of nonlinearity and (fast) algebraic immunity which is superior to what is achieved by any other efficiently implementable function. The main novelty of our approach is to apply a judicious combination of simple integer and binary field arithmetic to Boolean function construction.