Elliptic Curves and Resilient Functions

In this paper, we propose a novel relationship between the correlation of two polynomial-type Boolean functions and the order of an associated algebraic curve. By this relationship, we propose a method to generate a resilient(correlation immune and balanced) function from a cubic polynomial. Since our resilient function is derived from a polynomial over a finite field, its nonlinearity is much easier to control. Moreover we can construct a resilient function with multi-bit outputs. We present several examples of a resilient function with 2 outputs.