Highly Nonlinear t-Resilient Functions

: High resilient and high nonlinear Boolean functions are desirable for secure key generators in stream ciphers, for example. This paper first shows that there exists a tradeoff between resiliency and nonlinearity. Then we show a new simple design method for high resilient and high nonlinear Boolean functions. Our method gives higher nonlinearity than [Zhang and Zheng 95] while their method gives larger resiliency than our method. Further, the proposed method provides a tradeoff between resiliency t and nonlinearity NF by using an intermediate parameter l. If we choose a large l, then a small t and a large NF are obtained. If we choose a small l, then a large t and a small NF are obtained. Key Words: cryptology, Boolean function, nonlinearity, resiliency Category: E.3 1 Introduction An n-input and m-output function F (x 1 ; : : : ; xn ) = (f 1 ; : : : ; fm ) is called an (n; m; t)-resilient function if any function obtained from F by keeping any t input bits constant is uniformly...