Highly Nonlinear t-Resilient Functions

Kaoru Kurosawa (Tokyo Institute of Technology, Japan)

Takashi Satoh (Tokyo Institute of Technology, Japan)

Kentaro Yamamoto (Tokyo Institute of Technology, Japan)

Abstract: 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 non- linearity 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.

Keywords: Boolean function, cryptology, nonlinearity, resiliency

Categories: E.3