A new construction of resilient functions over GF(p) with good cryptographic properties

Abstract

A common structure of key stream generator for stream ciphers consisting of several linear feedback shift registers(LFSR) combined by a combining function. The combining function plays an important role in the cryptographic security of stream ciphers. Most combining functions are resilient functions. In this paper we first show some lemmas about the cryptographic properties of functions over the Galois Field GF(p) where p is a prime. These lemmas are useful for demonstrations and constructions of resilient functions. Finally, we propose a new strategy to construct resilient functions. The nonlinearity, algebraic degree, and the order of correlation immunity of these resilient functions are also discussed.