ON A CHARACTERIZATION OF SECURE TRINOMIALS ON ℤ2n

Abstract

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on <TEX>${\mathbb{Z}}_{2^n}$</TEX> which generates an n-bit word sequence without consecutive elements of period <TEX>$2^n$</TEX>.