ON A T-FUNCTION f (x) = x + h(x) WITH A SINGLE CYCLE ON Z2n

Abstract

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large (e.g., n = 64) 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 we study T-functions which are probably invertible and are very useful in stream ciphers. In this paper we study some conditions on a T-function h(x) such that f (x) = x + h(x) has a single cycle on Z2n .

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