Abstract
Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large 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 transformations and are very useful in stream ciphers. In this paper we study the number of single cycle T-functions satisfying some conditions and characterize single cycle T-functions on <TEX>$(\mathbb{Z}_2)^n$</TEX> generated by some elements in <TEX>$(\mathbb{Z}_2)^{n-1}$</TEX>.
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