In this paper we study the GGHN stream cipher presented in CISC 2005. This cipher has been motivated from RC4 with the idea to obtain further speed-up by considering word-oriented keystream output instead of byte-oriented ones. We prove that there exist a large number of short cycles of length equal to the length of the state array used in the cipher. Then towards having a theoretical analysis of GGHN type evolution, we study a randomized model of this cipher. Using Markovian process, we show how this model evolves to all zero state much faster than what is expected in an ideal scenario. © 2011 Springer-Verlag.