On the period of GSM's A5/1 stream cipher and its internal state transition structure

The A5/1 algorithm is one of the most applicable and famous stream cipher algorithms. However, the period of A5/1 keystream sequence and the exact structure of its internal state transition were not investigated thoroughly, until now. This paper deals with the transition of the internal state of A5/1 algorithm and tries to present a model for such a transition. Additionally, the internal states are divided into two groups, initially periodic and ultimately periodic. The presented model is verified using a variety of simulations and it is consistent with theoretical results as well.