Linear Feedback Shift Registers (LFSRs) are used in a variety of cryptographic security protocols. They are used in an encryption algorithm, called A5/1 found in the Global Systems for Mobile Communications (GSM) network. While their use in the GSM has deceased, A5/1 encryption is still found in many GSM-based mobile devices. In this paper, we examine the generalization of the A5/1 encryption to include any chosen LFSRs that are still 64-bit long as in the original algorithm. This generalization is also applicable to the A5/2 algorithm. The clocking mechanism employed to provide irregular clocking and nonlinearity in the generated keystreams was found to degrade the algorithms due to the reduction in the period of the LFSR-based encryption algorithm.