The best way to secure and to get safe electronic payment systems through computer networks is with encryption. The strength of the encryption technique is mainly depending upon the encryption key. One of the basic criterion to evaluate the strength of the key is the complexity measure. In this paper, the Ziv-Lempel complexity for a binary random sequences, as well as for finite sequences employed to generate the encryption keys is examined. The complexity versus the sequence length is investigated, and the comparison with the lower bound is done. The obtained results show many interesting points. Among of them: first the random sequence satisfies the lower-bound in all different lengths. Second, Ziv-Lempel complexity for the linear feedback shift register (LFSR) sequences depends on both the initial condition and on the characteristic polynomial of the LFSR. Third, the complexity depends on the length of the sequence.