Complexity measure of encryption keys used for securing computer networks

The best way to secure and to obtain 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 criteria to evaluate the strength of the key is the complexity measure. In this paper, the Ziv-Lempel (1976) complexity for 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 a comparison with the lower bound is carried out. The obtained results show many interesting points. First, the random sequence satisfies the lower bound for all different lengths. Second, the Ziv-Lempel complexity for 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.