**
14th Annual Computer Security Applications Conference**

December 7-11, 1998

Phoenix, Arizona

# Abstract

### Complexity Measure of Encryption Keys Used for Securing Computer Networks

Mostafa A. Bahie-Eldin Egyptian Armed Forces

Alaa A. Omar Egyptian Armed Forces

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.