Slovak University of Technology, Bratislava

Faculty of Electrical Engineering and Information Technology

Degree Course: INFORMATICS

Author: Bc. Ján Ulický

Diploma thesis: Linear and sphere complexity of linear recurring sequences

Supervisor: RNDr. Karol Nemoga, CSc.

Pedagogical supervisor: RNDr. Ľubica Beňušková, CSc.

May 2001

Nowadays most mathematician and informatician all over the world pay their interest in securing information being transmitted by some manner. One of the methods that are used concern the theory of linear recurring sequences.

There exist many indicators that help us judge the linear recurring sequence as a candidate that acts in encryption. Linear complexity of a linear recurring sequence is an indicator that is being used most frequently.

In 1991 C.Ding in his work [1] defined a new parameter of a linear recurring sequences - sphere complexity. It comes from the definition that sphere complexity should also act as an indicator of a "good" linear recurring sequence.

The aim of this work is to observe the properties of the sphere complexity on the statistical base.

[1] Ding, C., Xiao, G., Shan, W.: The Stability Theory of Stream Ciphers, LNCS vol. 561, Springer-Verlag, Berlin, 1991.