On the linear complexity and linear complexity profile of sequences in finite fields

Abstract

Pseudo random sequences, that are used for stream ciphers, are required to havetheproperties of unpredictability and randomness. An important tool for measuringthese features is the linear complexity profile of the sequence in use.In this thesis we present a survey of some recent results obtained on linearcomplexity and linear complexity profile of pseudo random sequences. The relationbetween the polynomial degree and the linear complexity of a function over a finite field is given, bounds for linear complexity of the "power generator" and "the selfshrinking generator" are presented and a new method of construction of sequences of high linear complexity profile is illustrated.