The Improvement of Period of Pseudo Random Number Sequence: an Algebraic Approach

Abstract

Linear feedback shift registers are the fundamental structure of pseudo random number generators that are used in formation of channel key. Many methods were proposed for determining linear recurring sequences generated by Linear Feedback Shift Registers to enhance the period. In view of large scale application of this sequence in security and privacy, a clocked controlled linear feedback shift register has been introduced, known as dynamic linear feedback shift register. In this article, we emphasis on dynamic linear feedback shift register scheme using combinatorial design having constant block length and algebraic structure to enhance the period. Such sequence has the vulnerability from attack. Our proposal for designing dynamic linear feedback shift register involves primitive polynomial over a finite fields of prime power. A counter example shown the practical implication of our theory that improve the period of the sequence than existing scheme. Finally an effort was thru on properties of the generated sequence in terms of security aspect. Mathematics Subject Classification Code[2020]: 68W30, 12L15.