On quasigroup pseudo random sequence generator

Abstract

Pseudo random sequence generators (PRSG) produce sequences of elements that imitate natural random behavior. They have extensive use in (1) scientific experiments as input sequences for different kinds of simulators, (2) cryptography for preparation of keys and establishing communication and (3) authentication for preparation of identification numbers, smart cards, serial numbers, etc. However, widely available PRSGs have limited periods (for example, 264) which means that the pseudo random sequences start repeating the same elements (after at most 264 elements). This makes them inappropriate for large scale scientific experiments, cryptography and authentication. In this paper we investigate the properties of a new type of PRSG which overcomes these difficulties. The PRSG is designed using quasigroup processing. We show that the quasigroup PRSG is highly scalable and with arbitrary large period. Also we present experimental results on some properties of the quasigroups which make them appropriate for implementation of PRSG.