Extended Period LFSR Using Variable TAP Function

Abstract

This paper presents a method to extend the period of a linear feedback shift register (LFSR) by proposing an algorithm to generate primitive polynomials, this is archived by using basic LFSR with a maximum period equal to a prime number. The period extension achieved with our proposed method is statistically robust and has a very long extension of the LFSR period, as long of (2120)!(2N - 1) for a 127 bit length register. Also by separating the phases of setup and running in the algorithm avoid losing the characteristically speed of the LFSRs.