Phase-Shift Analysis of Linear Feedback Shift Register Structures Generating Pseudorandom Sequences

We propose a systematic way for analyzing split-up feedback shift register structures which generate parallel p-n sequences. The analysis aims towards determining the relative phase shifts among the various realizations of the same p-n sequence. The main design criterion is derived when such systems are used as pseudorandom number generators. The results of this analysis are incorporated in the procedure for constructing pseudorandom number sequences. A case study is presented to demonstrate the construction procedure and in the light of our analysis a critical assessment of a class of generators proposed by W. J. Hurd, is given. Two polynomials of degree n = 20 contained in the table reported by W. J. Hurd have been checked and proved to be nonprimitive. The purpose of this study is to ensure "safe" designs when pseudorandom number generating algorithms are constructed, based on high-degree recursions with many nonzero terms.