Improved Bounds in the Multiple-Recursive Matrix Method for Pseudorandom Number and Vector Generation

Abstract

DEDICATED TO PROFESSOR E. HLAWKA ON THE OCCASION OF HIS 80TH BIRTHDAYThe multiple-recursive matrix method is a general linear method for the generation of uniform pseudorandom numbers and vectors which was introduced and studied in earlier papers of the author. In this paper we improve on various bounds in this method by using information on -splitting subspaces of finite fields.

Primitive polynomials, singer cycles and word-oriented linear feedback shift registers

“…After a preliminary version of this paper was prepared, we found that the seemingly new notion of a σ-LFSR can, in fact, be traced back to the work of Niederreiter (1993Niederreiter ( -1996 mainly in the context of pseudorandom number generation. Indeed, in a series of papers [12,13,14,15], Niederreiter has introduced the so called multiple recursive matrix method and the notion of recursive vector sequences. The latter are essentially the same as sequences generated by a σ-LFSR, modulo a natural isomorphism between the field F q m with q m elements and the vector space F m q of dimension m over The question of counting the number of primitive σ-LFSRs of a given order n over F q m is considered in [13, p. 11] under a different guise (cf.…”

“…After a preliminary version of this paper was prepared, we found that the seemingly new notion of a σ-LFSR can, in fact, be traced back to the work of Niederreiter (1993Niederreiter ( -1996 mainly in the context of pseudorandom number generation. Indeed, in a series of papers [12,13,14,15], Niederreiter has introduced the so called multiple recursive matrix method and the notion of recursive vector sequences.…”