Parallel generation of pseudo-random sequences

Abstract

Nonlinear filtering of the states of LFSR is proposed to generate parallel pseudo-random (PR) sequences. The result of filtering is a set of sequences over GF(2^m) called exponent sequences. Each exponent sequence can be regarded as m parallel component sequences. Assessment of the parallel generator is discussed and statistical properties of individual component sequences and their mutual statistical dependence are examined. Upper bounds on the linear equivalence of exponent sequences and their associated component sequences are developed and it is shown that in both cases higher linear complexity can only be achieved in higher exponents. It is noticed that exponents that are prime to 2 ^m-1 produce sequences of maximum period and their component sequences have small cross correlation (equal to -1) and low statistical dependence. Finally directions for further research are proposed.