International Association
for Cryptologic Research

We investigate a well-known way to construct pseudo-random sequences by separation p-adic coordinate sequences of linear recurrences over Galois ring. Commonly

it is necessary to know rank estimations of separated sequences.

In this article we describe divisors of the minimal polynomial of the second p-adic

coordinate sequence of the linear recurrent sequence of maximal period/MP-LRS

over non-trivial Galois ring of odd characteristic in dependence of the initial vector

of this LRS.

Also we describe polynomials divisible by that minimal polynomial in dependence of the initial vector of this LRS.

As a corollary we get non-trivial upper and lower estimations for the rank of the

second coordinate sequence of such MP-LRS which provides us by possibility to use

it in pseudo-random generation.

We say that the Galois ring is non-trivial, if it differs from Galois field and from

quotient ring too.

These results were worked out with participation of V.L.Kurakin as a supervisor.

Author is very grateful to V.L.Kurakin for his participation in this work