**SECOND COORDINATE SEQUENCE OF MP-LRS OVER NONTRIVIAL GALOIS RING OF ODD CHARACTERISTIC**

*Vadim N.Tsypyschev *

**Abstract: **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

**Category / Keywords: **secret-key cryptography / linear recurrent sequence, minimal polynomial, rank estimations, pseudo-random sequences

**Date: **received 22 Oct 2015

**Contact author: **tsypyschev at yandex ru

**Available format(s): **PDF | BibTeX Citation

**Note: **I have fixed your reprimand and have given an explanation you had required .

As previously it's only thesis form with omitted proofs.

**Version: **20151026:203600 (All versions of this report)

**Short URL: **ia.cr/2015/1030

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