**Linear Complexity of Designs based on Coordinate Sequences of LRS and on Digital Sequences of Matrix/Skew LRS Coordinate Sequences over Galois Ring**

*Vadim N. Tsypyschev*

**Abstract: **This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it.

Previous work is available at http://eprint.iacr.org/2016/212

In this work we provide low rank estimations for sequences generated by two different designs based on coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP) over Galois ring $R=GR(p^n,r)$, $p\ge 5$, $r\ge2$, with numbers $s$ such that $s=kr+2$, $k\in \mathbb{N}_0$, and based on digital sequences of coordinate sequences of matrix/skew MP LRS over such Galois rings.

**Category / Keywords: **secret-key cryptography / linear recurrent sequence, linear complexity/rank estimations, pseudo-random sequences, matrix linear recurrent sequence, matrix linear congruent generator, skew linear recurrent sequence

**Date: **received 28 Sep 2016, last revised 29 Sep 2016

**Contact author: **tsypyschev at yandex ru

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

**Note: **This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it.
Previous work is available at http://eprint.iacr.org/2016/212

**Version: **20160929:103904 (All versions of this report)

**Short URL: **ia.cr/2016/936

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