On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers

Qun-Xiong Zheng; Wen-Feng Qi; Tian Tian

Paper 2012/003

On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers

Qun-Xiong Zheng, Wen-Feng Qi, and Tian Tian

Abstract

Let M be a square-free odd integer and Z/(M) the integer residue ring modulo M. This paper studies the distinctness of primitive sequences over Z/(M) modulo 2. Recently, for the case of M = pq, a product of two distinct prime numbers p and q, the problem has been almost completely solved. As for the case that M is a product of more prime numbers, the problem has been quite resistant to proof. In this paper, a partial proof is given by showing that a class of primitive sequences of order 2k+1 over Z/(M) is distinct modulo 2. Besides as an independent interest, the paper also involves two distribution properties of primitive sequences over Z/(M), which related closely to our main results.

Note: The manuscript was summitted to IEEE Transactions on Information Theory in Aug. 2011.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: integer residue rings linear recurring sequences primitive polynomials primitive sequences modular reduction
Contact author(s): qunxiong_zheng @ 163 com
History: 2012-01-05: received
Short URL: https://ia.cr/2012/003
License: CC BY

BibTeX

@misc{cryptoeprint:2012/003,
      author = {Qun-Xiong Zheng and Wen-Feng Qi and Tian Tian},
      title = {On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/003},
      year = {2012},
      url = {https://eprint.iacr.org/2012/003}
}