Paper 2012/003 Original: eprint.iacr.org/2012/003 ↗
On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2012-01-05: last updated
- 2012-01-05: published
- Short URL
- https://ia.cr/2012/003
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}