A Property of a Class of Gaussian Periods and Its Application

Yuhua SUN; Qiang WANG; Qiuyan WANG; Tongjiang YAN

doi:10.1587/transfun.E101.A.2344

A Property of a Class of Gaussian Periods and Its Application

Yuhua SUN, Qiang WANG, Qiuyan WANG, Tongjiang YAN

Full Text Views

0

Cite this

Summary :

In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.12 pp.2344-2351

Publication Date: 2018/12/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E101.A.2344

Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)

Category: Communication Theory and Signals

Authors

Yuhua SUN
  China University of Petroleum,Shandong Provincial Key Laboratory of Computer Networks,Carleton University
Qiang WANG
  Carleton University
Qiuyan WANG
  Tianjin Polytechnic University
Tongjiang YAN
  China University of Petroleum,Fujian Province University

Keyword

binary sequences, Whiteman's generalized cyclotomic sequence, Gaussian periods, 2-adic complexity

Cite this

Copy

Yuhua SUN, Qiang WANG, Qiuyan WANG, Tongjiang YAN, "A Property of a Class of Gaussian Periods and Its Application" in IEICE TRANSACTIONS on Fundamentals, vol. E101-A, no. 12, pp. 2344-2351, December 2018, doi: 10.1587/transfun.E101.A.2344.
Abstract: In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2344/_p

Copy

@ARTICLE{e101-a_12_2344,
author={Yuhua SUN, Qiang WANG, Qiuyan WANG, Tongjiang YAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Property of a Class of Gaussian Periods and Its Application},
year={2018},
volume={E101-A},
number={12},
pages={2344-2351},
abstract={In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.},
keywords={},
doi={10.1587/transfun.E101.A.2344},
ISSN={1745-1337},
month={December},}

Copy

TY - JOUR
TI - A Property of a Class of Gaussian Periods and Its Application
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2344
EP - 2351
AU - Yuhua SUN
AU - Qiang WANG
AU - Qiuyan WANG
AU - Tongjiang YAN
PY - 2018
DO - 10.1587/transfun.E101.A.2344
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.
ER -