The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Nas últimas duas décadas, muitas sequências ciclotômicas generalizadas foram construídas e utilizadas em criptografia e sistemas de comunicação por sua alta complexidade linear e baixa autocorrelação. Mas existem alguns artigos enfocando as complexidades 2-ádicas de tais sequências. Neste artigo, primeiro damos uma propriedade de uma classe de períodos gaussianos baseada nas classes ciclotômicas generalizadas de ordem 4 de Whiteman. Em seguida, como aplicação dessa propriedade, estudamos a complexidade 2-ádica de uma classe de sequências ciclotômicas generalizadas de Whiteman construídas de dois primos distintos p e q. Provamos que a complexidade 2-ádica desta classe de sequências de período pq é limitado inferiormente por pq-p-q-1. Este limite inferior é pelo menos maior que metade do seu período e, portanto, mostra que esta classe de sequências pode resistir ao ataque do algoritmo de aproximação racional (RAA).
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
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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
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@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},}
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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 -