A Property of a Class of Gaussian Periods and Its Application
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 thi...
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| Veröffentlicht in: | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Communications and Computer Sciences, 2018/12/01, Vol.E101.A(12), pp.2344-2351 |
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| container_title | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
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| creator | SUN, Yuhua WANG, Qiang WANG, Qiuyan YAN, Tongjiang |
| description | 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. |
| doi_str_mv | 10.1587/transfun.E101.A.2344 |
| format | Article |
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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. 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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.</description><subject>2-adic complexity</subject><subject>Algorithms</subject><subject>binary sequences</subject><subject>Communications systems</subject><subject>Complexity</subject><subject>Cryptography</subject><subject>Gaussian periods</subject><subject>Lower bounds</subject><subject>Whiteman's generalized cyclotomic sequence</subject><issn>0916-8508</issn><issn>1745-1337</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNplkLFOwzAQhi0EEqXwBgyWmBN8sVM7A0NUlYJUiQ4wW2fHgVQhCbYz9O1pVKiQWO6_4f_upI-QW2Ap5EreR49dqMcuXQGDtEwzLsQZmYEUeQKcy3MyYwUsEpUzdUmuQtgxBioDMSMPJd36fnA-7mlfU6TLFkOY1jWOITTY0a3zTV8Fil1Fn2Og5TC0jcXY9N01uaixDe7mJ-fk7XH1unxKNi_r52W5SWwOeTxMZ3mhZFGIXAmUC7eorKiNyCvBmclMpQxWzBi0lQMprWEKhMI64wYzA3xO7o53B99_jS5EvetH3x1e6owzoZSQgh9a4tiyvg_Bu1oPvvlEv9fA9CRK_4rSkyhd6knUAdscsV2I-O5OEPrY2Nb9gyD7i59q9gO9dh3_BoZNeRw</recordid><startdate>20181201</startdate><enddate>20181201</enddate><creator>SUN, Yuhua</creator><creator>WANG, Qiang</creator><creator>WANG, Qiuyan</creator><creator>YAN, Tongjiang</creator><general>The Institute of Electronics, Information and Communication Engineers</general><general>Japan Science and Technology Agency</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20181201</creationdate><title>A Property of a Class of Gaussian Periods and Its Application</title><author>SUN, Yuhua ; WANG, Qiang ; WANG, Qiuyan ; YAN, Tongjiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c515t-c5ec3987994584a76e6dc4fb45d430b2bd8bad0bbacde177cb08148af23ba2b13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>2-adic complexity</topic><topic>Algorithms</topic><topic>binary sequences</topic><topic>Communications systems</topic><topic>Complexity</topic><topic>Cryptography</topic><topic>Gaussian periods</topic><topic>Lower bounds</topic><topic>Whiteman's generalized cyclotomic sequence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>SUN, Yuhua</creatorcontrib><creatorcontrib>WANG, Qiang</creatorcontrib><creatorcontrib>WANG, Qiuyan</creatorcontrib><creatorcontrib>YAN, Tongjiang</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>SUN, Yuhua</au><au>WANG, Qiang</au><au>WANG, Qiuyan</au><au>YAN, Tongjiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Property of a Class of Gaussian Periods and Its Application</atitle><jtitle>IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences</jtitle><addtitle>IEICE Trans. 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| source | J-STAGE (Japan Science & Technology Information Aggregator, Electronic) Freely Available Titles - Japanese |
| subjects | 2-adic complexity Algorithms binary sequences Communications systems Complexity Cryptography Gaussian periods Lower bounds Whiteman's generalized cyclotomic sequence |
| title | A Property of a Class of Gaussian Periods and Its Application |
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