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Legendre序列在GF(p)上的线性复杂度 被引量：1

On the GF(p) linear complexity of legendre sequence
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摘要 线性复杂度是度量流密码安全性的一个重要指标。GF(2)上序列可以把它看成GF(p)上的序列,因此需要研究序列在GF(p)(p是较小的奇素数)上的线性复杂度。从这个观点出发,讨论了Legendre序列在GF(p)上的线性复杂度,在应用部分发现了Legendre序列在分圆多项式分解上一个应用,并对此做了一些扩展。 Linear complexity is an important cryptographic criterion of stream ciphers. The sequences over GF（2） can be considered as sequences over GF（p） （p is a small odd prime number）, therefore, their linear complexity needs to be studied over GF（p）. From this perspective,the linear complexity of legendre sequence over GF（p） was discussed. Its application on cyclotomic polynomial factoring and some extensions are also covered.
作者 何贤芒
机构地区 复旦大学计算机与信息技术系
出处 《通信学报》 EI CSCD 北大核心 2008年第3期16-22,共7页 Journal on Communications
关键词 Legendre序列 线性复杂度 分圆多项式 二次剩余 Legendre sequence linear complexity cyclotomic polynomial quadratic residue
分类号 TP309.7 [自动化与计算机技术—计算机系统结构]
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参考文献6

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同被引文献10

  • 1Sanders J,Kandrot E.GPU高性能编程CUDA实战[M].聂雪军,译.北京:机械工业出版社,2011.
  • 2李继国,余纯武,张福泰,等.信息安全数学基础[M].武汉:武汉大学出版社,2006.
  • 3Damgard I B.On the randomness of Legendre and Jacobi sequences[C]//Advances in Cryptology CRYPTO' 88.Ger- many: Springer-Verlag, 1988,403 : 163-172.
  • 4Ding C,Tor H.On cyclotomic generator of order r[J]. Information Processing Letters, 1998,66( 1 ) :21-25.
  • 5Ding C.Pattern distributions of Legendre sequences[J]. IEEE Transactions on Information Theory, 1998,44(4): 1693-1698.
  • 6Sidel' nikov V M.Some k-valued pseudorandom sequences and nearly equidistant codes[J].Problems of Information Transmission, 1969,5 ( 1 ) : 12-16.
  • 7Su M, Winterhof A.Autocorrelation of Legendre-Sidelnikov sequences[J].IEEE Transactions on Information Theory, 2010,56(4) : 1714-1718.
  • 8Su M, Winterhof A.Correlation measure of order k and linear complexity profile of Legendre-Sidelnikov sequences[J]. IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences, 2012, E95-A (11) : 1851-1854.
  • 9Ding C, Tor H, Shan W.On the linear complexity of Legendre sequences[J].lEEE Transactions on Informa- tion Theory, 1998,44(3) : 1276-1278.
  • 10Mauduit C, Sarktizy A.On finite pseudorandom binary sequences I. measure of pseudorandornness, the Legendre symbol[J].Acta Arith, 1997,82 (4) : 365-377.

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通信学报
2008年 第3期

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