Linear Complexity of Binary Sequences Derived from Polynomial Quotients

  • Zhixiong Chen
  • Domingo Gómez-Pérez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)


We determine the linear complexity of p 2-periodic binary threshold sequences derived from polynomial quotient, which is defined by the function \((u^w-u^{wp})/p \pmod p\). When w = (p − 1)/2 and \(2^{p-1}\not\equiv 1 \pmod{p^2}\), we show that the linear complexity is equal to one of the following values \(\left\{p^2-1,\ p^2-p,\ (p^2+p)/2+1,\ (p^2-p)/2\right \}\), depending whether \(p\equiv 1,\ -1,\ 3,\ -3\pmod 8\). But it seems that the method can’t be applied to the case of general w.


Fermat quotients polynomial quotients finite fields pseudorandom binary sequences linear complexity cryptography 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhixiong Chen
    • 1
    • 2
  • Domingo Gómez-Pérez
    • 3
  1. 1.Department of MathematicsPutian UniversityPutianP.R. China
  2. 2.State Key Laboratory of Information Security, Institute of SoftwareChinese Academy of SciencesBeijingP.R. China
  3. 3.University of CantabriaSantanderSpain

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