Linear Complexity of Binary Sequences Derived from Polynomial Quotients

  • Zhixiong Chen
  • Domingo Gómez-Pérez
Conference paper

DOI: 10.1007/978-3-642-30615-0_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)
Cite this paper as:
Chen Z., Gómez-Pérez D. (2012) Linear Complexity of Binary Sequences Derived from Polynomial Quotients. In: Helleseth T., Jedwab J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg

Abstract

We determine the linear complexity of p2-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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations