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Construction of Pseudo-random Binary Sequences from Elliptic Curves by Using Discrete Logarithm

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

An upper bound is established for certain exponential sums with respect to multiplicative characters defined on the rational points of an elliptic curve over a prime field. The bound is applied to investigate the pseudo-randomness of a large family of binary sequences generated from elliptic curves by using discrete logarithm. That is, we use this estimate to show that the resulting sequences have the advantages of ‘small’ well-distribution measure and ‘small’ multiple correlation measure.

The work was supported in part by the National Natural Science Foundation of China (No. 60473028). Research of the first author was partially supported by the Natural Science Foundation of Fujian Province of China (No.A0540011), the Science and Technology Foundation of Fujian Educational Committee (No.JA04264) and the Science and Technology Foundation of Putian City (No.2005S04).

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Author information

Authors and Affiliations

  1. National Key Lab. of I.S.N, Xidian Univ., Xi’an, 710071, China

    Zhixiong Chen, Shengqiang Li & Guozhen Xiao

  2. Depart. of Math., Putian Univ., Putian, Fujian, 351100, China

    Zhixiong Chen

  3. University of Electronic Science and Technology of China, Chengdu, 610054, China

    Shengqiang Li

Authors
  1. Zhixiong Chen
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  2. Shengqiang Li
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  3. Guozhen Xiao
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2006 Springer-Verlag Berlin Heidelberg

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Chen, Z., Li, S., Xiao, G. (2006). Construction of Pseudo-random Binary Sequences from Elliptic Curves by Using Discrete Logarithm. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_24

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  • DOI: https://doi.org/10.1007/11863854_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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