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New LFSR-Based Cryptosystems and the Trace Discrete Log Problem (Trace-DLP)

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Sequences and Their Applications - SETA 2004 (SETA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3486))

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Abstract

In order to reduce key sizes and bandwidth, cryptographic systems have been proposed using minimal polynomials to represent finite field elements. These systems are essentially equivalent to systems based on characteristic sequences generated by a linear feedback shift register (LFSR). We propose a general class of LFSR-based key agreement and signature schemes based on n-th order characteristic sequences. These schemes have the advantage that they do not require as much bandwidth as their counterparts based on finite fields. In particular, we present a signature scheme based on a new computational problem, the Trace Discrete Logarithm Problem (Trace-DLP). The Trace-DLP and its variants are discussed and their relationship with well-known finite field-based computational problems is examined. In addition, we prove the equivalence between several LFSR-based computational problems and their finite field-based counterparts.

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Author information

Authors and Affiliations

  1. Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Kenneth J. Giuliani

  2. Dept. of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Guang Gong

Authors
  1. Kenneth J. Giuliani
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  2. Guang Gong
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Editor information

Editors and Affiliations

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

    Tor Helleseth

  2. University of Ilinois at Urbana-Champaign, 1406 West Green Street, IL 61801, Urbana, USA

    Dilip Sarwate

  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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© 2005 Springer-Verlag Berlin Heidelberg

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Giuliani, K.J., Gong, G. (2005). New LFSR-Based Cryptosystems and the Trace Discrete Log Problem (Trace-DLP). In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_22

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  • DOI: https://doi.org/10.1007/11423461_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26084-4

  • Online ISBN: 978-3-540-32048-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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