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The Security of Fixed versus Random Elliptic Curves in Cryptography

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Information Security and Privacy (ACISP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2727))

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Abstract

This paper examines the cryptographic security of fixed versus random elliptic curves over the field GF(p). Its basic assumption is that a large precomputation to aid in breaking the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve. We take this into account when examining curve security as well as considering a variation of Pollard’s rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. We present a lower bound on the expected time to solve such ECDLPs using this method, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. We conclude that adding 5 bits to the size of a fixed curve to avoid general software attacks and an extra 6 bits to avoid attacks on special moduli and a parameters provides an equivalent level of security.

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Author information

Authors and Affiliations

  1. Information Security Research Centre, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia

    Yvonne Hitchcock & Ed Dawson

  2. Motorola Australia Software Centre, 2 Second Ave, Mawson Lakes, SA, 5095, Australia

    Paul Montague

  3. School of Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, Q 4001, Australia

    Gary Carter

Authors
  1. Yvonne Hitchcock
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  2. Paul Montague
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  3. Gary Carter
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  4. Ed Dawson
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Editor information

Editors and Affiliations

  1. School of Information Technology and Computer Science, University of Wollongong, Wollongong, NSW, 2522, Australia

    Rei Safavi-Naini  & Jennifer Seberry  & 

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© 2003 Springer-Verlag Berlin Heidelberg

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Hitchcock, Y., Montague, P., Carter, G., Dawson, E. (2003). The Security of Fixed versus Random Elliptic Curves in Cryptography. In: Safavi-Naini, R., Seberry, J. (eds) Information Security and Privacy. ACISP 2003. Lecture Notes in Computer Science, vol 2727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45067-X_6

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  • DOI: https://doi.org/10.1007/3-540-45067-X_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40515-3

  • Online ISBN: 978-3-540-45067-2

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