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The efficiency of solving multiple discrete logarithm problems and the implications for the security of fixed elliptic curves

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Abstract

This paper examines the cryptographic security of fixed versus random elliptic curves over GF(p). It assumes a precomputation for use in breaking the elliptic curve discrete logarithm problem (ecdlp) can be made for fixed curves. A lower bound for the efficiency of a variation of Pollard’s rho method for solving multiple ecdlps is presented, 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 4 bits to the order of a fixed curve to avoid general software attacks plus 6 bits to avoid attacks on curves with special properties provides equivalent security.

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Authors and Affiliations

  1. Information Security Research Centre, Queensland University of Technology, 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, 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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Correspondence to Yvonne Hitchcock.

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Hitchcock, Y., Montague, P., Carter, G. et al. The efficiency of solving multiple discrete logarithm problems and the implications for the security of fixed elliptic curves. IJIS 3, 86–98 (2004). https://doi.org/10.1007/s10207-004-0045-9

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  • DOI: https://doi.org/10.1007/s10207-004-0045-9

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