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

Hitchcock, Yvonne R., Montague, Paul, Carter, Gary P., & Dawson, Edward P. (2004) The efficiency of solving multiple discrete logarithm problems and the implications for the security of fixed elliptic curves. International Journal of Information Security, 3(2), pp. 86-98.

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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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ID Code: 10186
Item Type: Journal Article
Refereed: Yes
Additional Information: For more information, please refer to the journal’s website (see hypertext link) or contact the author.
Keywords: Elliptic curve discrete logarithm problem (ecdlp), Baby, step giant, step method (bsgs), Pollards rho method, Fixed elliptic curve, Precomputation
DOI: 10.1007/s10207-004-0045-9
ISSN: 1615-5270
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2004 Springer
Copyright Statement: The original publication is available at SpringerLink
http://www.springerlink.com
Deposited On: 16 Oct 2007 00:00
Last Modified: 29 Feb 2012 13:07

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