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A Fast Diffie—Hellman Protocol in Genus 2

N. P. Smart1 and S. Siksek1

(1)  Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent CT2 7NF, England N.P.Smart@ukc.ac.uk S.Siksek@ukc.ac.uk, UK
(2)  Current address: Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol, England. nsma@hplb,hpl.hp.com., UK
Abstract.    In this paper it is shown how the multiplication by M map on the Kummer surface of a curve of genus 2 defined over can be used to construct a Diffie—Hellman protocol. We show that this map can be computed using only additions and multiplications in . In particular we do not use any divisions, polynomial arithmetic, or square root functions in , hence this may be easier to implement than multiplication by M on the Jacobian. In addition we show that using the Kummer surface does not lead to any loss in security.

Key words. Curves of genus 2, Diffie—Hellman problem, Discrete logarithms.

Received 21 November 1996 and revised 28 March 1997

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Referenced by
2 newer articles

  1. Duquesne, Sylvain (2010) Traces of the Group Law on the Kummer Surface of a Curve of Genus 2 in Characteristic 2. Mathematics in Computer Science
    [CrossRef]
  2. Gaudry, P. (2007) Fast genus 2 arithmetic based on Theta functions. Journal of Mathematical Cryptology 1(3)
    [CrossRef]
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