A fast Diffie-Hellman protocol in genus 2

Smart, Nigel P. and Siksek, S. (1999) A fast Diffie-Hellman protocol in genus 2. Journal of Cryptology, 12 (1). pp. 67-73. ISSN 0933-2790. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1007/PL00003818

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 F-q can be used to construct a Diffie-Hellman protocol. We show that this map can be computed using only additions and multiplications in F-q. In particular we do not use any divisions, polynomial arithmetic, or square root functions in F-q, 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.

Item Type: Article
Uncontrolled keywords: curves of genus 2; Diffie-Hellman problem; discrete logarithms
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Q Science > QA Mathematics (inc Computing science)
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: F.D. Zabet
Date Deposited: 25 Mar 2009 20:44
Last Modified: 25 Jun 2014 08:37
Resource URI: https://kar.kent.ac.uk/id/eprint/16627 (The current URI for this page, for reference purposes)
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