On the Decisional Diffie-Hellman Problem in Genus 2

Jordi Pujol`as Boix

(2009)

Jordi Pujol`as Boix (2009) On the Decisional Diffie-Hellman Problem in Genus 2.

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Abstract

We investigate the Decisional Diffie-Hellman problem in the Jacobian variety of supersingular curves of genus two over finite fields. A solution to this problem is useful in Public Key Cryptography, for example in Digital Signatures and Identity-Based Cryptography. The existence of a non-degenerate, bilinear pairing reduces the solution to DDH to the existence of sufficiently many distortion maps. These maps are found in the endomorphism ring of the Jacobian variety. We show examples of supersingular curves over finite fields of both even and odd characteristics such that the endomorphism algebra is 16-dimensional over the rationals, and we solve DDH in some cases.

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This is a Published version
This version's date is: 04/03/2009
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https://repository.royalholloway.ac.uk/items/d954e210-2653-08bb-4ccd-547f472af91c/1/

Item TypeMonograph (Technical Report)
TitleOn the Decisional Diffie-Hellman Problem in Genus 2
AuthorsBoix, Jordi Pujol`as
DepartmentsFaculty of Science\Mathematics

Deposited by () on 24-Jun-2010 in Royal Holloway Research Online.Last modified on 15-Dec-2010

Notes

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