### The Vector Decomposition Problem for Elliptic and Hyperelliptic Curves

Iwan Duursma and Negar Kiyavash

##### Abstract

The group of m-torsion points on an elliptic curve, for a prime number m, forms a two-dimensional vector space. It was suggested and proven by Yoshida that under certain conditions the vector decomposition problem (VDP) on a two-dimensional vector space is at least as hard as the computational Diffie-Hellman problem (CDHP) on a one-dimensional subspace. In this work we show that even though this assessment is true, it applies to the VDP for m-torsion points on an elliptic curve only if the curve is supersingular. But in that case the CDHP on the one-dimensional subspace has a known sub-exponential solution. Furthermore, we present a family of hyperelliptic curves of genus two that are suitable for the VDP.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Elliptic curve cryptographyCurves of genus two
Contact author(s)
duursma @ math uiuc edu
History
Short URL
https://ia.cr/2005/031

CC BY

BibTeX

@misc{cryptoeprint:2005/031,
author = {Iwan Duursma and Negar Kiyavash},
title = {The Vector Decomposition Problem for Elliptic and Hyperelliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2005/031},
year = {2005},
note = {\url{https://eprint.iacr.org/2005/031}},
url = {https://eprint.iacr.org/2005/031}
}

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