Paper 2005/031 Original: eprint.iacr.org/2005/031 ↗
The Vector Decomposition Problem for Elliptic and Hyperelliptic Curves
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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2005-02-10: last updated
- 2005-02-10: published
- Short URL
- https://ia.cr/2005/031
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2005/031}
}