## CryptoDB

### Paper: ElGamal type signature schemes for n-dimensional vector spaces

Authors: Iwan M. Duursma SeungKook Park URL: http://eprint.iacr.org/2006/312 Search ePrint Search Google We generalize the ElGamal signature scheme for cyclic groups to a signature scheme for n-dimensional vector spaces. The higher dimensional version is based on the untractability of the vector decomposition problem (VDP). Yoshida has shown that under certain conditions, the VDP on a two-dimensional vector space is at least as hard as the computational Diffie-Hellman problem (CDHP) on a one-dimensional subspace. (Added November 19: Steven Galbraith recently showed that for the examples that are used in the paper, the VDP is at most as hard as the Discrete Logarithm problem (DLP) on a one-dimensional subspace. This has as a consequence for the proposed signature scheme that the given examples provide the same security as (ordinary) Elliptic Curve DLP based signature schemes.)
##### BibTeX
@misc{eprint-2006-21803,
title={ElGamal type signature schemes for n-dimensional vector spaces},
booktitle={IACR Eprint archive},
keywords={ElGamal signature scheme, Vector decomposition problem},
url={http://eprint.iacr.org/2006/312},
note={ skpark@uiuc.edu 13472 received 8 Sep 2006, last revised 19 Nov 2006},
author={Iwan M. Duursma and SeungKook Park},
year=2006
}