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

Authors:
Iwan M. Duursma
SeungKook Park
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URL: http://eprint.iacr.org/2006/312
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Abstract: 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
}