International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: An Efficient CDH-based Signature Scheme With a Tight Security Reduction

Benoit Chevallier-Mames
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Abstract: At Eurocrypt'03, Goh and Jarecki showed that, contrary to other signature schemes in the discrete-log setting, the EDL signature scheme has a tight security reduction, namely to the Computational Diffie-Hellman (CDH) problem, in the Random Oracle (RO) model. They also remarked that EDL can be turned into an off-line/on-line signature scheme using the technique of Shamir and Tauman, based on chameleon hash functions. In this paper, we propose a new signature scheme that also has a tight security reduction to CDH but whose resulting signatures are smaller than EDL signatures. Further, similarly to the Schnorr signature scheme (but contrary to EDL), our signature is naturally efficient on-line: no additional trick is needed for the off-line phase and the verification process is unchanged. For example, in elliptic curve groups, our scheme results in a 25% improvement on the state-of-the-art discrete-log based schemes, with the same security level. This represents to date the most efficient scheme of any signature scheme with a tight security reduction in the discrete-log setting.
  title={An Efficient CDH-based Signature Scheme With a Tight Security Reduction},
  booktitle={IACR Eprint archive},
  keywords={signature schemes, discrete logarithm problem, Diffie-Hellman problem, EDL},
  note={Full version of Crypto'05 paper 13171 received 10 Feb 2005, last revised 23 Jan 2006},
  author={Benoit Chevallier-Mames},