An Efficient CDH-Based Signature Scheme with a Tight Security Reduction

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.