Efficient Signature Schemes with Tight Reductions to the Diffie-Hellman Problems*
20 Pages Posted: 9 Jul 2008
Abstract
We propose and analyze two efficient signature schemes whose security is tightly related to the Diffie-Hellman problems in the random oracle model. Security of our first scheme relies on the hardness of the computational Diffie-Hellman problem; security of our second scheme | which is more efficient than the first | is based on the hardness of the decisional Diffie-Hellman problem, a stronger assumption.
Given current state of the art, it is as difficult to solve the Diffie-Hellman problems as it is to solve the discrete logarithm problem in many groups of cryptographic interest. Thus, the signature schemes shown here can currently over substantially better efficiency (for a given level of provable security) than existing schemes based on the discrete logarithm assumption.
The techniques we introduce can be also applied in a wide variety of settings to yield more efficient cryptographic schemes (based on various number-theoretic assumptions) with tight security reductions.
Suggested Citation: Suggested Citation