A Pairing-Free Signature Scheme from Correlation Intractable Hash Function and Strong Diffie-Hellman Assumption

Goh and Jarecki (Eurocrypt 2003) showed how to get a signature scheme from the computational Diffie-Hellman assumption, and they introduced the name EDL for signatures of this type. The corresponding EDL family of signature schemes is remarkable for several reasons: elegance, simplicity and tight security. However, EDL security proofs stand in the random oracle model, and, to the best of our knowledge, extending this family without using an idealization of hash functions has never been successful. In this paper, we propose a new signature scheme belonging to the EDL family, which is simple, natural and efficient, without using the random oracle model. Our scheme is based on the very same assumption than the Boneh-Boyen scheme, namely the strong Diffie-Hellman assumption, with the precision that our groups are not bound to being bilinear. We also make use of a correlation-intractable hash function, for a particular relation related to discrete-logarithm. In addition to the theoretical interest of extending the EDL family without the random oracle model, our scheme is also one of the very few schemes which achieve discrete-log security properties without relying on pairings.