A Variant of BLS Signature Scheme with Tight Security Reduction

In 2001, Boneh, Lynn and Shacham designed a signature scheme using the properties of bilinear pairing from elliptic curve, and based its security under the Computational Diffie-Hellman (CDH) assumption. However, the security reduction is not tight as there is a loss of roughly \(q_s\), the number of sign queries. In this paper, we propose a variant of the BLS signature with tight security reduction based on the co-CDH assumption. Besides upgraded to the notion of strong existential unforgeability under chosen message attack, the variant is backward-compatible with the original BLS signature.