Generic construction for tightly-secure signatures from discrete log

Tightly secure signature plays a significant role in the research of cryptography and has been studied extensively in the literature. In this paper, we present a generic construction for tightly-secure signatures from the discrete log (DL) assumption in the existential-unforgeability against key only attacks (EUF-KOA) security model, where the adversary is allowed to obtain only the public key, but not any sample signature. Moreover, the generic construction can also be extended into the multi-user setting with corruptions (MU-C) model. Roughly speaking, given any signature scheme, we can efficiently convert it into a signature scheme that features tight security under the DL assumption in the MU-EUF-KOA-C security model with random oracles. Our transformation shows it is easy to construct a DL-equivalent signature in the EUF-KOA security model, although many known DL-based signatures are not equivalent to DL. If the given signature scheme is key-re-randomizable, the transformed scheme is also key-re-randomizable. Hence, our result provides a supplement to Bader et al.'s work (EUROCRYPT 2016).