Tightly Secure Chameleon Hash Functions in the Multi-user Setting and Their Applications

We define the security notion of strong collision resistance for chameleon hash functions in the multi-user setting (S-MU-CR security). We also present three specific constructions CHFdl, CHFrsa and CHFfac of chameleon hash functions, and prove their tight S-MU-CR security based on the discrete logarithm, RSA and factoring assumptions, respectively. In applications, we show that tightly S-MU-CR secure chameleon hash functions can lift a signature scheme from (weak) unforgeability to strong unforgeability with a tight security reduction in the multi-user setting.