Tighter Reductions for Deterministic Identity-Based Signatures

Abstract

Deterministic ID-based signatures are digital signatures where secret keys are probabilistically generated by a key generation center while the signatures are generated deterministically. Although the deterministic ID-based signatures are useful for both systematic and cryptographic applications, to the best of our knowledge, there is no scheme with a tight reduction proof. Loosely speaking, since the security is downgraded through dependence on the number of queries by an adversary, a tighter reduction for the security of a scheme is desirable, and this reduction must be as close to the difficulty of its underlying hard problem as possible. In this work, we discuss mathematical features for a tight reduction of deterministic ID-based signatures, and show that the scheme by Selvi et al. (IWSEC 2011) is tightly secure by our new proof framework under a selective security model where a target identity is designated in advance. Our proof technique is versatile, and hence a reduction cost becomes tighter than the original proof even under an adaptive security model. We furthermore improve the scheme by Herranz (The Comp. Jour., 2006) to prove tight security in the same manner as described above. We furthermore construct an aggregate signature scheme with partial aggregation, which is a key application of deterministic ID-based signatures, from the improved scheme.