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On the Tightness of Deterministic Identity-Based Signatures

Deterministic ID-based signatures are digital signatures where secret keys are generated with random numbers 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. In this work, we show that the scheme by Selvi et al. (IWSEC 2011) whose original proof is loose in the random oracle model is tightly secure by our new proof framework. We furthermore shed light on mathematical features necessary for achieving a tight reduction, and improve the scheme by Herranz (The Comp. Jour., 2006) to proving tightly secure in the random oracle model. The schemes described above are motivated to construct aggregate signatures with partial aggregation, and our technique is able to prove the security without the loss of the original aggregation capability.