A Tightly Secure ID-Based Signature Scheme Under DL Assumption in AGM

Identity-based signatures (IBS) can be verified using the signer identity information as the public key, and hence, there is no need for certificate management that proves the corresponding public key ownership. Unfortunately, none of the existing IBS schemes has security proven as tight as the discrete logarithm (DL) problem, the hardest problem in the cyclic group setting, under the standard EUF-CMA security model. Recently, the introduction of proving security in the algebraic group model (AGM), where the adversary’s computation is algebraic, enables some ordinary signature schemes to be proven tightly reducible under DL assumption and EUF-CMA. To date, however, it remains unknown whether IBS schemes can also be proven as secure as the DL problem in the AGM. Achieving tight security in IBS schemes under standard EUF-CMA is challenging, due to the need to take extra precautions against adaptive queries on user private keys by the adversary. In this work, we show, for the first time, an IBS scheme with tight security under DL assumption and EUF-CMA in the AGM. The scheme features a minimal signature size of two group elements, with a reduction loss factor of two.