Abstract
In this paper, we present a generic construction of tightly secure signature schemes in the multi-user setting, which is in turn used to construct tightly secure identity-based signature schemes. Both of the securities of the constructions are based on the hardness of some subset membership problems (SMP). By instantiating SMP with the Decisional Composite Residuosity (DCR) and Matrix Decisional Diffie–Hellman (MDDH) problems, we obtain tightly secure signature schemes and tightly secure identity-based signatures based on the DCR and MDDH assumptions, respectively.
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