| Summary: | This paper addresses the certificate revocation problem and proposes the first revocable pairing-based signature scheme with implicit and explicit certificates (IE-RCBS-kCAA). We should no longer discuss whether to revoke certificates but how to do it effectively, ensuring both the scalability of the revocation operation and the non-repudiation of the signature in the short or long term. Under the computational difficulty assumptions of the modified collusion attack algorithm with <i>k</i> traitors (<i>k</i>-mCAA) and discrete logarithm (DL) problems, we demonstrate that our scheme is secure against existential unforgeability under chosen message attacks (EUF-IERCBS-kCAA-CMA) in a random oracle model. The proposed solution is scaled and allows the use of many trusted status authorities that issue explicit short-term certificates confirming the validity of explicit long-term certificates. Furthermore, we demonstrate that our signature scheme has a short-term non-repudiation property for the shell validity model.
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