Certificate-based public key cryptographic is a novel cryptographic primitive solving the heavy management problem in the conventional public key cryptographic. Verifiable encrypted signature is useful for many cryptographic protocols and often is used as to construct an optimistic fair exchange, it can convince a verifier that a given cipher text is an encryption of signature on a given message. In this paper, we propose an efficient certificate-based verifiable encrypted signature scheme by combining certificate-based public key cryptographic with a verifiable encrypted signature. We first give the formal definition of the certificate-based verifiable encrypted signature and its security goal, then we construct a secure certificate-based verifiable encrypted signature scheme, and gives the security analysis. The analysis shows that our scheme satisfies the security properties including validity, unforgeability, and opacity, and simplifies the certificate management process, solves the escrow problem, and there are fewer pairing operations and the least number of the total operations comparing with the other existing verifiable encrypted signature schemes.
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