Verifiably encrypted signatures without random oracles

Verifiably encrypted signatures are employed when a signer wants to sign a message for a verifier but does not want the verifier to possess his signature on the message until some certain requirements of his are satisfied. This paper presented new verifiably encrypted signatures from bilinear pairings. The proposed signatures share the properties of simplicity and efficiency with existing verifiably encrypted signature schemes. To support the proposed scheme, it also exhibited security proofs that do not use random oracle assumption. For existential unforgeability, there exist tight security reductions from the proposed verifiably encrypted signature scheme to a strong but reasonable computational assumption.