Proxy signcryption means that the proxy signcrypter obtains the delegate authorization from the original signcrypter and then signcrypts the specified message on behalf of the original signcrypter. In this paper, we construct an identity-based proxy signcryption protocol (IBPSP) based on the universally composable (UC) framework. In the random oracle model, we prove that this protocol has the semantic security under the gap bilinear Diffie-Hellman and computational Diffie-Hellman assumptions. At the same time, an ideal functionality of the identity-based proxy signcryption protocol is defined in the UC security framework, and we also prove the equivalence between the universally composable identity-based proxy signcryption protocol and its IND-CCA2 and UF-CMA security. Analysis shows this IBPSP has both low computation complexity and semantic security together with UC security.

As a cryptography primitive for secure data transmission, certificateless proxy signcryption (CLPS) allows an original signcrypter to entrust his signing authority to a proxy signcrypter for signing specified message on his behalf. In this paper, we combine CLPS with cyclic multiplication groups (CMGs) to construct a new certificateless proxy signcryption scheme from CMGs (CMGs-CLPSS). CMGs-CLPSS will receive significant attention because it simplifies the traditional public key cryptosystem (PKC) and solves the key escrow issue suffered by identity-based public key cryptosystem (IB-PKC). In CMGs-CLPSS, an encrypted message can only be decrypted by a designated receiver who is also responsible for verifying the message; moreover, if a later dispute over repudiation occurs, the designated receiver can readily announce ordinary CLPS for public verification without any extra computation effort. CMGs-CLPSS is proved to have the indistinguishability under adaptive chosen-ciphertext attacks (IND-CCA2 security) and existential unforgeability under adaptive chosen-message attacks (UF-CMA security) in the random oracle model. CMGs-CLPSS outperforms the existing schemes on the basis of computational complexity and is suitable for applications in digital contract signing and online proxy auction, and so on.

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