ID-Based Signcryption with Restrictive Unsigncryption

We introduce a novel cryptographic primitive, the Signcryption with Restrictive Unsigncryption (SRU), which means that the sender sign crypts a message and sends the cipher text to a receiver, however, the sender embeds some restrictive conditions into this cipher text. Hence the receiver cannot completely unsigncrypt the cipher text and obtain the original message unless the cipher text is authorized by a third party who is appointed by the sender. Based on this property, the SRU scheme can be applied to many scenarios, such as, digital will, scheduled payment, sealed-bid auction, and so on. We present the formal definitions and security models for the SRU scheme in the identity-based setting, and also construct a concrete ID-SRU scheme using bilinear pairings. Our proposed scheme is provably secure in the random oracle model under the bilinear Diffie-Hellman (BDH) assumption.