Many ID-based strong designated verifier signature schemes have been proposed in recent years. However, most of them did not give the rigorous security proofs and did not satisfy the strongness property that anyone except the designated verifier can not check the validity of a designated verifier signature, In addition, considering some special applications, these schemes have larger data size of communication. To overcome those problems, exploiting message recovery techniques which are regarded as a useful method to shorten ID-based signatures size, we put forward an efficient ID-based strong designated verifier signature schemes with message recovery and give its rigorous security proof in the random oracle model based on the hardness assumptions of the computational Bilinear Diffie-Hellman problem in this paper. To the best of our knowledge, it is the first ID-based strong designated verifier signature schemes with message recovery and rigorous security proofs. Due to its merits, it can be used in some special environments where the bandwidth is one of the main concerns, such as PDAs, cell phones, RFID etc.
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