Efficient ID-based digital signatures with message recovery

A digital signature with message recovery is a signature that the message itself is not required to be transmitted together with the signature. Comparing with other (non-short) digital signatures, it has the advantage of small data size of communication. This kind of signature schemes have been widely investigated a decade ago, but, no ID-based message recovery signature is proposed until 2005 by Zhang et al. Since, up to the present, no method can be used to shorten ID-based signatures directly, ID-based message recovery signatures are regarded as a useful method to shorten ID-based signatures, in contrast to proposing a short signature scheme. In this paper, two new ID-based signature schemes with message recovery are proposed. The first one can deal with messages of fixed length and the second one can deal with messages of arbitrary length. Similar to Zhang et al.'s schemes, our schemes shows the idea of shortening ID-based signatures. However, our schemes are more efficient than Zhang et al.'s schemes. In addition, after comparing with Boneh et al.'s short signature (which is not ID-based), we find that although the communication cost is still a little larger than that of a short signature, the computational cost of our scheme is less than that of Boneh et al.'s short signature in the verification phase and our schemes surpass a short signature scheme in the concept of ID-based property. Under the hardness of k-BDHI problem, our schemes are proven secure in the random oracle model.