Verifiably encrypted short signatures from bilinear maps

In 2003, Boneh et al. proposed the first efficient verifiably encrypted signature scheme (BGLS) from bilinear maps, which can be used in fair exchange protocols of short signatures. However, there are two weaknesses in the scheme. The security proof is built on a weaker security model, in which the key pair of the adjudicator is chosen by the simulator instead of the signature forger. The other is that the ordinary signatures to be verifiably encrypted are deterministic. They suffer from strong collision attacks of hash functions. In this paper, we propose an enhanced verifiably encrypted short signature scheme. The new scheme is strongly unforgeable in the random oracle model under a stronger security model, where two inside adversaries, malicious adjudicator and malicious verifier, have more power than ever. The new scheme would tally with the actual circumstances of electronic commerce.