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A fuzzy identity-based signature (FIBS) scheme allows a user with identity ID to issue a signature that could be verified with identity ID if and only if ID and ID lie within a certain distance. To obtain an FIBS scheme that can resist known quantum attacks, we use the double-trapdoor technique from ABB10a for secret key extracting and the vanishing trapdoor technique from Boyen10 for message signing. In addition, in order to reflect the functionality of fuzziness, Shamir secret sharing scheme is also used in our construction. In this paper, we propose an FIBS scheme from lattices and prove that this new scheme achieves strong unforgeability under selective chosen-identity and adaptive chosen-message attacks (SU-sID-CMA) in the standard model. To the best of our knowledge, our scheme is not only the first FIBS scheme from lattices without random oracles but also the first FIBS scheme that achieves strong unforgeability.

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Through analysis, we point out Luo et al.’s and Sun et al.’s signcryption-based concurrent signature schemes have the same defect in ambiguity and therefore the fair exchange protocols based on their schemes are not fair. Thus based on the notions of signcryption and concurrent signature, a new signcryption-based concurrent signature scheme from bilinear pairing is presented, and based on this scheme, a new fair exchange protocol is proposed. Since we adopt a new method to construct the new signcryption-based concurrent signature scheme, the new scheme redresses the flaw of Luo et al.’s and Sun et al.’s schemes, and the fair exchange protocol based on the new scheme is also fair. Besides, due to the new scheme’s independence of the ring signature and simplification of encryption operations, the new scheme has the advantage of short signatures and low computation cost. We improve Luo et al.’s definition of the security model of a signcryption-based concurrent signature scheme and prove the proposed scheme and protocol are secure under the computational Diffie-Hellman assumption in the random oracle model.

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