Research On Some Multi-Party Signature Schemes

With the rapid development of computer network technology,many electronic transaction systems were implemented to carry out such traditional transactions through networks. In these systems,many parties are often involved.The security needs of these systems promoted the emergence of many new types of multi-party signatures.Defining the formal security models for these multi-party signature schemes and putting forward multi-party signatures schemes with provable security are the focus in this field.Thereby our point in this thesis is to study and design a series of multi-party schemes via formalization means.Our main achievements are as follows:1.We propose a new type of multi-party signature:hybrid proxy multisignature(HPMS). Using the game-based approach,we define the formal security model for the HPMS schemes.In addition,we propose a concrete HPMS scheme and prove the security of the scheme in the random oracle model.2.We propose a multi-proxy multi-signature scheme which can be proven secure in the standard model under the assumption that the computational Diffie-Hellman problem on the bilinear group is hard.The scheme is flexible for it can be used to generate multi-proxy signatures and to generate proxy multi-signatures.3.We propose a threshold signature scheme which can resist an adaptive adversary. The scheme neither needs the parties to erase their local data,nor needs using zeroknowledge proofs.And the security proof does not need random oracles.Thus the scheme is more practical.4.We propose two efficient multi-signature schemes with tight reductions to the hardness of the computational Diffie-Hellman problem and to the hardness of decision Diffie-Hellman problem respectively.To the best of our knowledge,there is no multi-signature scheme with tight reduction in discrete logarithm settings.With the proof-of-possession(POP)based key registration protocol,the schemes can resist the notorious rogue key attacks.Thus the schemes can easily be implemented in the current public key infrastructures(PKI).5.We define the universally composable security of multi-signature schemes,i.e.the idea functionality F_MS.We propose a multi-signature scheme which UC-realizes F_MS. 6.We analysis a threshold-group scheme and a structured multi-signature scheme with signers' intentions.We point out the flaws in the two schemes and propose the improvements to overcome them.