Generally speaking, the signer can generate a signature for the message with his privatekey, and the verifer can verify the validity of this signature by using the signer’s public key.For the signer’s public key is public for everyone, so everyone can verify the signature’svalidity. However, in some time, the public verification is not desired, the signer does notwant everyone to verify the signature in some scenarios, such as in the competitive bidding,the electronic voting and the electronic auctions and so on. So, the contradiction between theauthentication and the privacy is emerged unavoidable.To satisfy the above requirements, Jakobsson proposed the concept of designated verifiersignature (DVS) schemes in1996. Jakobsson’s signature needed a special verifier designatedby the signer, and only the designated verifier was able to verify the signature’s validity. Dueto the designated verifier himself can simulate the signature which is indistinguishable fromthe one generated by the signer, the DVS scheme is considered as a special type of digitalsignature which provides the message authentication without non-repudiation. The DVSsolves the contradiction of the authentication and the privacy admirably.In this paper, we fully think over that the research of the designated verifier signatureis quite thorough, but designated multi-verifiers signature schemes are more than enough.The computational cost and communication cost of most designated Multi-verifiers signatureschemes are very large. Most of the designated verifier signature schemes are based on thebilinear pairings. For the operation of the bilinear pairings needs large amount ofcomputational cost, so, reducing the number of the bilinear pairings will be helpful forimproving the efficiency of the signature. At the same time, the designated verifier signaturecombined with other special signature has been become a research hotspot in recent years.Based on the situation mentioned obove, we mainly finished the following work in thispaper:1. Design a designated verifier signature scheme based on the discrete logarithm whichhas a low computational cost. We prove its security in the random oracle model.2. Analyze the existed designated verifier signature scheme thoroughly, and design anew ID-based Universal Designated Multi-verifiers Signature Scheme. In the proposedscheme, every designated verifier can verify the validity of the signature and simulate thesignature without the other designated Verifier’s participation. The method has used theknowledge of Lagrange interpolation polynomial. We embed designated Verifier’s the publickey in the interpolation polynomial, and each verifier can verify the signature by inputing hisprivate key and the signer’s public key. We also prove its security in the random oracle model. 3. Analyze the security of He’s a strong designated verifier proxy signature scheme(IDB-SDVPS). At the same time, we design a improve strong designated verifier proxysignature scheme, and we heuristic analyze the security of the improved scheme. |