Public Key Cryptosystem Base On Bilinear Pairing And It’s Application

Boneh deduced bilinear pairing from the Tate pairing, Weil pairing of hyperelliptic curves in recent years. Moreover, the bilinear pairing acts as an effective tool for constructing cryptographic schemes. Therefore, the paper takes the bilinear pairng as a tool which resolves some security issues in public key cryptography system and designs a series of public key cryptosystem based on bilinear pairings and makes further research on some applications of the public key cryptography system.Firstly,For some signature schemes with tracking identity, there are some problems in them.First, they are merely the threshold signature scheme based on the identity of system key managers, but did not point out the identity of threshold signature members. Second, the system manager can not effectively control on signaturing of the members, and thus there is no way to revoke these members’s signature power. Therefore, taking place of the system key manager, these members can make use of the old signature key and make signatures again. With the help of bilinear pairing, the paper proposes a threshold signature scheme with a tracing identity which can solve the above problems.Nextly, to resolve the problem of delegation of key in an IBE scheme or a HIBE scheme and the problem of trust in everyday life(i.e.,we do not believe anyone is honest and reliable in life,but do some ones of one group), the paper presents a certificateless threshold public key encryption scheme.ln the scheme,the decryption party generates his whole private key share for decryption,togethering with an administration while the administration does not know the decryption party’s private key share for decryption. Making use of q-SDH assumption, the paper constructes the scheme.The security of the scheme is reduced to the solving of Decisional Bilinear Diffie-Hellman problem.Moreover, the scheme is secure under chosen ciphertext attack in the standard model.Furthering the application of certificateless threshold encryption scheme in practice and combining application of the electronic voting system,the paper proposes two concrete scheme about the electronic voting which are a threshold-based electronic voting scheme and a hierarchical electronic voting scheme.In an electronic voting scheme based on threshold, checking of ballot requires some ballot checkers’s cooperation in the author’s scheme.This makes the result of ballot checking be acceptable. In the hierarchical electronic voting shceme,the administrator separates the voters into many districts and takes some participants as the administrators and the ballot inspectors who manage the cast vote and check ballot in the districts,respectively.Every district has an electronic bulletin board on which there are a list of commitments to vote license,a vote list and a list of ballot classification.The districts are not divided into some smaller ones until they are moderate in size.Compared with the no-hierarchical electronic voting scheme,The efficiency of counting vote is very high in the hierarchical electronic voting scheme works efficiently.Lastly,the paper furthers research on ABE(Attributed-Based Encryption).For the relationship between the set of properties and its subset, the authors propose a hierarchical attribute-based encryption scheme in which the private key is associated with a collection of properties. If a user has the attributes set the appropriate key, the user can be managed with a collection of properties, any subset of the relevant key. In addition, we also proved to meet the IND-sSET-the CPA security of the encryption scheme in the standard model.For the case that the user possesses the attributes which is distributed and authenticated by the different authorities, the author proposed an attribute-based encryption scheme with many authorities. The universal set of attribute is divided into a number of subsets of attribute. Moreover,the result which these attribute subsets intersect is null set.For an attribute subset, an authority A takes charge of monitoring it and assigning a value to an attribute in the attribute subset.Moreover,He still genernates the private key corresponding to an attribute in the attribute subset. Anybody encrypts a plaintext with an attribute set and get a ciphertext which is sent out.The user, who possesses the attribute set, can decrypt the ciphertext. The author’s chemc meets the security of IND-sSET-CPA.