Design And Research Of Group Digital Signature Schemes

Since Diffie and Hellman proposed the concept of digital signature, the technique of it has been extensively and deeply mined. Besides following the traditional research of digital signature, researchers have derived Blind Signature, Threshold Signature, Proxy Signature, Forward-Secure Signature, and so on. The Group Signature Scheme researched in this dissertation is among them, which has attracted a lot of attentions in this world.The Group Signature extends the traditional Digital Signature concept to a multi-party setting. In a group digital signature scheme, members of a given group are allowed to sign on behalf of the entire group. The signatures can be verified using a single group public key. However, the signatures are anonymous, which means nobody except the designated member, called group manager, can open the signature or revoke the identity of the signer. In addition, the signatures are unlinkable. It is impossible to distinguish whether the different signatures come from the same signer. There exist several other group-oriented concepts for signature schemes. The most important ones are multi-signatures and proxy signatures. Multi-signatures can be seen as generalized group signature without the ability of "opening" signatures, while proxy signatures are group signatures that do not provide anonymity.In this dissertation, from chapter 3 to 5, it takes a deep research on three aspects of Group Signature. The first one is to design a new type of group signature, the second is to design a kind of group signature scheme with authorization, and the third is to design two new kinds of group blind signature scheme. The details are as follows:In section 3.3 of chapter 3, it derives a new type of signature scheme based on the scheme proposed by Boneh and Boyen.In section 3.4 of chapter 3, taking advantage of CS98 encryption scheme and our new signature scheme, it designs a new type of group signature scheme. The security of the new group signature scheme is based on the q-Strong Diffie-Hellman assumption and the Decisional Diffie-Hellman assumption in the random oracle model. The length of the new group signature is a little longer than that of BBS short group signature scheme. However, in the group signature scheme, giving certificates and private keys to group members do not need any third trusted party, while in BBS short group signature scheme it does need.In section chapter 4, it adds algorithm AuthGen to the BMW groupsignature scheme. Using AuthGen, we obtain member authorization auth_i. Bymeans of key generation algorithm, we obtain issuing key for authorization certificate sk_a and verifying key for authorization certificate pk_a. With thehelp of sk_a, we can sign on to produce member's authorizationcertificate authcert_i. Compared with BMW's scheme, although the speed ofinstance production of group signature scheme slows down, the new scheme strengthens group signature scheme with authorization characteristic. Furthermore, the proof of full traceability security of group signature in this paper is simpler than that of BMW's scheme.In section 5.3 of chapter 5, it constructs a new group blind signature scheme on the basis of ACJT group signature scheme. The security of the new scheme is based on the strong RSA assumption and the decisional Diffie-Hellman assumption, of which is different from the scheme of LR98. In the mean time, the efficiency of the user to blind the content of the signer is improved. To blind the group signature of ACJT, this paper only adds the computation of modular exponentiation and modular addition; while the scheme in LR98 adds the computation of double discreet logarithm, root of the discreet logarithm and random permutation in order to blind the group signature of CS97. As a result, the scheme proposed by this paper is much lower than the one in LR98 with respect to computation complexity and higher with respect to efficiency.In section 5.4 of chapter 5, it constructs a provably security ID-baesd group blind signature scheme on the basis of CZK's ID-based group signature scheme. The security of the new scheme is based on the computational Diffie-Hellman assumption under the random oracle model, of which is different from the scheme of LR98. In the mean time, the efficiency of the user to blind the content of the signer is improved. To blind the group signature of CZK, this paper only adds the computation of modular addition; while the scheme in LR98 adds the computation of double discreet logarithm, root of the discreet logarithm and random permutation in order to blind the group signature of CS97. As a result, the scheme proposed by this paper is much lower than the one in LR98 with respect to computation complexity and higher with respect to efficiency.