Group Signature And Its Applications In Electronic Cash

With the rapid development of information science and technology, digital signatures find more and more application in our lives. The group signature, a special signature scheme, can allow any member of the group to sign on the behalf of the whole group. Any one who know the group public key is able to verify whether the signature is legitimate or not, but he can not know who sign the signature. If any dispute, there is group manager who can open the signature to reveal the identity of the actual signer. As group signatures are anonymous and also are anonymous control, for these characteristcs, group signature can be used in government, business, and military. However, security and efficiency make group signature hard to use in social.Many group signature schemes are insecurity, And others security group signature schemes is unefficient. Especially some group signature schemes cannot allow member revocation. Though some group schemes have member revocation algorithm, the algorithm is unefficient. These made group signatures hard to use in large group. So propose secure and efficient group signature and attack group signature are two important questions on group signature field. The main work of us is to solve these problems.The other work is about how to propose electronic cash scheme based group signature, as an important tool in electronic payment systems, E-cash (electronic cash) allow customers to pay anonymously. We propose a new fair E-cash scheme based on a secure group signature. Our scheme has many good characteristics: such as high efficiency, support cash tracing and owner tracing, and secure in standard assumptions, etc.When we proposed group signature or E-cash scheme, We use tools such as the knowledge prove, Elgamal encryption pairing, Chinese remainder theorem, schnorr signature scheme. and our schemes also based on number- theoretic assumptions. When talk about security of the group signature, we pay most attentation to coalition-resistant and unforgeability.Our researching results:1:Proposed a new group signature scheme,2:We proposed an attack of a group signature scheme , which based on Chinese Remainder Theorem. We show this scheme is insecurity. We also improved this scheme used Schnorr signature scheme. Our improved scheme is secure to our attack.3:A security flaw is identified in a revocation algorithm, an attack to this...