Democratic group signatures （DGSs） attract many researchers due to their appealing properties, i.e., anonymity, traceability and no group manager. Security results of existing work are based on decisional Diffie-Hellman （DDH） assumption. In this paper, we present a democratic group signature scheme based on any gap Diffie-Hellman （GDH） group where DDH problem is easily but computational Diffe-Hellman （CDH） problem is hard to be solved. Besides the properties of ordinary DGSs, our scheme also provides the property of linkability, i.e., any public verifier can tell whether two group signatures are generated using the same private key. Security properties of our scheme employ a new and independently interesting decisional product Diffie-Hellman （DPDH） assumption which is weaker than DDH one.
Cryptography is an important tool in the design and implementation of e-voting schemes since it can provide verifiability, which is not provided in the traditional voting. But in the real life, most voters can neither understand the profound theory of cryptography nor perform the complicated cryptographic computation. An e-voting system is presented in this paper to leverage the use of cryptography. It combines the advantages of voting scheme of Moran-Naor and voting scheme based on homomorphic encryption. It makes use of the cryptographic technique, but it hides the details of cryptographic computation from voters. Compared with voting scheme of Moran-Naor, the new system has three advantages: the ballots can be recovered when the voting machine breaks down, the costly cut-and-choose zero-knowledge proofs for shuffling votes made by the voting machine are avoided and the partial tally result in each voting machine can be kept secret.
This paper presents a concrete democratic group signature scheme which holds （t, n）-threshold traceability. In the scheme, the capability of tracing the actual signer is distributed among n group members. It gives a valid democratic group signature such that any subset with more than t members can jointly reconstruct a secret and reveal the identity of the signer. Any active adversary cannot do this even if he can corrupt up to t - 1 group members.
