Simulation-Sound NIZK Proofs for a Practical Language and Constant Size Group Signatures
Non-interactive zero-knowledge proofs play an essential role in many cryptographic protocols. The authors suggest several NIZK proof systems based on prime order groups with a bilinear map. They obtain linear size proofs for relations among group elements without going through an expensive reduction to an NP-complete language such as circuit satisfiability. Security of all their constructions is based on the decisional linear assumption. The NIZK proof system is quite general and has many applications such as digital signatures, verifiable encryption and group signatures.