Pairing-based non-interactive zero-knowledge proofs

A non-interactive zero-knowledge proof permits the construction of a proof of the truth of a statement that reveals nothing else but the fact that the statement is true. Non-interactive zero-knowledge proofs are used in the construction of numerous cryptographic schemes such as public-key cryptosystems and advanced digital signatures. The only practically efficient constructions of non-interactive zero-knowledge proofs that are based on standard intractability assumptions come from pairing based-cryptography. These pairing-based non-interactive zero-knowledge proofs integrate smoothly with other pairing-based cryptographic schemes making the combined schemes quite efficient.

We will sketch how to construct non-interactive zero-knowledge and non-interactive witness-indistinguishable proofs from modules with a bilinear map. The general approach based on modules with a bilinear map implies that different types of groups with pairings can be used in the construction of non-interactive cryptographic proofs and that security can be based on a number of different decisional assumptions.