Title: Non-interactive Zero-Knowledge Proofs from Elliptic Curves

Speaker: Jens Groth, UCLA

Abstract:

A system for non-interactive zero-knowledge (NIZK) proofs allows a prover to send a single message to a verifier to prove some statement. The system must have the following three properties: 1) Completeness: A true statement can be proved. 2) Soundness: A false statement cannot be proved. 3) Zero-knowledge: The proof reveals that the statement is true, but nothing else! NIZK proofs play a central role in cryptology with numerous applications, including digital signatures and secure encryption.

While very useful, it is very hard to construct efficient NIZK proofs. Recently, in joint work with Ostrovsky and Sahai, we have for the first time constructed an NIZK proof that is efficient enough to be of practical value. The central building block in this construction is elliptic curves over a prime order field and the Weil-pairing.