Pairing-based non-interactive zero-knowledge arguments and applications

Abstract

Elliptic curves with a bilinear map, or pairing, have a rich algebraic structure that has been fundamental to develop practical Non-Interactive Zero-Knowledge (NIZK) proofs. On the theoretical side, we explore how efficient can NIZK proofs be under weak complexity assumptions. Specifically, we reduce the cost of proofs of satisfiability of quadratic equations, we define a new commitment scheme that is compatible with other pairing-based NIZK arguments, and we construct a simulation-sound argument that results in a new a signature of knowledge with communication sublinear in the circuit size under standard assumptions. Additionally, we study how to reduce the cost of verification in one of the most widely deployed NIZK arguments in practice.