Plonk is a widely used succinct non-interactive proof system that uses univariate polynomial
commitments. Plonk is quite flexible: it supports circuits with low-degree “custom” gates as …

Abstract zk-SNARK constructions that utilize an updatable universal structured reference
string remove one of the main obstacles in deploying zk-SNARKs [GKMMM, Crypto 2018] …

We present a methodology to construct preprocessing zkSNARKs where the structured
reference string (SRS) is universal and updatable. This exploits a novel use of holography …

We propose Bulletproofs, a new non-interactive zero-knowledge proof protocol with very
short proofs and without a trusted setup; the proof size is only logarithmic in the witness size …

Ever since their introduction, zero-knowledge proofs have become an important tool for
addressing privacy and scalability concerns in a variety of applications. In many systems …

This paper introduces Spartan, a new family of zero-knowledge succinct non-interactive
arguments of knowledge (zkSNARKs) for the rank-1 constraint satisfiability (R1CS), an NP …

This paper presents Prio, a privacy-preserving system for the collection of aggregate
statistics. Each Prio client holds a private data value (eg, its current location), and a small set …

We present a zero-knowledge argument for NP with low communication complexity, low
concrete cost for both the prover and the verifier, and no trusted setup, based on standard …

We provide a zero-knowledge argument for arithmetic circuit satisfiability with a
communication complexity that grows logarithmically in the size of the circuit. The round …

We present Libra, the first zero-knowledge proof system that has both optimal prover time
and succinct proof size/verification time. In particular, if C is the size of the circuit being …