Paper 2020/1318 Original: eprint.iacr.org/2020/1318 ↗

Poppins: A Direct Construction for Asymptotically Optimal zkSNARKs

Abstract

We present Poppins, a direct construction of a zero-knowledge argument system for general computation that features an $O_{\lambda}(n)$ time prover and an $O_{\lambda}(1)$ time verifier (after a single $O_{\lambda}(n)$ public setup) for computations of size $n$. Our scheme utilizes a universal linear-size structured reference string (SRS) that allows a single trusted setup to be used across all computation instances of a bounded size. Concretely, for computations of size $n$, our prover's cost is dominated by $35$ multi-exponentiations of size $n$ and our verifier's cost is dominated by $34$ pairings. To achieve the stated asymptotics, we first construct a nearly-optimal zkSNARK with a logarithmic verifier in the random oracle model. We then show how to achieve a constant-time verifier using (single-layer) proof composition. Along the way we design (1) a new polynomial commitment scheme for evaluation-based representations of polynomials, (2) an asymptotically optimal inner-product argument system, (3) an asymptotically optimal multi-Hadamard-product argument system, and (4)~a new constraint system for NP that is particularly well-suited for our bundle of techniques.