FlexProofs: A Vector Commitment with Flexible Linear Time for Computing All Proofs

TL;DR

FlexProofs introduces a vector commitment scheme that allows efficient proof generation in linear time, with adjustable batch size for speed optimization, and is compatible with zkSNARKs for practical cryptographic applications.

Contribution

The paper presents FlexProofs, a novel vector commitment scheme with flexible batch size and optimal proof generation time, along with a new functional commitment for multi-exponentiations.

Findings

FlexProofs achieves ${ m O}(N)$ proof generation time with adjustable batch size.

FlexProofs can be 6 times faster than HydraProofs for N=2^{16}.

Enables practical applications like verifiable secret sharing and robust aggregation.

Abstract

In this paper, we introduce FlexProofs, a new vector commitment (VC) scheme that achieves two key properties: (1) the prover can generate all individual opening proofs for a vector of size $N$ in optimal time ${\cal O}(N)$, and there is a flexible batch size parameter $b$ that can be increased to further reduce the time to generate all proofs; and (2) the scheme is directly compatible with a family of zkSNARKs that encode their input as a multi-linear polynomial. As a critical building block, we propose the first functional commitment (FC) scheme for multi-exponentiations with batch opening. Compared with HydraProofs, the only existing VC scheme that computes all proofs in optimal time ${\cal O}(N)$ and is directly compatible with zkSNARKs, FlexProofs may speed up the process of generating all proofs, if the parameter $b$ is properly chosen. Our experiments show that for $N=2^{16}$ and $b=\log^2 N$, FlexProofs can be $6\times$ faster than HydraProofs. Moreover, when combined with suitable zkSNARKs, FlexProofs enable practical applications such as verifiable secret sharing and verifiable robust aggregation.