Lite-PoT: Practical Powers-of-Tau Setup Ceremony

2025-03-06

AI Summary

To address the high on-chain overhead, low participation, and centralization risks inherent in Powers-of-Tau (PoT) trusted setup ceremonies for zk-SNARKs, this paper proposes a lightweight decentralized PoT protocol. Methodologically, it introduces: (1) a fraud-proof-based verification mechanism that reduces per-participant on-chain cost to O(1); (2) SNARK proof aggregation, enabling m participants’ contributions to incur only O(d) on-chain operations—decoupling participation scale from computational complexity; and (3) optimizations combining bilinear-pairing curve scalar multiplication with efficient smart contract design. The protocol supports PoT generation up to order 2¹⁵, achieves a 16× improvement in on-chain operation efficiency, and reduces individual participation cost to 1/m of prior schemes. These contributions significantly enhance the decentralization, scalability, and practicality of zk-SNARK trusted setups.

Technology Category

• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) schemes have gained significant adoption in privacy-preserving applications, decentralized systems (e.g., blockchain), and verifiable computation due to their efficiency. However, the most efficient zk-SNARKs often rely on a one-time trusted setup to generate a public parameter, often known as the ``Powers of Tau"(PoT) string. The leakage of the secret parameter, $ au$, in the string would allow attackers to generate false proofs, compromising the soundness of all zk-SNARK systems built on it. Prior proposals for decentralized setup ceremonies have utilized blockchain-based smart contracts to allow any party to contribute randomness to $ au$ while also preventing censorship of contributions. For a PoT string of $d$-degree generated by the randomness of $m$ contributors, these solutions required a total of $O(md)$ on-chain operations (i.e., in terms of both storage and cryptographic operations). These operations primarily consisted of costly group operations, particularly scalar multiplication on pairing curves, which discouraged participation and limited the impact of decentralization In this work, we present Lite-PoT, which includes two key protocols designed to reduce participation costs: emph{(i)} a fraud-proof protocol to reduce the number of expensive on-chain cryptographic group operations to $O(1)$ per contributor. Our experimental results show that (with one transaction per update) our protocol enables decentralized ceremonies for PoT strings up to a $2^{15}$ degree, an $approx 16x$ improvement over existing on-chain solutions; emph{(ii)} a proof aggregation technique that batches $m$ randomness contributions into one on-chain update with only $O(d)$ on-chain operations, independent of $m$. This significantly reduces the monetary cost of on-chain updates by $m$-fold via amortization.

Problem

• Reduces costly on-chain operations in zk-SNARK setup ceremonies.
• Enables decentralized Powers-of-Tau setup with improved scalability.
• Minimizes monetary costs via proof aggregation and fraud-proof protocols.

Innovation

• Reduces on-chain operations to O(1) per contributor
• Aggregates m contributions into one on-chain update
• Enables decentralized ceremonies for high-degree PoT strings