Pianist: Scalable zkRollups via Fully Distributed Zero-Knowledge Proofs

In the past decade, blockchains have seen various financial and technological innovations, with cryptocurrencies reaching a market cap of over 1 trillion dollars. However, scalability is one of the key issues hindering the deployment of blockchains in many applications. To improve the throughput of the transactions, zkRollups and zkEVM techniques using the cryptographic primitive of zero-knowledge proofs (ZKPs) have been proposed and many companies are adopting these technologies in the layer-2 solutions. However, in these technologies, the proof generation of the ZKP is the bottleneck and the companies have to deploy powerful machines with TBs of memory to batch a large number of transactions in a ZKP.In this work, we improve the scalability of these techniques by proposing new schemes of fully distributed ZKPs. Our schemes can improve the efficiency and the scalability of ZKPs using multiple machines, while the communication among the machines is minimal. With our schemes, the ZKP generation can be distributed to multiple participants in a model similar to the mining pools. Our protocols are based on Plonk, an efficient zero-knowledge proof system with a universal trusted setup. The first protocol is for data-parallel circuits. For a computation of M sub-circuits of size T each, using M machines, the prover time is O(T log T + M log M), while the prover time of the original Plonk on a single machine is O(MT log(MT )). Our protocol incurs only O(1) communication per machine, and the proof size and verifier time are both O(1), the same as the original Plonk. Moreover, we show that with minor modifications, our second protocol can support general circuits with arbitrary connections while preserving the same proving, verifying, and communication complexity. The technique is general and may be of independent interest for other applications of ZKP.We implement Pianist (Plonk vIA uNlimited dISTribution), a fully distributed ZKP system using our protocols. Pianist can generate the proof for 8192 transactions in 313 seconds on 64 machines. This improves the scalability of the Plonk scheme by 64×. The communication per machine is only 2.1 KB, regardless of the number of machines and the size of the circuit. The proof size is 2.2 KB and the verifier time is 3.5 ms. We further show that Pianist has similar improvements for general circuits. On a randomly generated circuit with 2
²⁵
gates, it only takes 5 s to generate the proof using 32 machines,24.2× faster than Plonk on a single machine.