Polyhedra Network has achieved Ethereum full node ZK proof.

Source: Polyhedra Network

Overview

The full nodes of Ethereum PoS are crucial for building zkBridge and any interoperability protocol on Ethereum. Sync committees are not secure enough for these purposes, as the cryptographic economic security of sync committees (currently only about 32 million USD in ETH staking) is far from ideal. Any cross-chain infrastructure, oracle, and data processing service that relies on the sync committee deployment on Ethereum is insecure.

Polyhedra Network has designed and implemented the zkBridge system to demonstrate the full node of Ethereum PoS (the total value of ETH currently staked is about $40 billion). All Ethereum and its rollups (such as Arbitrum, Linea, Optimism, zkSync, Mantle, etc.) on LayerZero will have a zk client based on the ZK proof of Ethereum full node. Polyhedra Network uses its efficient proof system deVirgo, which is efficient enough to generate Ethereum full node proof within 10 seconds, and the proof speed is fast enough to catch up with the block generation speed of Ethereum.

The implementation of zero-knowledge proofs for Ethereum full nodes will enable Ethereum and its rollups to achieve completely trustless, efficient, and secure interoperability. The Polyhedra Network system also allows any L1 and L2 (such as BNB Smart Chain and opBNB) as well as any application to transfer all current and historical Ethereum data. This allows smart contracts to access Ethereum data without trust and implement various computational logic, while its security is ensured by Ethereum PoS full nodes.

Proof of Stake (PoS) Full Nodes are Crucial for Ethereum Security

Compared with Ethereum light clients, Ethereum full node proof has higher security guarantees. The security of Ethereum light clients depends entirely on a system called the "sync committee". However, the size of the sync committee is only 512 members, rotating approximately every day (about 27.3 hours). The total staked assets are only 16384 ETH (512 * 32), which is very small compared to the daily transaction volume of cross-chain bridges connecting the Ethereum ecosystem with other networks (over $300 million). Currently, only $32 million worth of ETH is staked.

Another issue is that the synchronization committee does not always sign the blocks (such as block 17239413 and block 17239414). Statistical data shows that 1.6% of blocks are not signed by the majority of members of the synchronization committee, and this issue may occur on average once every 12 minutes.

Overview of the Ethereum Full Node Verification System

In order to solve these problems, Polyhedra Network has decided to abandon the use of synchronous committees and utilize the full PoS consensus of the Ethereum blockchain since the merge of Ethereum. This will prove that each block on the Ethereum mainnet contains over 20,000 signatures (40 times more than the 512 synchronous committees).

In order to handle a 40-fold increase in workload, Polyhedra Network has adopted its unique proof system - deVirgo. This proof system has unparalleled processing power, thanks to its theoretical improvements and significant engineering progress. The deVirgo protocol theoretically eliminates the need for very large FFT or MSM, making proof generation time linearly related to the number of signatures. The protocol has been deployed on zkBridge and supports parallel and distributed computing.

Proof system experiments conducted on circuits with a scale of billions have shown proof generation times of less than 10 seconds, which can keep up with the speed of Ethereum block generation (approximately 12 seconds), without increasing proof size or verification time.

Using efficient proof systems to prove Ethereum full nodes

In order to quickly prove the Ethereum full node, Polyhedra Network uses its efficient proof system deVirgo. deVirgo is a distributed version of the Virgo protocol, aimed at parallelizing the GKR protocol by distributing computation across multiple machines. By using deVirgo, zkBridge can support fast and flexible interoperability between different blockchains without relying on external trust assumptions. zkBridge uses recursive proof to prove the proof generated by deVirgo, recursively proving the corresponding block header. Recursive proof reduces the on-chain verification cost to about 220K fuel on any EVM-compatible blockchain network.

deVirgo's key breakthrough is the confirmation that the consensus of Ethereum full nodes can be represented as the property of a data parallel circuit. Assuming there is a data parallel arithmetic circuit and N machines, deVirgo proves that the system can divide the data parallel circuit into N sub-circuits, with each machine calculating only one sub-circuit. The verification of Ethereum's full consensus is such a data parallel circuit, which contains over 30,000 identical signature verification algorithms and hashes.

deVirgo's core technology is a distributed sumcheck protocol. In deVirgo, the sumcheck protocol is divided into two stages. In the first stage, each machine processes its own sub-circuit and collectively generates an aggregated proof. The remaining work is small enough for one machine to handle. At this point, the machine can execute the second stage and complete the distributed sumcheck.

Evaluating the Performance of Ethereum Full Nodes' ZK Proofs

In order to evaluate the implementation of BLS signature aggregation, Polyhedra Network measured the runtime of deVirgo proof and recursive verification using two AMD EPYC 7763 CPUs. The results are as follows:

Polyhedra Network has deployed an Ethereum full node proof system on zkBridge. zkBridge sets Ethereum as the sending chain and other networks such as BNB Chain and Avalanche as the receiving chains. Results show that, in the case of delays containing all components, zkBridge can generate proof of Ethereum full node within 12 seconds and verify block headers on BNB Chain and other networks.

Polyhedra Network will continue to optimize its implementation. The plan is to use GPU acceleration in the near future to reduce upfront costs and achieve better decentralization. However, the current zkBridge proof system is already efficient enough to keep up with Ethereum's block time.

Summary

By implementing Ethereum full node proof, Polyhedra Network uses zkBridge to achieve completely trustless, efficient, and secure interoperability to connect the Ethereum ecosystem (including L1 and L2) with other networks. In addition, all zk clients of Ethereum and its rollups (such as Arbitrum, Linea, Optimism, zkSync, Mantle) on LayerZero of Polyhedra Network will be equipped with Ethereum full node ZK proof. This will bring the staking security of Ethereum full nodes (about $40 billion) to zk clients on LayerZero.

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