Polyhedra Network has achieved Ethereum full-node ZK proof.

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Polyhedra Network Overview

Proving full-node Ethereum PoS is crucial for building zkBridge and any interoperability protocol on Ethereum. A synchronous committee is not secure enough for these purposes, as the current total value of ETH staked in the synchronous committee's cryptographic economic security is only about 32 million USD, which is far from ideal. Any cross-chain infrastructure, oracle, and data processing services relying on the synchronous committee deployment on Ethereum are insecure.

Polyhedra Network has designed and implemented the zkBridge system to prove full-node Ethereum PoS (currently a total value of approximately 400 billion USD staked).

All Ethereum and its rollups (such as Arbitrum, Linea, Optimism, zkSync, Mantle, etc.) on LayerZero at Polyhedra Network will have a zk client based on Ethereum full-node ZK proofs. Polyhedra Network adopts its efficient proof system deVirgo, which is efficient enough to generate proofs for Ethereum full nodes within 10 seconds, keeping pace with Ethereum's block generation speed.

The implementation of zero-knowledge proofs for Ethereum full nodes will enable Ethereum and its rollups to achieve fully trustless, efficient, and secure interoperability. Polyhedra Network's system also allows any L1 and L2 networks such as BNB Smart Chain and opBNB, as well as any applications, to access all current and historical Ethereum data without trust, while their security is guaranteed by Ethereum PoS full nodes.

Polyhedra Network: The Importance of Proving Full-Node Ethereum PoS for Security

Compared to Ethereum light clients, proving full-node Ethereum has higher security guarantees. The security of Ethereum light clients depends entirely on a system called the "synchronous committee." However, the synchronous committee consists of only 512 members, rotating approximately every 27.3 hours. With a total staked asset of only 16384 ETH (512 * 32) and a daily transaction volume exceeding 300 million USD connecting the Ethereum ecosystem with other networks through cross-chain bridges, the number is very small compared to the current staked 32 million USD in ETH.

Another issue is that the synchronous committee does not always sign blocks, for example, blocks 17239413 and 17239414. Statistics show that 1.6% of blocks are not signed by the vast majority of the synchronous committee members, and this issue may occur on average every 12 minutes.

Polyhedra Network: System Overview of Proving Full-Node Ethereum

To address these issues, Polyhedra Network decided to abandon the use of the synchronous committee and utilize the full PoS consensus of the Ethereum blockchain since the Ethereum merge. This will prove over 20,000 signatures included in every block on the Ethereum mainnet (40 times more than the 512 synchronous committee).

To handle the 40x increase in workload, Polyhedra Network 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 computation.

Experiments with the proof system on a billion-scale circuit show proof generation times of less than 10 seconds, keeping up with Ethereum's block generation speed (approximately 12 seconds) without increasing proof size or verification time.

Polyhedra Network: Proving Full-Node Ethereum Efficiently with a High-Performance Proof System

To swiftly prove full-node Ethereum, Polyhedra Network utilizes its efficient proof system deVirgo. deVirgo is a distributed version of the Virgo protocol designed to parallelize GKR protocols by distributing computations 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 proofs to prove the proofs generated by deVirgo, recursively proving the corresponding block headers. Recursive proofs reduce the on-chain verification cost to about 220K gas on any EVM-compatible blockchain network.

The key breakthrough of deVirgo lies in recognizing that Ethereum full-node consensus can be represented as the property of a data-parallel arithmetic circuit. Assuming a data-parallel arithmetic circuit 𝐶 and N machines, the deVirgo proof system can split the data-parallel circuit into N sub-circuits, with each machine computing one sub-circuit. The verification of Ethereum full consensus is such a data-parallel circuit, containing over 30,000 identical signature verification algorithms and hashes.

The core of deVirgo is a distributed sumcheck technique. In deVirgo, the sumcheck protocol is divided into two stages. In the first stage, each machine processes its sub-circuit and collectively generates an aggregate proof. The remaining work for a machine is small enough at this point. The machine can then execute the second stage, completing the distributed sumcheck.

Polyhedra Network: Performance Evaluation of Full-Node Ethereum ZK Proofs

To evaluate the implementation on BLS signature aggregation, Polyhedra Network measured the runtime of deVirgo proofs and recursive verification on two AMD EPYC™ 7763 CPUs. The results are as follows:

Polyhedra Network has deployed the full-node Ethereum proof system on zkBridge. zkBridge configures Ethereum as the sending chain and other networks such as BNB Chain and Avalanche as receiving chains. Results show that with all components' latency, zkBridge can generate full-node Ethereum proofs within 12 seconds and verify block headers on BNB Chain and other networks.

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

Polyhedra Network Summary

By implementing full-node Ethereum proofs, Polyhedra Network achieves fully trustless, efficient, and secure interoperability using zkBridge to connect the Ethereum ecosystem, including L1 and L2, with other networks. Additionally, all Ethereum and its rollups on LayerZero (such as Arbitrum, Linea, Optimism, zkSync, Mantle) at Polyhedra Network will be equipped with Ethereum full-node ZK proofs. This brings the security of full-node Ethereum staking, approximately 400 billion USD, into the zk clients on LayerZero.

The full-node Ethereum proof system also allows current and historical Ethereum data, including block headers and transaction data, to be accessed by any network and application. This enables smart contracts on any blockchain to access Ethereum data without trust and handle various computation logics. All security is ensured by Ethereum PoS full-node ZK proofs.