How does Polyhedra Network use zkBridge to achieve Ethereum full node ZK proof?

Author: ABCDE Capital


It is crucial to prove that full nodes on Ethereum’s PoS are essential for building zkBridge and any interoperability protocols on Ethereum. The security of a synchronous committee is not sufficient because the economic security of the synchronous committee (currently only about 32 million USD worth of ETH staked) is far from ideal. Any cross-chain infrastructure, oracle, and data processing services that rely on the deployment of a synchronous committee on Ethereum are insecure.

Polyhedra Network has designed and implemented the zkBridge system to prove the importance of full nodes on Ethereum’s PoS (with a total value of approximately 40 billion USD staked). All zk clients of Ethereum and its rollups (such as Arbitrum, Linea, Optimism, zkSync, Mantle, etc.) on LayerZero will be based on ZK proofs generated by Ethereum full nodes. Polyhedra Network has adopted its efficient proof system, deVirgo, which is capable of generating proofs for Ethereum full nodes within 10 seconds, fast enough to keep up with the block generation speed of Ethereum.

The zero-knowledge proof implementation of Ethereum full nodes enables complete trustless, efficient, and secure interoperability for Ethereum and its rollups. Polyhedra Network’s system also allows any L1 and L2 networks (such as BNB Smart Chain and op BNB) and any applications to transfer all current and historical Ethereum data. This enables smart contracts to access Ethereum data without trust and implement various computational logics, with security ensured by Ethereum PoS full nodes.

Proving the importance of Ethereum PoS full nodes for security

Compared to Ethereum light clients, Ethereum full node proofs offer higher security guarantees. The security of Ethereum light clients relies entirely on a system called the “synchronous committee.” However, the synchronous committee consists of only 512 members, rotating approximately once a day (about 27.3 hours). The total staked assets are only 16,384 ETH (512 * 32), which is significantly smaller compared to the daily transaction volume (over 300 million USD) of cross-chain bridges connecting the Ethereum ecosystem with other networks (currently only 32 million USD worth of ETH staked).

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

System overview of proving Ethereum full nodes

To address these issues, Polyhedra Network has decided to abandon the use of the synchronous committee and leverage the full PoS consensus of the Ethereum blockchain since the merge. This will prove the inclusion of over 20,000 signatures in each block on the Ethereum mainnet (increasing the number of signatures by 40 times compared to the 512 synchronous committee).

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

The proof-of-concept experiment conducted on a billion-scale circuit shows that the proof generation time is less than 10 seconds, which can catch up with the speed of Ethereum block generation (about 12 seconds) without increasing proof size or verification time.

Proving Ethereum Full Nodes Using an Efficient Proof System

To quickly prove Ethereum full nodes, Polyhedra Network uses its efficient proof system deVirgo. deVirgo is a distributed version of the Virgo protocol, designed to parallelize the GKR protocol 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 fuel on any EVM-compatible blockchain network.

The key breakthrough of deVirgo is the recognition 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 C and N machines, the deVirgo proof system can divide the data-parallel circuit into N sub-circuits, with each machine computing only one sub-circuit. The verification of Ethereum full consensus is such a data-parallel circuit, which includes 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 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 ZK Proofs for Ethereum Full Nodes

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

Polyhedra Network has deployed the 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. The results show that, in the case of including all components’ latency, zkBridge can generate proofs for Ethereum full nodes 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 reduce upfront costs and achieve better decentralization through GPU acceleration in the near future. However, the current zkBridge proof system is already efficient enough to keep up with Ethereum’s block generation time.


By implementing proofs of Ethereum full nodes, Polyhedra Network achieves fully trustless, efficient, and secure interoperability using zkBridge to connect the Ethereum ecosystem (including L1 and L2) with other networks. In addition, Polyhedra Network’s zk clients for all Ethereum and its rollups (such as Arbitrum, Linea, Optimism, zkSync, Mantle) on LayerZero will be equipped with ZK proofs of Ethereum full nodes. This brings the staking security of Ethereum full nodes (about $40 billion) to zk clients on LayerZero.

The Ethereum full-node proof-of-stake 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 the need for trust and process various computational logic. All security is ensured by the ZK proof of Ethereum PoS full nodes.

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