ZK Bridges: How does zero-knowledge proof empower the cross-chain world?

In the rapidly developing field of blockchain technology, many protocols have been proposed and implemented, but each protocol adopts a different consensus method—from computational proof-of-work (Proof-of-Work) to incentive-based Proof-of-Stake, etc. Since the early days of blockchain, liquidity and assets have been gradually dispersed among different chains due to differences in protocols in various aspects such as consensus, security, and programming language. The cross-chain bridge has become a solution to this problem, which can reduce fragmentation and integrate liquidity between various blockchains. One such cross-chain bridge protocol is Wormhole, which facilitates the circulation of cryptocurrencies and non-fungible tokens (NFTs) between different smart contract blockchains such as Solana and Ethereum.

Current Risks of Cross-Chain Bridges

Cross-chain bridges can be quite tricky. Ensuring the security of its cross-chain bridges is an important challenge, as assets stored in smart contracts or central custodians need to be protected. Since bridge funds are stored centrally, they have historically been a target for hackers. The ever-evolving design of bridges also opens up opportunities for attackers to find new vulnerabilities and exploits. In 2022, Wormhole was hacked after a security fix was uploaded to Github, causing a loss of $325 million, and the hacker took away the funds after succeeding. Chainalysis reports that cross-chain bridge attacks will account for 69% of total stolen funds in 2022.

ZK Bridges: How does zero-knowledge proof empower the cross-chain world?

Image credit Chainalysis

ZK Bridges: How does zero-knowledge proof empower the cross-chain world?

Image credit DEFIYIELD

Another challenge is poor performance and reliance on central entities. Current cross-chain bridges face scalability issues. In order to update and adjust the state of the two chains, the cross-chain bridge requires a lot of computing power and storage capacity, resulting in significant overhead. To alleviate this burden, some cross-chain bridges have turned to a committee-style approach, where only a limited set of validators (or even just multisig holders) approve state transfers. However, this approach exposes them to vulnerabilities and potential attacks.

It is these issues that have prompted developers to look for alternative solutions, especially those utilizing zero-knowledge cryptography. Among these methods, the use of zk-SNARKs technology eliminates the need for committee models while ensuring the scalability of the network.

Cross-chain bridge based on zk-SNARKs technology

Currently, several projects are developing bridge solutions based on ZK technology across different ecosystems and development stages, such as:

  • Succinct Labs
  • zkIBC by Electron Labs
  • zkBridge by Polyhedra Network

These initiatives leverage zk-SNARKS technology to revolutionize the design of cross-chain bridges. However, in order to implement all of these methods successfully, a key requirement is a light client protocol - a piece of software that connects to full nodes and facilitates interaction with the blockchain. This protocol ensures that nodes can efficiently synchronize the block headers of the confirmed blockchain state.

Two main challenges arise when applying zk-SNARKs technology to cross-chain bridges. First, compared with rollups, cross-chain bridges require a larger circuit size. Second, the problem of minimizing on-chain storage and computing overhead needs to be addressed.

Succinct Labs

Succinct Labs is developing a light client for Ethereum 2.0's PoS (Proof of Stake) consensus, building a trust-minimized cross-chain bridge between Gnosis and Ethereum. This cross-chain bridge uses the efficiency of zk-SNARKS to verify the consensus validity proof in a concise way on the chain.

The setup involves a synchronous committee of 512 validators randomly selected every 27 hours. These validators are responsible for signing each block header within their allotted time period. The state of Ethereum is considered valid if more than ⅔ of validators sign each block header. The verification process mainly includes verifying the following:

  1. Merkle proof of the block header
  2. Merkle proofs of validators in the synchronization committee
  3. BLS signatures to ensure proper rotation of the sync committee

This process incurs significant computational costs because the basic concept is that light clients utilize zk-SNARKs (Groth16) to create a constant-sized proof (proof of validity) that can be efficiently verified on the Gnosis chain. Proofs are generated via off-chain computation, which involves building circuits for verifying validators and their signatures, and then generating zk-SNARK proofs. Proofs and block headers are then submitted to smart contracts on the Gnosis Chain for verification.

Adopting zk-SNARKs helps reduce storage overhead and circuit complexity, thereby reducing trust assumptions. Nonetheless, this approach is optimized specifically for the Ethereum 2.0 consensus protocol and EVM and may require greater adaptation to other blockchain networks.

Just this past July, Succinct Labs made a major announcement, confirming that its Ethereum ZK light client had been officially integrated into mainnet to enhance the security of Gnosis Omnibridge. The integration will put Succinct Labs in charge of securing the Gnosis Omnibridge, which currently has a total value locked (TVL) of over $40 million and has facilitated more than $1.5 billion in stablecoin asset flows to date.

zkIBC by Electron Labs

Electron Labs is building a cross-chain bridge that originated from the Cosmos SDK ecosystem, a framework for application-specific blockchains. Its cross-chain bridge will utilize IBC (Inter-chain Communication) technology to enable seamless communication between all independent blockchains defined within the framework.

However, implementing light clients of the Cosmos SDK into Ethereum is fraught with difficulties. The Tendermint light client used by the Cosmos SDK runs on a twisted Edwards curve (Ed25519), which is not natively supported by the Ethereum blockchain. Therefore, it is expensive and inefficient to verify Ed25519 signatures on Ethereum's BN254 curve. To overcome this obstacle, Electron Labs is developing a solution based on zk-SNARKs technology. This system would generate an off-chain proof of signature validity and only verify the proof on the Ethereum chain, effectively solving this problem.

By taking this approach, Ed25519 signatures in the Cosmos SDK can be efficiently and cost-effectively verified on the Ethereum blockchain while avoiding introducing any additional trust assumptions. One potential problem you might face with this approach, though, is latency. The block generation rate in the Cosmos SDK is 7 seconds, and in order to keep up with this rate, the proof time has to be significantly reduced. Electron Labs intends to solve this problem by using multiple computers to generate proofs simultaneously and then combining them into a single zk-SNARK proof.

zkBridge by Polyhedra Network

Compared with the other two industry-leading zero-knowledge proof-based cross-chain bridge constructions, zkBridge stands out with its flexible and diverse framework, which facilitates the development of multiple applications on its platform. It effectively uses zk-SNARKs to establish an efficient communication process, enabling the prover to convince the receiving chain that a certain state transition occurred on the sending chain. The zkBridge framework consists of two key components:

  1. Block header relay network: This component gets the block header from the sending chain, generates a proof for verifying the block header, and then transmits both the block header and the proof to the update contract on the receiving chain.
  2. Update contract: This part maintains a light client state and automatically includes the block header of the sending chain after the association proof is verified. In addition, it also keeps the current main chain state update of the sending chain.

ZK Bridges: How does zero-knowledge proof empower the cross-chain world?

Image source Polyhedra Network

The main difference between zkBridge and other industry-leading approaches is that zkBridge only requires the presence of an honest node in the relay network and assumes the reliability of zk-SNARKs.

A key advance in this construction lies in the parallel use of zk-SNARKs: the Virgo prover (deVirgo), which introduces a novel distributed proof system to speed up the proof generation process and uses recursive proofs to reduce on-chain proof verification. the cost of. deVirgo relies on the GKR protocol and a polynomial commitment scheme to generate proofs for circuits that verify multiple signatures. Subsequently, deVirgo proofs are compressed by a Groth16 prover and verified by an update contract on the target blockchain. The combination of these proof systems enables zkBridge to enable efficient cross-chain communication without relying on external trust assumptions.

The mainnet Alpha version of zkBridge was released in April 2023 and is now facilitating cross-chain interoperability between several L1 and L2 blockchain networks, such as BNB Chain, Ethereum, and Arbitrum. At the ETHCC Paris zkDAY event in 2023, Polyhedra Network’s CTO, Tiancheng Xie, highlighted that since its mainnet launch, the protocol has attracted more than 50,000 daily active users and 800,000 monthly active users.

With its modular architecture, zkBridge opens up vast possibilities for developers and users. These possibilities include token bridging and swapping, message passing, and computational logic that adapts to state changes between different blockchain networks.

Summarize

Incorporating zk-SNARKs technology into the cross-chain bridge design can effectively solve the problems related to decentralization and security. However, this also creates a computational bottleneck due to the large circuit scale involved. As the focus on interoperability continues to increase, it is believed that more developers will work hard to develop secure and scalable cross-chain bridge technology. These advances are expected to have a positive impact on the overall advancement and application of ZK technology. As such, we can expect significant advances in research, innovative implementation, and wider adoption of cross-chain applications in the near future.

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