# Announcing Polyhedra Networks & Lagrange Labs Partnership: zkBridge Fast Finality for Rollups with Lagrange State Committees

#### August 7, 2023

Polyhedra Network designs and implements zkBridge, providing trustless and efficient cross-chain infrastructures for layer-1 and layer-2 interoperability. zkBridge uses zero-knowledge proof constructions to prove the full Ethereum PoS consensus and the state transitions of various layer-1 and layer-2 networks. With their efficient proof system, deVirgo, the proving time for Ethereum full PoS can be as fast as 10 seconds per block, which is enough to catch up with the block time of Ethereum.

Using Polyhedra’s zkLightClient infrastructure, developers can easily build applications on top of LayerZero while leveraging ZKP-based cross-chain security. Currently, zkBridge supports more than 20 networks such as Ethereum (full PoS), BNB Chain, Polygon, and Linea.

Lagrange Labs specializes in developing infrastructure to increase the security and expressivity of how contract states can be used. Their team develops a novel proving system, called ZK Big Data, that supports generating batched storage proofs concurrently with dynamic zero-knowledge distributed computation.

Lagrange also builds an offering called State Committees based on restaked EigenLayer security, which allows bridges and messaging protocols to share restaked security to attest to the finality of optimistic rollup blocks.

## Why zkBridging Is Challenging for Optimistic Rollups

zkBridge provides the most secure design for general message passing and asset bridging between chains. When using zkBridge, any state transition that happens on a source chain is trustlessly verified on a destination chain without reliance on an intermediary protocol’s security. While optimistic rollups provide a high transaction throughput, they represent a formidable challenge to zkBridge. Currently, zkBridge can only track finalized states from L2-to-L1 withdrawal transactions and L2-to-L1 messagings in order to generate state proofs.

The current approach for building zkBridge from optimistic rollups first triggers an L2-to-L1 withdrawal transaction or a L2-to-L1 messaging, and then waits for the fraud proof to finalize (could be as long as 7 days or even 14 days). zkBridge needs to prove both the consensus of the settlement chain (Ethereum full PoS) and the finalized state for the L2-to-L1 transaction, so that the rollup block written on the settlement chain can be used. While this is secure, it creates a high latency for cross-chain applications.

Lagrange Labs and Polyhedra Network have partnered together to enable efficient zkBridging from optimistic rollups by providing immediate finality. By combining Lagrange State Committees and Polyhedra Network’s zkBridge and zkLightClient infrastructure, trustless interoperability can be extended to any optimistic rollup with settlement on Ethereum.

## How Polyhedra and Lagrange Solve zkBridging For Optimistic Rollups

To start with, State Committees provide a mechanism for generating zero-knowledge state proofs for optimistic rollups based on the use of restaked Ethereum validators. Each validator within the State Committee is restaked through EigenLayer. Each State Committee attests to the finality of a proposed state transition submitted by an optimistic rollup’s sequencers to Ethereum.

Whenever a rollup block is considered either safe (OP stack) or has reached Ethereum equivalent finality (Arbitrum), each restaked validator in a State Committee is required to attest to the block using its Ethereum BLS12–381 consensus key.

Broadly, each signature is executed on a tuple containing three essential elements:

```
struct block {
var block_header,
var current_committee,
var next_committee,
}
```

The *current_committee* is the group of nodes permitted to sign for a given block *b* and the *next_committee* is the group of nodes permitted to sign for the next block (*b+1*). Each of these committees is defined permissionlessly on-chain based on which nodes have nominated themselves to join the State Committee.

Using these three fields, it is possible to succinctly prove the validity of an arbitrary block *b* if the following recursive properties hold:

- At least 2/3 of the
*n*attestors restaked for a given block*b*have signed the block header. The public keys of these nodes must be stored in the*current_committee*Merkle tree. - The
*current_committee*of*block b*equals the*next_committee*tree of block*b-1*. *Block**b-1*is either the genesis block or is valid with respect to these three conditions.

Polyhedra Network’s deVirgo proving system is being used on top of these signatures to generate a zero-knowledge proof showing the validity of every optimistic rollup block. As such, Polyhedra Network can extend its technology to offer zkBridge for any optimistic rollup with 1 block finality. These proofs can be generated for Arbitrum or any OP stack chain, such as Optimism, Base, Mantle, Manta or Zora.

Polyhedra’s zkLightClient technology, built on LayerZero, can soon also be extended to support low latency and trustless proofs of optimistic rollup states. This will further expand the number of chains that can benefit from both LayerZero’s extensive developer tooling and community support, as well as Polyhedra’s zkBridging technology.

It’s worth mentioning that the fast finality mechanism provided by the State Committees can also be used for zk-rollups, as the current finality time for the L2-to-L1 messaging of a zk-rollup can be as long as several hours. For zk-rollups, the cross-chain applications can choose to wait for the finality of a L2-to-L1 messaging, or use the instant finality provided by the State Committees with zkBridge.

Moreover, the State Committees can enhance the security of cross-chain transactions from L1 blockchains by adding another layer of the crypto-economic security by EigenLayer restaking. Without increasing the cross-chain latency, the zkBridge can generate the proofs for both the sender L1 blockchain consensus and the State Committees, and then get them verified on the receiver chain. Thus, the Lagrange State Committees will serve as a plug-and-play security layer for any blockchain system, by adding the crypto-economic security by EigenLayer restaking to zkBridge.

## Concluding Remarks

In summary, the strategic partnership between Polyhedra Network and Lagrange Labs marks the first instance of enabling zkBridging with immediate finality off of optimistic rollups. By working together, both teams are pushing forward the state of the art of how trustless interoperability can secure applications across web3.

Both Polyhedra Network and Lagrange Labs are teams with strong cryptography research backgrounds who are committed to using zero-knowledge proofs to advance the state of the art in cross-chain infrastructure and computation on data. Their partnership to enable zkBridging for optimistic rollups marks the first step in their collaboration to use ZKPs to enhance the security of cross-chain applications. In the future, both teams will continue to collaborate to empower new cross-chain use cases leveraging both their innovative and novel proof systems.