Source: Bitcoin Magazine; Compilation: Wuzhu, Golden Finance

Rollups have recently become the focus of BTC expansion, becoming the first thing to truly steal the spotlight from the Lighting Network in a more widespread attention. Rollups aims to be an off-chain second layer that is not constrained or restricted by the core Liquidity of the Lighting Network, meaning end users need someone to allocate (or "lend out") funds in advance to receive money, or intermediary routing Nodes need channel balances to facilitate the full flow of payment amounts from sender to receiver.

These systems were initially designed to run on Ethereum and other Turing Complete systems, but recently the focus has shifted to porting them to UTXO-based blockchains like BTC. This article does not intend to discuss the current state of implementation on BTC, but rather the desired functionality of an idealized Rollup that depends on capabilities not currently supported by BTC, namely the ability to directly verify Zero-Knowledge Proofs (ZKPs) on BTC.

The basic architecture of Roll is as follows: a single account (UTXO in BTC) stores the balance of all users in Rollup. This UTXO includes a commitment, which exists in the form of the Merkle root of the Merkle tree, committing to the current balances of all existing accounts in Rollup. All these accounts are authorized using Public Key/Private Key pairs, so users still need to sign certain content with the Secret Key to propose off-chain spending. This part of the structure allows users to exit at any time without permission, just by making a transaction proving that their account is part of the Merkle tree, they can unilaterally exit Rollup without the permission of the operator.

The operator of Rollup must include a ZKP in the transaction to update the merkle root of the on-chain account balance during the process of completing off-chain transactions. Without this ZKP, the transaction will be invalid and cannot be included in the blockchain. This proof allows people to verify that all changes to the off-chain account are properly authorized by the account holder and that the operator has not maliciously updated the balance to steal user funds or dishonestly reallocate them to other users.

The problem is, if only the root of the Merkle tree is published on-chain, and users can view and access it, how do they put their branches in the tree so that they can exit without permission when they want to?

Appropriate Rollup

In the appropriate Rollup, each time a new off-chain transaction is confirmed and the status of the Rollup account changes, the information is directly placed on the blockchain. Not the entire tree, that would be absurd, but the information needed to rebuild the tree. In a simple implementation, the summary of all existing accounts in Rollup will include the balance, and the account is only added in the updated transactions of Rollup.

In more advanced implementations, balance differences are used. This is essentially a summary of which accounts have increased or decreased funds during the update process. This allows each Rollup update to only include balance changes that have occurred in accounts. Then, users can simply scan the chain and 'compute' from the beginning of the Rollup to derive the current state of account balances, which allows them to reconstruct the Merkle tree of the current balance.

This can save a lot of expenses and Block space (thus saving funds), while still allowing users to ensure access to the information required for unilateral exit. The rollup rule requires that this data be included in the formal rollup provided to users using the blockchain, so transactions that do not include an account summary or account differences are considered invalid transactions.

Expiration date

Another way to address the issue of user data availability in withdrawals is to store the data outside of the Block chain. This introduces subtle issues as rollups still need to enforce the availability of the data elsewhere. Traditionally, other Block chains are used for this purpose, specifically designed as data availability layers for systems like rollups.

This has created a dilemma where security is equally strong. When data is directly posted to the BTCBlock chain, Consensus rules can ensure that it is absolutely correct. However, when it is posted to an external system, the best it can do is verify the SPV proof, that is, the data has been posted to another system.

This requires verifying that the data exists in other on-chain proofs, which ultimately is an Oracle Machine problem. The BTC Block chain cannot fully verify anything other than what happens on its own Block on-chain. The best it can do is verify ZKP. However, ZKP cannot verify whether the Block containing rollup data is truly publicly broadcasted after generation. It cannot verify whether external information is truly publicly accessible to everyone.

This opens the door to data withholding attacks, that is, creating a commitment to publish data and using it to advance rollup, but the data is not actually available. This prevents users from withdrawing funds. The only real solution is to rely entirely on the value and incentive structure of systems other than BTC.

Dilemma

This has brought a dilemma to rollup. When it comes to data availability issues, there is basically a binary choice of whether to publish the data to the BTC blockchain or elsewhere. This choice has significant implications for the security, sovereignty, and scalability of rollup.

On the one hand, using BTCBlock chain as the data availability layer will set a hard limit on the scalability of rollup. Block space is limited, which sets a limit on the number of rollups that can exist at once and the total number of transactions that can be processed off-chain in all rollups. Each rollup update requires Block space in proportion to the number of accounts whose balances have changed since the last update. Information theory only allows data to be compressed to a certain extent, and at this point, there is no more potential for expansion.

On the other hand, using different layers to achieve data availability eliminates the hard upper limit of scalability gains, but it also brings new security and sovereignty issues. In Rollups that use BTC to achieve data availability, if the data that users need to extract is not automatically published to the blockchain, the state of the Rollup cannot change. With Validiums, this guarantee depends entirely on the ability of the external system used to resist fraud and data hiding.

Now, any Block producer on the external data availability system can hijack the funds of BTCRollup users by producing Blocks instead of actually broadcasting the Block, thereby making the data available.

So, if we really achieve the ideal Rollup implementation on BTC and truly realize unilateral user withdrawals, what would that be like?