Source: Bitcoin Magazine; Translation: Wuzhu, Golden Finance

Rollups have recently become the focus of BTC expansion and the first thing that truly stole the spotlight from the Lighting Network, in terms of broader attention. Rollups aim to be an off-chain second layer that is not constrained or limited 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 intermediate routing Nodes need channel balances to facilitate the full flow of payment amounts from sender to receiver.

These systems were initially run on Ethereum and other Turing Complete systems, but the recent focus has shifted to porting them to UTXO-based blockchains (e.g. BTC). This article is not intended to discuss the current implementation on BTC, but to discuss the idealized Rollup functionality that people have been pursuing for a long time, which depends on the capability of directly verifying Zero-Knowledge Proof (ZKP) on BTC, a feature that BTC currently does not support.

The basic architecture of Roll is as follows: a single account (UTXO in BTC) stores the balances of all users in Rollup. This UTXO contains a commitment, which exists in the form of the Merkle root of a Merkle tree, committing all current balances of accounts in Rollup. All these accounts are authorized using Public Key/Private Key, so in order to make off-chain expenditures, users still need to sign certain contents with their Secret Key. This part of the structure allows users to exit at any time without permission, simply 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 whether all changes to the off-chain account have been properly authorized by the account holder and whether the operator has not maliciously updated the balance to steal funds from users 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 can they place their branches in the tree to be able to exit without permission whenever they want?

Proper Rollup

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

In a more advanced implementation, use balance difference. This is essentially a summary of which accounts have added or subtracted funds during the update process. This allows each Rollup update to only include changes in account balances that have occurred. Then, users can simply scan the chain and "compute" from the beginning of the Rollup to determine the current state of account balances, allowing them to rebuild the Merkle tree of current balances.

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 rules require that this data be included in the formal rollup provided to users using the Block chain, so transactions that do not include account summaries or account differences are considered invalid transactions.

Validity

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

This has created a dilemma where the security guarantee is equally strong. When data is directly published to the BTCBlock chain, Consensus rules can ensure that it is absolutely correct. However, when it is published to an external system, the best it can do is verify the SPV proof, which means the data has been published 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 broadcast after generation. It cannot verify whether external information is truly made public to everyone.

This opens the door to data withholding attacks, where a commitment to publish data is made and used to drive rollup, but the data is not actually available. This results in users being unable to withdraw funds. The only real solution is to rely on value and incentive structures outside of BTC completely.

Dilemma

This poses a dilemma for rollups. When it comes to data availability issues, there is basically a binary choice of whether to publish data to the BTC blockchain or elsewhere. This choice has significant implications for the security and sovereignty, as well as the scalability, of the 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 one time and the total number of transactions that all rollups can process off-chain. Each rollup update requires Block space proportional 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, at which 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 the Rollup using 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 deception and data hiding.

Now, any Block producer on the external data availability system is able to hijack the funds of BTCRollup users by producing Blocks instead of actually broadcasting those Blocks, thus making the data available.

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