Source: Bitcoin Magazine; Compilation: Wuzhu, Golden Finance

Rollups has recently become the focus of BTC expansion, becoming the first thing to truly steal the spotlight from the Lighting Network in a broader sense of attention. Rollups aims to be an off-chain second layer that is not subject to the core Liquidity constraints or restrictions of the Lighting Network, i.e., end users need someone to allocate (or "lend") funds in advance in order 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 originally running 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 ability to directly verify 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) holds the balances of all users in Rollup. This UTXO contains a commitment that exists in the form of the Merkle root of a 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 in order to propose off-chain spending, users still need to sign certain content with their Secret Key. This part of the structure allows users to exit unilaterally at any time without permission, just by creating a transaction proving that their account is part of the Merkle tree, they can 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 users' funds or dishonestly reallocate them to other users.

The question 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 whenever they want?

Appropriate Rollup

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

In more advanced implementations, use balance differences. This is essentially a summary of which accounts have increased or decreased funds during the update process. This allows each Rollup update to only contain the account balance changes 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 reconstruct 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 needed for unilateral exit. The rollup rule requires that this data be included in the formal rollup provided to users using the Block chain, and transactions that do not include account summaries or account differences are considered invalid transactions.

Validity Period

Another approach to addressing the issue of user withdrawal data availability is to place the data elsewhere outside the Block chain. This introduces subtle issues, as rollup still needs to ensure that the data is available elsewhere. Traditionally, other Block chains are used for this purpose, specifically designed to serve as data availability layers for systems such as rollup.

This creates a dilemma of having equally strong security safeguards. When data is directly published to the BTCBlock chain, Consensus rules can ensure its absolute correctness. However, when it is published to an external system, the best it can do is to verify 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 is ultimately an Oracle Machine problem. The BTC blockchain cannot fully verify anything that happens outside of its own block on-chain, the best it can do is verify ZKP. However, ZKP cannot verify whether a block containing rollup data is truly publicly broadcasted after generation. It cannot verify whether external information is truly publicly available to everyone.

This opens the door to data withholding attacks, which means creating commitments to published data and using them to advance rollup, but the data is not actually available. This prevents users from withdrawing funds. The only real solution is to rely on value and incentive structures outside of BTC completely.

Dilemma

This poses a dilemma for 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 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 rollups. Block space is limited, which sets a limit on the number of rollups that can exist at a time and the total number of transactions that can be processed off-chain for all rollups. 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, 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 on scalability gains, but it also brings new security and sovereignty issues. In Rollups that achieve data availability using BTC, 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 external system's ability to resist deception and data concealment.

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, thus making the data available.

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