Source: Bitcoin Magazine; Compilation: Wuzhu, Golden Finance

Rollups have recently become the focus of BTC scalability, becoming the first thing that truly steals the limelight from the Lighting Network, in terms of broader attention. Rollups aim to be an off-chain second layer that is not constrained or restricted by the core Liquidity of the Lighting Network. In other words, end users need someone to pre-allocate (or "lend") funds 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 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 functionality of Rollup that people have been pursuing for a long time, which depends on the capability that BTC currently does not support, namely the ability to directly verify Zero-Knowledge Proof (ZKP) on BTC.

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, which 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 making a transaction proving that their account is part of the Merkle tree, without the need for operator permission.

Rollup operators 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 are properly authorized by the account holder and whether 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 place their branches in the tree so that they can exit without permission when they want?

Suitable Rollup

In the appropriate Rollup, each 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 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 account is only added in the updated Rollup transactions.

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 makes each Rollup update only include the account balance changes that have occurred. Then, users can simply scan the chain and "compute" from the beginning of the Rollup to derive 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 to unilaterally exit. The rollup rules require that this data be included in the formal rollup provided to users using the Block chain, so transactions without account summaries or account differences are considered invalid transactions.

Expiry Date

Another approach to addressing the accessibility of user withdrawal data is to store the data elsewhere outside of 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 the data availability layer for systems such as rollup.

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, that is, 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 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 actually publicly broadcasted after it is generated. It cannot verify whether external information is truly made public to everyone.

This opens the door to data withholding attacks, which involves creating commitments to publish data and using it to advance rollup, but the data is actually not available. This results in users being unable to withdraw 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 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 with balance changes 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 will eliminate 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 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 can hijack the funds of BTCRollup users by producing Blocks instead of actually broadcasting the Blocks, 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?