Source: Bitcoin Magazine; Compilation: Wuzhu, Golden Finance

Rollups have recently become the focus of BTC expansion, becoming the first thing to truly steal the limelight from the Lighting Network, in terms of wider attention. Rollups aim to be an off-chain second layer that is not constrained or restricted by the core Liquidity of the Lighting Network, meaning that end users need someone to allocate (or 'lend') funds in advance in order 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 run on Ethereum and other Turing Complete systems, but recently the focus has shifted to porting them to UTXO-based blockchains, such as BTC. This article does not intend to discuss the current status of implementation on BTC, but rather 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, which is currently not supported.

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

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 Block chain. 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 question is, if only the root of the merkle tree is published on-chain, and users can view and access it, then how do they put their branches in the tree so that they can exit without permission when they want?

Proper Rollup

In the appropriate Rollup, whenever a new off-chain transaction is confirmed and the state of the Rollup account changes, the information will be directly put into the blockchain. It's not the whole tree, which would be ridiculous, 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 accounts are only added in the updated transactions of the Rollup.

In more advanced implementations, 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 balance 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 balance, allowing 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 rules require that this data be included in the formal rollup provided to users using the Block chain, i.e. transactions that do not include account summaries or account differences are considered invalid transactions.

Expiration Date

Another way to address 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 like rollup.

This has created a dilemma where security 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, i.e. 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. BTC's 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 public to everyone.

This opens the door to data withholding attacks, 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 presents a dilemma for rollups. When it comes to data availability, there is essentially a binary choice of whether to publish the data on the BTC blockchain or elsewhere. This choice has significant implications for the security, sovereignty, and scalability of rollups.

On the one hand, using BTC blockchain 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 once 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 degree, at which point there is no more room 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 a Rollup that uses 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 can hijack BTCRollup users' funds by producing a Block instead of actually broadcasting that Block, thus making the data available.

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