ZK-rollups have emerged as one of the most promising scalability solutions on the Ethereum. The funding raised by leading projects in this space, such as and , has surpassed millions of dollars. As Bitcoin scalability gradually becomes a significant narrative in the crypto space, exploring the possibilities of integrating ZK-rollups with Bitcoin has become increasingly important. zkSync StarkWare Before delving into the exploration, it is essential to have a clear understanding of the technical concepts of ZK-rollups in the context of Bitcoin scalability. These concepts can be broadly categorized into three aspects. The Stored Data of ZK-Rollups ZK-rollups require running verification code and storing result data on the Bitcoin layer 1. However, solutions that only store the final validated state data root (Merkle Root) of ZK-rollups on the Bitcoin layer are not considered genuine solutions. For instance, the sovereign rollup solution by , a Bitcoin scalability project, solely stores state data on the Bitcoin. However, this approach faced immediate ridicule from Ethereum influencer regarding its implementation mechanism. Rollkit ryanb.eth Storing state data on the Bitcoin layer 1 is currently the easiest way to implement ZK-rollups. However, this practice lacks true significance. Submitting and storing state data on the Bitcoin layer 1 is merely a self-verification act and does not constitute a complete solution. Turing-Complete ZK-Rollups To achieve EVM-compatible ZK-rollups, it is necessary to have support for Turing-complete smart contracts on the Bitcoin layer 1 to handle various types of ZK verifications. This approach, which requires smart contract verification for ZK-rollups, is an imaginative and ambitious technological goal. However, the current progress in this area remains uncertain, involving extensive foundational research and development that are still being explored. Customized ZK-Rollups For certain limited and specific use cases, such as payment, customized ZK-rollups technology solutions can be developed. These solutions have well-defined and simplified functionality, often not requiring Turing-complete smart contract support, and can be implemented through hard-coding on the Bitcoin layer 1. This specific category of ZK technology has the potential to evolve into a foundational component, similar to elliptic-curve cryptography, that underpins blockchain technology. After clarifying the technical concepts of ZK-rollups in the context of Bitcoin scalability, we can undertake a comprehensive exploration and summary of the various possibilities and potential issues that arise from the integration of Bitcoin with ZK-rollups based on these three aspects. 1.Enabling Turing-Complete ZK-Rollups On The Bitcoin Layer 1 To embark on the path of supporting Turing-complete ZK-Rollups, it implies a significant upgrade for the Bitcoin mainnet. Following the upgrade, various applications on ZK-rollups will benefit from the decentralization and security of the Bitcoin network, thereby addressing sustainability issues within the Bitcoin network's economic model to some extent. However, this also means the collapse of Bitcoin's long-held narrative as a money and store of value, transitioning it into a better version of Ethereum. Additionally, large-block approach represented by may resurface as a valid alternative, causing a weakening of Bitcoin's network decentralization. The core narrative and the derived value foundation will face scrutiny. Bitcoin Cash The challenge with this direction lies in the need to upgrade the Bitcoin mainnet. This requires the overwhelming consensus and unified efforts of Bitcoin developers, miners, significant Bitcoin holders, and related market institutions. Otherwise, an alternative approach, such as the proposal of BIP300/301 by , would involve forking the Bitcoin mainnet directly, with the expectation of gaining consensus within the Bitcoin community based on the subsequent performance of the forked chain. LayerTwo Labs 2.Optimization Of Bitcoin In Specific Aspects Through ZK-Rollups Whether or not Bitcoin upgrades to support Turing-complete ZK-rollups, it does not hinder the technical optimization of ZK technology in specific aspects of Bitcoin. If Bitcoin does not upgrade to support Turing-complete ZK-rollups and only focuses on technical optimization in specific use cases, it means that the core narrative of Bitcoin as a money and store of value can continue to be preserved. For example, in the realm of payments, ZK-rollups can bring higher efficiency than the through mathematical rather than economic means. However, this would entail increased computational costs and higher operating expenses for nodes. When other existing technical solutions can achieve similar outcomes, the market tends to favor the technology solution with lower overall costs. Lightning Network The challenge with this direction lies in whether Bitcoin has enough specific use cases that require the adoption of ZK-rollups and whether ZK-rollups can achieve optimal efficiency and cost-effectiveness. Otherwise, there is a risk of projects engaging in coin speculation by solely relying on technical narratives. 3.ZK-Rollups Supported By Bitcoin-Compatible Chains Due to the high difficulty in implementing ZK-Rollups with full Turing completeness on Bitcoin, as well as the risk of collapsing the Bitcoin narrative, there is a significant possibility of transferring Bitcoin to compatible chains for ZK-rollups scalability. Currently, there are two main approaches for Bitcoin-compatible chains to support ZK-Rollups: sidechain and one-way transfer to new chains. 3.1 Sidechain Approach of ZK-Rollups Sidechain solutions have represented a direction for Bitcoin scalability, where specific cross-chain technologies are used to transfer BTC to EVM-compatible chains for scalability. By adding ZK-Rollups on these chains, further scalability improvements can be achieved. There are already several sidechains in the Bitcoin ecosystem focused on scalability, such as , , and . The possibility of this direction depends on whether future competitors will add ZK-rollups to existing sidechains or lead with entirely new sidechains dedicated to ZK-rollups. Stacks Rootstock Liquid Network 3.2 One-Way Transfer Approach of ZK-Rollups The one-way transfer approach for Bitcoin scalability has been proposed by the . The basic principle is to unidirectionally transfer BTC from the main network to a new chain that supports ZK-rollups for scalability. Hacash chain Both approaches for Bitcoin-compatible chains supporting ZK-rollups require sufficient incentive mechanisms to facilitate the transfer of BTC to the chains. The main difference lies in whether the transferred BTC can return to the main network. Therefore, for the one-way transfer approach of ZK-rollups to become more feasible, the issues with the sidechain approach of ZK-rollups need to be addressed, preferably with additional advantages. The key challenge with sidechain scalability lies in achieving sufficient decentralization in the process of cross-chain management for BTC. Currently, most cross-chain bridge solutions have various centralization flaws. On the other hand, the one-way transfer approach achieves transfer by maintaining the unchanged private keys of Bitcoin, eliminating the need for any form of centralized management or traditional cross-chain bridges. Additionally, it is important to consider the advantages that the one-way transfer approach offers compared to the sidechain approach of ZK-Rollups. Taking Hacash as an example, the PoW decentralization mechanism and the self-regulating money supply stabilization system based on the Hacash layer 1 can improve the lack of monetary properties of Bitcoin. Conclusion The combination of Bitcoin and ZK-rollups presents three main possibilities: Bitcoin supporting Turing-complete ZK-Rollups, ZK-Rollups optimizing specific functionalities and use cases of Bitcoin, and Bitcoin-compatible chains supporting ZK-Rollups. To achieve Bitcoin supporting Turing-complete ZK-rollups, broad support from the entire community is necessary. However, this may trigger a crisis in the core narrative of Bitcoin. The optimization of specific functionalities and use cases of Bitcoin through ZK-rollups needs to be evaluated based on specific circumstances. If there are already existing solutions, the cost implications of implementing ZK-rollups need to be weighed. Bitcoin-compatible chains supporting ZK-rollups can be achieved through sidechains and one-way transfers. Both approaches require sufficient incentive mechanisms to attract BTC participation. Sidechain solutions need to consider competition between existing and emerging projects, while one-way transfer approaches need to address centralization concerns and possess advantages in other aspects of the economic model to increase their chances of success. These are the key possibilities summarized regarding the combination of Bitcoin and ZK-Rollups.

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