This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Dipankar Sarkar, Cryptuon Research and me@dipankar.name Table of Links Abstract and Introduction
Formal Model - Rollups with Decentralized Common Pool (DCP)
Atomic composability & ZK-proofs
Incorporating Zk-proofs
Application of the Formal Model
Conclusion and References Abstract In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. In this paper, we introduce a comprehensive formal model to address atomic composability across multiple rollups on Ethereum. The proposed model incorporates mechanisms like buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs. Moreover, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. The application of the proposed model to shared sequencers and other existing solutions accentuates its versatility and universality. 1 Introduction In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. Ethereum, recognized as a pioneering smart contract platform, has initiated a myriad of advancements, with rollups being a significant answer to the blockchain trilemma: balancing scalability, security, and decentralization [5]. However, as rollups appear promising for scalability, they might unintentionally lead to fragmented composability. Given the intertwining nature of systems and applications, ensuring atomicity in transactions across systems is vital. Atomic composability is predicated on the principle that a transaction (A) can only be finalized if another transaction (B) is likewise finalized [8]. For decentralized applications that operate over multiple rollups, this assurance is critical. Yet, actualizing this atomicity with disconnected rollups on Ethereum presents major obstacles. This paper offers a thorough formal model that addresses atomic composability across multiple rollups on Ethereum. Incorporating insights from established distributed system solutions and contemporary cryptographic methodologies, the proposed model encompasses buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs [1]. Beyond proposing the model, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. Our intent extends beyond presenting a solution; we seek to stimulate a wider discourse on the future trajectory of interconnected blockchains. With a surge in applications shifting to a multi-rollup framework on Ethereum and elsewhere, a robust system guaranteeing atomic composability becomes indispensable. Through our model and ensuing discussions, we aim to make substantial contributions to this burgeoning field of blockchain study. 1.1 What are Rollups? Rollups, in the Ethereum context, are scaling mechanisms that bolster network throughput. They operate by conducting transactions off-chain and subsequently submitting a transaction summary to the primary Ethereum chain, thus enhancing transaction capacity without overloading the main Ethereum network [5]. 1.2 What is Composability? Within blockchain and Ethereum paradigms, composability pertains to the capability of decentralized applications (dApps) and smart contracts to effortlessly integrate and leverage one another’s features [11]. This can be analogized to “money Legos”, where each protocol or dApp represents an individual Lego piece, capable of diverse combinations. 1.3 Limits of Composability Between Rollups With the deployment of multiple rollups on Ethereum, challenges arise in ensuring seamless interaction of dApps and contracts across these rollups. This dilemma is intensified if rollups operate in isolation or lack an effective bridging mechanism. Atomic Transactions Across Rollups: Ensuring atomic composability between rollups necessitates that a transaction in one rollup is only finalized if its counterpart in another rollup is as well. This is intricate because each rollup might possess unique consensus algorithms, validation methodologies, and operational latency. Data Availability: For a contract in one rollup to interface with data or another contract on a distinct rollup, the requisite data from the latter may not be readily accessible or may be costly to retrieve. Differing Rules and Standards: Distinct rollups with divergent standards or rules regarding transaction processing can further impede cross-rollup interactions. This paper is available on arxiv under CC 4.0 license. Authors: (1) Dipankar Sarkar, Cryptuon Research and me@dipankar.name This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Dipankar Sarkar, Cryptuon Research and me@dipankar.name Table of Links Abstract and Introduction Formal Model - Rollups with Decentralized Common Pool (DCP) Atomic composability & ZK-proofs Incorporating Zk-proofs Application of the Formal Model Conclusion and References Abstract and Introduction Abstract and Introduction Formal Model - Rollups with Decentralized Common Pool (DCP) Formal Model - Rollups with Decentralized Common Pool (DCP) Atomic composability & ZK-proofs Atomic composability & ZK-proofs Incorporating Zk-proofs Incorporating Zk-proofs Application of the Formal Model Application of the Formal Model Conclusion and References Conclusion and References Abstract In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. In this paper, we introduce a comprehensive formal model to address atomic composability across multiple rollups on Ethereum. The proposed model incorporates mechanisms like buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs. Moreover, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. The application of the proposed model to shared sequencers and other existing solutions accentuates its versatility and universality. 1 Introduction In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. Ethereum, recognized as a pioneering smart contract platform, has initiated a myriad of advancements, with rollups being a significant answer to the blockchain trilemma: balancing scalability, security, and decentralization [5]. However, as rollups appear promising for scalability, they might unintentionally lead to fragmented composability. Given the intertwining nature of systems and applications, ensuring atomicity in transactions across systems is vital. Atomic composability is predicated on the principle that a transaction (A) can only be finalized if another transaction (B) is likewise finalized [8]. For decentralized applications that operate over multiple rollups, this assurance is critical. Yet, actualizing this atomicity with disconnected rollups on Ethereum presents major obstacles. This paper offers a thorough formal model that addresses atomic composability across multiple rollups on Ethereum. Incorporating insights from established distributed system solutions and contemporary cryptographic methodologies, the proposed model encompasses buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs [1]. Beyond proposing the model, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. Our intent extends beyond presenting a solution; we seek to stimulate a wider discourse on the future trajectory of interconnected blockchains. With a surge in applications shifting to a multi-rollup framework on Ethereum and elsewhere, a robust system guaranteeing atomic composability becomes indispensable. Through our model and ensuing discussions, we aim to make substantial contributions to this burgeoning field of blockchain study. 1.1 What are Rollups? 1.1 What are Rollups? Rollups, in the Ethereum context, are scaling mechanisms that bolster network throughput. They operate by conducting transactions off-chain and subsequently submitting a transaction summary to the primary Ethereum chain, thus enhancing transaction capacity without overloading the main Ethereum network [5]. 1.2 What is Composability? 1.2 What is Composability? Within blockchain and Ethereum paradigms, composability pertains to the capability of decentralized applications (dApps) and smart contracts to effortlessly integrate and leverage one another’s features [11]. This can be analogized to “money Legos”, where each protocol or dApp represents an individual Lego piece, capable of diverse combinations. 1.3 Limits of Composability Between Rollups 1.3 Limits of Composability Between Rollups With the deployment of multiple rollups on Ethereum, challenges arise in ensuring seamless interaction of dApps and contracts across these rollups. This dilemma is intensified if rollups operate in isolation or lack an effective bridging mechanism. Atomic Transactions Across Rollups: Ensuring atomic composability between rollups necessitates that a transaction in one rollup is only finalized if its counterpart in another rollup is as well. This is intricate because each rollup might possess unique consensus algorithms, validation methodologies, and operational latency. Atomic Transactions Across Rollups: Data Availability: For a contract in one rollup to interface with data or another contract on a distinct rollup, the requisite data from the latter may not be readily accessible or may be costly to retrieve. Data Availability: Differing Rules and Standards: Distinct rollups with divergent standards or rules regarding transaction processing can further impede cross-rollup interactions. Differing Rules and Standards:

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