Adaptive Tree-Based Solutions for Optimizing Blockchain Verification and Storage

Authors: (1) Oleksandr Kuznetsov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA and Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30/32, 62100 Macerata, Italy (kuznetsov@karazin.ua); (2) Dzianis Kanonik, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (3) Alex Rusnak, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA (alex@proxima.one); (4) Anton Yezhov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (5) Oleksandr Domin, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA. Table of Links Abstract and 1. Introduction 1.1. The Blockchain Paradigm and the Challenge of Scalability 1.2. State of the art 1.3. Our contribution and 1.4. Article structure 2. Conceptualizing the Problem 3. Our Idea for Optimizing Trees in Blockchain 4. Efficiency of adaptive Merkle trees 5. Algorithm for Merkle Tree Restructuring 6. Examples of Merkle Tree Restructuring Algorithm Execution and 6.1 Example 1: Restructuring a Binary Tree by Adding One Leaf 6.2. Example 1.1: Binary Tree Restructuring Through Leaf Node Swapping 6.3. Example 2.1: Restructuring a Non-Binary Tree by Adding a Single Leaf 6.4. Example 2.2: Restructuring a Non-Binary Tree Through Leaf Pair Swapping 6.5. Example 2.3: Restructuring a Patricia-Merkle Tree Fragment Through Leaf Pair Swapping 7. Path Encoding in the Adaptive Merkle Tree 8. Enhancing Verkle Trees Through Adaptive Restructuring and 8.1. Application of Adaptive Trees in Verkle Tree Technology 8.2. Technology and Advantages 9. Discussion 9.1. Our Contribution 9.2. Comparison with Existing Solutions 10. Conclusion and References 1.2. State of the art In the realm of blockchain scalability, Kottursamy et al. (2023) [9] introduce a novel blockchain architecture termed Mutable Block with Immutable Transaction (MBIT), aiming to enhance scalability through a trapdoor cryptographic hash function for quantifying unspent coins. While their approach significantly reduces verification and confirmation times, it primarily focuses on transaction efficiency without addressing the broader scalability challenges related to blockchain's data structure and state management. Li et al. (2023) [10] propose PRI, a Payment Channel Hubs (PCH) solution enhancing privacy, reusability, and interoperability for blockchain scalability. Despite its innovative approach to solving the deposit lock-in problem and supporting multi-party participation, PRI's reliance on trusted hardware and its limited scope in addressing the fundamental architectural scalability issues of blockchain remain unaddressed. Nasir et al. (2022) [11] provide a systematic review of scalable blockchains, identifying key strategies for enhancing blockchain capabilities and analyzing scalability solutions. Their work highlights the multifaceted nature of blockchain scalability but leaves a gap in practical implementation strategies for optimizing blockchain data structures, particularly in the context of state management and verification processes. Sanka and Cheung (2021) [12] offer a comprehensive review of blockchain scalability issues and solutions, emphasizing the need for efficient consensus mechanisms and system throughput improvements. While their analysis sheds light on the scalability challenges, the exploration of adaptive data structures for optimizing blockchain's underlying architecture is not thoroughly explored. Sharma et al. (2023) [13] introduce BLAST-IoT, a blockchain-assisted scalable trust model for the Internet of Things (IoT), focusing on secure dissemination and storage of trust information. Their model addresses scalability in the context of IoT devices but does not extend to the broader blockchain scalability challenges, particularly in relation to adaptive restructuring of blockchain data structures. Wang and Wu (2024) [14] present Lever-FS, a validation framework for intensive blockchain validation, achieving scalability through optimistic execution and dispute resolution. While their work advances the scalability of validation processes, it does not directly tackle the optimization of blockchain's state tree structure for overall network efficiency. Wang et al. (2023) [15] propose a scalable, efficient, and secured consensus mechanism for Vehicle-to-Vehicle (V2V) energy trading, leveraging blockchain technology. Their consensus mechanism addresses scalability in the specific context of V2V energy trading but does not address the broader application of scalable data structures within the blockchain. Xiao et al. (2024) [16] develop CE-PBFT, a high availability consensus algorithm for large-scale consortium blockchain, focusing on improving system throughput and reducing latency. While their algorithm enhances consensus efficiency, the exploration of adaptive and scalable blockchain data structures remains an area for further research. Yu et al. (2023) [17] introduce OverShard, a full sharding approach for scaling blockchain, which significantly improves throughput and reduces confirmation latency. However, the application of sharding to optimize blockchain's state tree and the exploration of adaptive restructuring techniques are not fully addressed. Zhen et al. (2024) [18] propose a dynamic state sharding blockchain architecture for scalable and secure crowdsourcing systems, addressing the scalability and security of blockchain in crowdsourcing applications. While their architecture offers improvements in throughput and security, the potential for adaptive restructuring of blockchain data structures to further enhance scalability is not explored. Transitioning from the broader challenges of blockchain scalability, we delve into the specific realm of tree-based data structures within blockchain technology. These structures, notably Merkle and Verkle trees, are pivotal for ensuring data integrity, enhancing verification processes, and optimizing storage within blockchain systems. The following literature review highlights significant advancements and identifies gaps that our research aims to fill. Ayyalasomayajula and Ramkumar (2023) [19] explore the optimization of Merkle Tree structures, comparing linear and subtree implementations. Their findings favor the subtree method for its efficiency in handling large-scale databases. However, their work primarily focuses on theoretical advantages without addressing the practical challenges of integrating these optimized structures into existing blockchain frameworks. Jeon et al. (2023) [20] introduce a hardware-accelerated approach for generating reusable Merkle Trees for Bitcoin blockchain headers, significantly reducing execution time and power consumption. While their solution enhances the efficiency of block candidate generation, it is tailored to Bitcoin and does not explore the adaptability of their approach to other blockchain architectures or the potential for further optimization in tree structure. Jing, Zheng, and Chen (2021) [21] provide a comprehensive review of Merkle Tree's technical principles and applications across various fields. Their work underscores the versatility and potential of Merkle Trees but stops short of proposing innovative methods for dynamic restructuring or optimization of these trees in response to the evolving needs of blockchain systems. Knollmann and Scheideler (2022) [22] present a self-stabilizing protocol for the Hashed Patricia Trie, a distributed data structure enabling efficient prefix search. Their protocol addresses selfstabilization in distributed systems but does not explore the scalability implications of their data structure within the broader context of blockchain technology. Lin and Chen (2023) [23] propose a file verification scheme based on Verkle Trees, highlighting the efficiency and security benefits over traditional Merkle Trees. While their work demonstrates the potential of Verkle Trees in file verification, the exploration of these trees for broader blockchain scalability and optimization remains limited. Liu et al. (2021) [24] offer systematic insights into Merkle Trees, emphasizing their role in blockchain data verification and retrieval. Their discussion on the advantages and applications of Merkle Trees provides a solid foundation but lacks a detailed exploration of innovative approaches to enhance these trees' efficiency and scalability in blockchain systems. Mardiansyah, Muis, and Sari (2023) [25] introduce the Multi-State Merkle Patricia Trie (MSMPT) for high-performance data structures in multi-query processing. Their work addresses performance and efficiency in lightweight blockchain but does not delve into the scalability challenges of more complex blockchain systems. Mitra, Tauz, and Dolecek (2023) [26] propose the Graph Coded Merkle Tree to mitigate Data Availability Attacks in blockchain systems. While their approach offers a novel solution to a specific problem, the broader application of their design for general blockchain scalability and data structure optimization is not addressed. Zhao et al. (2024) [27] focus on minimizing block incentive volatility through Verkle tree-based dynamic transaction storage. Their innovative approach addresses a crucial aspect of blockchain economics but does not explore the structural optimization of Verkle Trees for enhanced scalability and efficiency in blockchain systems. Our research fills these gaps by proposing adaptive restructuring techniques for Merkle and Verkle Trees, aiming to enhance blockchain scalability, optimize data verification and storage processes, and provide a flexible framework adaptable to various blockchain architectures and applications. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Authors: (1) Oleksandr Kuznetsov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA and Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30/32, 62100 Macerata, Italy (kuznetsov@karazin.ua); (2) Dzianis Kanonik, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (3) Alex Rusnak, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA (alex@proxima.one); (4) Anton Yezhov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (5) Oleksandr Domin, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA. Authors: Authors: (1) Oleksandr Kuznetsov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA and Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30/32, 62100 Macerata, Italy (kuznetsov@karazin.ua); (2) Dzianis Kanonik, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (3) Alex Rusnak, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA (alex@proxima.one); (4) Anton Yezhov, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA; (5) Oleksandr Domin, Proxima Labs, 1501 Larkin Street, suite 300, San Francisco, USA. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 1.1. The Blockchain Paradigm and the Challenge of Scalability 1.1. The Blockchain Paradigm and the Challenge of Scalability 1.2. State of the art 1.2. State of the art 1.3. Our contribution and 1.4. Article structure 1.3. Our contribution and 1.4. Article structure 2. Conceptualizing the Problem 2. Conceptualizing the Problem 3. Our Idea for Optimizing Trees in Blockchain 3. Our Idea for Optimizing Trees in Blockchain 4. Efficiency of adaptive Merkle trees 4. Efficiency of adaptive Merkle trees 5. Algorithm for Merkle Tree Restructuring 5. Algorithm for Merkle Tree Restructuring 6. Examples of Merkle Tree Restructuring Algorithm Execution and 6.1 Example 1: Restructuring a Binary Tree by Adding One Leaf 6. Examples of Merkle Tree Restructuring Algorithm Execution and 6.1 Example 1: Restructuring a Binary Tree by Adding One Leaf 6.2. Example 1.1: Binary Tree Restructuring Through Leaf Node Swapping 6.2. Example 1.1: Binary Tree Restructuring Through Leaf Node Swapping 6.3. Example 2.1: Restructuring a Non-Binary Tree by Adding a Single Leaf 6.3. Example 2.1: Restructuring a Non-Binary Tree by Adding a Single Leaf 6.4. Example 2.2: Restructuring a Non-Binary Tree Through Leaf Pair Swapping 6.4. Example 2.2: Restructuring a Non-Binary Tree Through Leaf Pair Swapping 6.5. Example 2.3: Restructuring a Patricia-Merkle Tree Fragment Through Leaf Pair Swapping 6.5. Example 2.3: Restructuring a Patricia-Merkle Tree Fragment Through Leaf Pair Swapping 7. Path Encoding in the Adaptive Merkle Tree 7. Path Encoding in the Adaptive Merkle Tree 8. Enhancing Verkle Trees Through Adaptive Restructuring and 8.1. Application of Adaptive Trees in Verkle Tree Technology 8. Enhancing Verkle Trees Through Adaptive Restructuring and 8.1. Application of Adaptive Trees in Verkle Tree Technology 8.2. Technology and Advantages 8.2. Technology and Advantages 9. Discussion 9. Discussion 9.1. Our Contribution 9.1. Our Contribution 9.2. Comparison with Existing Solutions 9.2. Comparison with Existing Solutions 10. Conclusion and References 10. Conclusion and References 1.2. State of the art In the realm of blockchain scalability, Kottursamy et al. (2023) [9] introduce a novel blockchain architecture termed Mutable Block with Immutable Transaction (MBIT), aiming to enhance scalability through a trapdoor cryptographic hash function for quantifying unspent coins. While their approach significantly reduces verification and confirmation times, it primarily focuses on transaction efficiency without addressing the broader scalability challenges related to blockchain's data structure and state management. Li et al. (2023) [10] propose PRI, a Payment Channel Hubs (PCH) solution enhancing privacy, reusability, and interoperability for blockchain scalability. Despite its innovative approach to solving the deposit lock-in problem and supporting multi-party participation, PRI's reliance on trusted hardware and its limited scope in addressing the fundamental architectural scalability issues of blockchain remain unaddressed. Nasir et al. (2022) [11] provide a systematic review of scalable blockchains, identifying key strategies for enhancing blockchain capabilities and analyzing scalability solutions. Their work highlights the multifaceted nature of blockchain scalability but leaves a gap in practical implementation strategies for optimizing blockchain data structures, particularly in the context of state management and verification processes. Sanka and Cheung (2021) [12] offer a comprehensive review of blockchain scalability issues and solutions, emphasizing the need for efficient consensus mechanisms and system throughput improvements. While their analysis sheds light on the scalability challenges, the exploration of adaptive data structures for optimizing blockchain's underlying architecture is not thoroughly explored. Sharma et al. (2023) [13] introduce BLAST-IoT, a blockchain-assisted scalable trust model for the Internet of Things (IoT), focusing on secure dissemination and storage of trust information. Their model addresses scalability in the context of IoT devices but does not extend to the broader blockchain scalability challenges, particularly in relation to adaptive restructuring of blockchain data structures. Wang and Wu (2024) [14] present Lever-FS, a validation framework for intensive blockchain validation, achieving scalability through optimistic execution and dispute resolution. While their work advances the scalability of validation processes, it does not directly tackle the optimization of blockchain's state tree structure for overall network efficiency. Wang et al. (2023) [15] propose a scalable, efficient, and secured consensus mechanism for Vehicle-to-Vehicle (V2V) energy trading, leveraging blockchain technology. Their consensus mechanism addresses scalability in the specific context of V2V energy trading but does not address the broader application of scalable data structures within the blockchain. Xiao et al. (2024) [16] develop CE-PBFT, a high availability consensus algorithm for large-scale consortium blockchain, focusing on improving system throughput and reducing latency. While their algorithm enhances consensus efficiency, the exploration of adaptive and scalable blockchain data structures remains an area for further research. Yu et al. (2023) [17] introduce OverShard, a full sharding approach for scaling blockchain, which significantly improves throughput and reduces confirmation latency. However, the application of sharding to optimize blockchain's state tree and the exploration of adaptive restructuring techniques are not fully addressed. Zhen et al. (2024) [18] propose a dynamic state sharding blockchain architecture for scalable and secure crowdsourcing systems, addressing the scalability and security of blockchain in crowdsourcing applications. While their architecture offers improvements in throughput and security, the potential for adaptive restructuring of blockchain data structures to further enhance scalability is not explored. Transitioning from the broader challenges of blockchain scalability, we delve into the specific realm of tree-based data structures within blockchain technology. These structures, notably Merkle and Verkle trees, are pivotal for ensuring data integrity, enhancing verification processes, and optimizing storage within blockchain systems. The following literature review highlights significant advancements and identifies gaps that our research aims to fill. Ayyalasomayajula and Ramkumar (2023) [19] explore the optimization of Merkle Tree structures, comparing linear and subtree implementations. Their findings favor the subtree method for its efficiency in handling large-scale databases. However, their work primarily focuses on theoretical advantages without addressing the practical challenges of integrating these optimized structures into existing blockchain frameworks. Jeon et al. (2023) [20] introduce a hardware-accelerated approach for generating reusable Merkle Trees for Bitcoin blockchain headers, significantly reducing execution time and power consumption. While their solution enhances the efficiency of block candidate generation, it is tailored to Bitcoin and does not explore the adaptability of their approach to other blockchain architectures or the potential for further optimization in tree structure. Jing, Zheng, and Chen (2021) [21] provide a comprehensive review of Merkle Tree's technical principles and applications across various fields. Their work underscores the versatility and potential of Merkle Trees but stops short of proposing innovative methods for dynamic restructuring or optimization of these trees in response to the evolving needs of blockchain systems. Knollmann and Scheideler (2022) [22] present a self-stabilizing protocol for the Hashed Patricia Trie, a distributed data structure enabling efficient prefix search. Their protocol addresses selfstabilization in distributed systems but does not explore the scalability implications of their data structure within the broader context of blockchain technology. Lin and Chen (2023) [23] propose a file verification scheme based on Verkle Trees, highlighting the efficiency and security benefits over traditional Merkle Trees. While their work demonstrates the potential of Verkle Trees in file verification, the exploration of these trees for broader blockchain scalability and optimization remains limited. Liu et al. (2021) [24] offer systematic insights into Merkle Trees, emphasizing their role in blockchain data verification and retrieval. Their discussion on the advantages and applications of Merkle Trees provides a solid foundation but lacks a detailed exploration of innovative approaches to enhance these trees' efficiency and scalability in blockchain systems. Mardiansyah, Muis, and Sari (2023) [25] introduce the Multi-State Merkle Patricia Trie (MSMPT) for high-performance data structures in multi-query processing. Their work addresses performance and efficiency in lightweight blockchain but does not delve into the scalability challenges of more complex blockchain systems. Mitra, Tauz, and Dolecek (2023) [26] propose the Graph Coded Merkle Tree to mitigate Data Availability Attacks in blockchain systems. While their approach offers a novel solution to a specific problem, the broader application of their design for general blockchain scalability and data structure optimization is not addressed. Zhao et al. (2024) [27] focus on minimizing block incentive volatility through Verkle tree-based dynamic transaction storage. Their innovative approach addresses a crucial aspect of blockchain economics but does not explore the structural optimization of Verkle Trees for enhanced scalability and efficiency in blockchain systems. Our research fills these gaps by proposing adaptive restructuring techniques for Merkle and Verkle Trees, aiming to enhance blockchain scalability, optimize data verification and storage processes, and provide a flexible framework adaptable to various blockchain architectures and applications. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

Adaptive Tree-Based Solutions for Optimizing Blockchain Verification and Storage

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