Authors:
(1) Hamid Bateni, Nobitex Labs (hamid@europe.com);
(2) Keyvan Kambakhsh, Nobitex Labs (keyvankambakhsh@gmail.com). Table of Links Abstract and 1 Introduction 2 Proof of Liability and 2.1 Commitment 2.2 Merkle Tree 2.3 Leaves Structure 2.4 Proof Statement 3 Proof of Reserve 3.1 Ethereum 3.2 Bitcoin 4 Proof of Solvency 5 Future Works and References 2.2 Merkle Tree A Merkle Tree is a tree in computer science in which every leaf node is labeled with the cryptographic hash of a data block, and each nonleaf node is labeled with the cryptographic hash of the labels of its child nodes. The value of a non-leaf node is determined by the hash of its children nodes, and this continues recursively until the tree’s root is achieved. This structure is particularly effective because it allows for efficient and secure verification of the contents of large data structures. The Merkle Tree allows us to verify data with a significantly smaller subset of the total information.[7] In the scenario of Proof of Solvency, we use the Merkle Tree as our cryptographic commitment. The root of the Merkle Tree acts as a commitment to all liabilities, and each leaf in the tree corresponds to a liability. This allows for an efficient and secure way to prove the existence and integrity of liabilities. By using a Merkle Tree, we can provide a proof path for any given leaf node (liability) up to the root. This path, also known as the Merkle path, allows anyone to verify that a specific liability is part of the tree. They can do this by recomputing the hashes from the leaf up to the root and comparing it with the root hash. This approach is particularly useful because it allows for verification without needing access to all data points, providing a balance between transparency and data efficiency. In the following sections, we will delve deeper into the leaf structure of the Merkle Tree and how we can use it to create proof statements. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Hamid Bateni, Nobitex Labs (hamid@europe.com); (2) Keyvan Kambakhsh, Nobitex Labs (keyvankambakhsh@gmail.com). Authors: Authors: (1) Hamid Bateni, Nobitex Labs (hamid@europe.com); (2) Keyvan Kambakhsh, Nobitex Labs (keyvankambakhsh@gmail.com). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Proof of Liability and 2.1 Commitment 2 Proof of Liability and 2.1 Commitment 2.2 Merkle Tree 2.2 Merkle Tree 2.3 Leaves Structure 2.3 Leaves Structure 2.4 Proof Statement 2.4 Proof Statement 3 Proof of Reserve 3 Proof of Reserve 3.1 Ethereum 3.1 Ethereum 3.2 Bitcoin 3.2 Bitcoin 4 Proof of Solvency 4 Proof of Solvency 5 Future Works and References 5 Future Works and References 2.2 Merkle Tree A Merkle Tree is a tree in computer science in which every leaf node is labeled with the cryptographic hash of a data block, and each nonleaf node is labeled with the cryptographic hash of the labels of its child nodes. The value of a non-leaf node is determined by the hash of its children nodes, and this continues recursively until the tree’s root is achieved. This structure is particularly effective because it allows for efficient and secure verification of the contents of large data structures. The Merkle Tree allows us to verify data with a significantly smaller subset of the total information.[7] In the scenario of Proof of Solvency, we use the Merkle Tree as our cryptographic commitment. The root of the Merkle Tree acts as a commitment to all liabilities, and each leaf in the tree corresponds to a liability. This allows for an efficient and secure way to prove the existence and integrity of liabilities. By using a Merkle Tree, we can provide a proof path for any given leaf node (liability) up to the root. This path, also known as the Merkle path, allows anyone to verify that a specific liability is part of the tree. They can do this by recomputing the hashes from the leaf up to the root and comparing it with the root hash. This approach is particularly useful because it allows for verification without needing access to all data points, providing a balance between transparency and data efficiency. In the following sections, we will delve deeper into the leaf structure of the Merkle Tree and how we can use it to create proof statements. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

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How Merkle Trees Enhance Data Integrity in Crypto Custody

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