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Merkle structures are widely used as commitment schemes: they allow a prover to publish a compact commitment to an ordered list $X$ of items, and then efficiently prove to a verifier that $x_i\in X$ is the $i$-th item in it. We compare…

Data Structures and Algorithms · Computer Science 2025-11-18 Alfonso Cevallos , Robert Hambrock , Alistair Stewart

This paper introduces the Cartesian Merkle Tree, a deterministic data structure that combines the properties of a Binary Search Tree, a Heap, and a Merkle tree. The Cartesian Merkle Tree supports insertions, updates, and removals of…

Cryptography and Security · Computer Science 2025-04-16 Artem Chystiakov , Oleh Komendant , Kyrylo Riabov

The scalability of blockchain technology remains a pivotal challenge, impeding its widespread adoption across various sectors. This study introduces an innovative approach to address this challenge by proposing the adaptive restructuring of…

Cryptography and Security · Computer Science 2024-08-08 Oleksandr Kuznetsov , Dzianis Kanonik , Alex Rusnak , Anton Yezhov , Oleksandr Domin

Merkle trees have become a widely successful cryptographic data structure. Enabling a vast variety of applications from checking for inconsistencies in databases like Dynamo to essential tools like Git to large scale distributed systems…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-11-30 Anoushk Kharangate

Committing to information is a central task in cryptography, where a party (typically called a prover) stores a piece of information (e.g., a bit string) with the promise of not changing it. This information can be accessed by another party…

Quantum Physics · Physics 2024-06-19 Lijie Chen , Ramis Movassagh

With the prevalence of online platforms, today, data is being generated and accessed by users at a very high rate. Besides, applications such as stock trading or high frequency trading require guaranteed low delays for performing an…

Databases · Computer Science 2020-03-03 Sepanta Zeighami , Raymond Chi-Wing Wong

The B-tree is a fundamental secondary index structure that is widely used for answering one-dimensional range reporting queries. Given a set of $N$ keys, a range query can be answered in $O(\log_B \nm + \frac{K}{B})$ I/Os, where $B$ is the…

Data Structures and Algorithms · Computer Science 2008-11-27 Ke Yi

Blockchain technology has emerged as a revolutionary tool in ensuring data integrity and security in digital transactions. However, the current approaches to data verification in blockchain systems, particularly in Ethereum, face challenges…

Cryptography and Security · Computer Science 2024-04-11 Oleksandr Kuznetsov , Alex Rusnak , Anton Yezhov , Dzianis Kanonik , Kateryna Kuznetsova , Stanislav Karashchuk

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

Programming Languages · Computer Science 2019-07-03 Reynald Affeldt , Jacques Garrigue , Xuanrui Qi , Kazunari Tanaka

Several B+-tree variants have been developed to exploit the performance potential of byte-addressable non-volatile memory (NVM). In this paper, we attentively investigate the properties of B+-tree and find that, a conventional B+-tree node…

Data Structures and Algorithms · Computer Science 2020-02-12 Chundong Wang , Gunavaran Brihadiswarn , Xingbin Jiang , Sudipta Chattopadhyay

B-slack trees, a subclass of B-trees that have substantially better worst-case space complexity, are introduced. They store $n$ keys in height $O(\log_b n)$, where $b$ is the maximum node degree. Updates can be performed in $O(\log_{\frac b…

Data Structures and Algorithms · Computer Science 2017-12-18 Trevor Brown

Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts.…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-12-17 Evangelos Bampas , Anissa Lamani , Franck Petit , Mathieu Valero

Merkle hash trees are the standard method to protect the integrity and freshness of stored data. However, hash trees introduce additional compute and I/O costs on the I/O critical path, and prior efforts have not fully characterized these…

Cryptography and Security · Computer Science 2025-01-30 Quinn Burke , Ryan Sheatsley , Rachel King , Owen Hines , Michael Swift , Patrick McDaniel

A Merkle tree is an information construction that is used in Blockchain to verify data or transactions in a large content pool in a safe manner. The role of the Merkle tree is crucial in Bitcoin and other cryptocurrencies in a Blockchain…

Cryptography and Security · Computer Science 2022-09-28 M. Gracy , B. Rebecca Jeyavadhanam

We propose BS-tree, an in-memory implementation of the B+-tree that adopts the structure of the disk-based index (i.e., a balanced, multiway tree), setting the node size to a memory block that can be processed fast and in parallel using…

Databases · Computer Science 2025-11-14 Dimitrios Tsitsigkos , Achilleas Michalopoulos , Nikos Mamoulis , Manolis Terrovitis

Blockchain systems face significant scalability challenges due to growing data volumes and increasing transaction demands, necessitating more efficient data structures and verification mechanisms. Verkle trees, a novel data structure…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-12 Zhikai Li , Xuekai Liu , Boyuan Xu , Eric Chen , Bhaskar Krishnamachari

In the rapidly evolving landscape of blockchain technology, ensuring the integrity and security of data is paramount. This study delves into the security aspects of Merkle Trees, a fundamental component in blockchain architectures, such as…

Cryptography and Security · Computer Science 2024-04-24 Oleksandr Kuznetsov , Alex Rusnak , Anton Yezhov , Kateryna Kuznetsova , Dzianis Kanonik , Oleksandr Domin

A Merkle tree is a data structure for representing a key-value store as a tree. Each node of a Merkle tree is equipped with a hash value computed from those of their descendants. A Merkle tree is often used for representing a state of a…

Programming Languages · Computer Science 2021-06-10 Sota Sato , Ryotaro Banno , Jun Furuse , Kohei Suenaga , Atsushi Igarashi

We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…

Data Structures and Algorithms · Computer Science 2020-10-20 Bryce Sandlund , Sebastian Wild

Merkle tree is a widely used tree structure for authentication of data/metadata in a secure computing system. Recent state-of-the art secure systems use a smaller-sized MT, namely Bonsai Merkle Tree (BMT) to protect the metadata such as…

Cryptography and Security · Computer Science 2023-09-19 Rakin Muhammad Shadab , Yu Zou , Sanjay Gandham , Amro Awad , Mingjie Lin
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