Treez

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Almost every week, it seems, another part of our world is analyzed in an as-a-service package. This growing trend should not surprise anyone. As hardware, software, bandwidth, and protocols evolve, more processes and resources can be outsourced. This subsequent development is driving digitalization that is transforming industries around the world. Financial services are no exception. Banking as a Service (BaaS) brings banking to the world. However, as with almost everything related to finance, BaaS is surrounded by mystery. In this article, we want to overview banking as a service to shed light on its benefits, uses, and challenges. What is Banking as a Service? BaaS is a model that allows online banks and third parties to connect directly to banking systems through APIs, building banking offerings on top of a regulated vendor infrastructure, and unlocking new experiences. Digital-savvy traditional firms can fend off the looming fintech threat by moving into the BaaS space to share their data and infrastructure. In a few years, access to this level of information will guarantee digitally accustomed clients, so banks that start now will be ahead of their rivals and likely to be rewarded with solid demand. How does Bank as a Service Work? The BaaS model starts with a fintech, digital bank, or third-party provider (TPP) paying a fee to access the BaaS platform. A financial institution exposes its APIs to TPP, providing access to the systems and information needed to create new banking products or offer white-label banking services. Besides advancing open banking, traditional institutions that launch their own BaaS platforms are also opening up new revenue streams. The two main BaaS monetization strategies include charging customers a monthly fee to access the BaaS platform or charging for each used service. Layers of Banking as a Service As the image below demonstrates, BaaS can have multiple service tiers, and customers can choose numerous of them for the business. It depends on the needs of the company. BaaS vs. Open Banking vs. Banking as a Service Platform You need to distinguish between these three terms. BaaS is often confused with Open Banking as the latter also uses an API to link banks to non-banks. Although, the core functions of open banking differ significantly. Under this model, non-banks use APIs to access banking data and embed it into their financial services. For example, people use a financial management app to keep track of their monthly expenses. The app uses an API to integrate transaction data from the user’s bank account and perform analytics to help them manage finances more efficiently and improve spending habits. The itself does not provide any new banking services. It simply integrates the data already stored in the bank into the account management functions. This is how open banking business models work. app Unlike open banking, BaaS provides the user with an entirely new type of service. ​​BaaS does not give customers what has already been created but uses it as a basis for making a new banking experience. Besides, there is a difference between BaaS and a banking platform. The leading players in banking platforms are not third parties but the banks themselves. They use the power of financial technology to provide access to the services offered by the bank. For example, a bank could create an AI-powered tool to help users select the best investment opportunity and quickly complete their day-to-day banking transactions. Currently, financial institutions are using banking platforms to retain clients and enable them to immerse themselves in the fintech industry fully. In the BaaS concept, the end-user interacts not with the bank but with a third party that offers new services. The brand front-end is connected to the BaaS provider via an API, which connects the provider to the bank. This chain allows distributors, brands, and fintech companies to integrate service banking directly into their products – e-commerce websites, fintech applications, or financial services. Banking as a Service Advantages Benefits for a Client BaaS brings innovation and customization to fund product development. Clients receive the following benefits: Excellent Services are Offered If there were no BaaS providers, customers would use banking services directly. So, it’s not that the client needs BaaS – BaaS requires a client. That’s why BaaS providers strive to offer a truly superior experience. They are making an effort to meet the needs of banking customers who are digital natives and genuinely tech-savvy. More Products to Choose From The wider the choice, the better for the client. High competition is not good news for service providers. But for clients, it gives more flexibility. Innovative solutions strive to be customer-centric and offer all the necessary functions in one place. This enhances financial transparency and simplifies cash management compared to traditional bank accounts. Benefits for the Banks Like customers, banks offering API-based data access also have a win-win strategy. At a minimum, they lose nothing and earn more money. Most importantly, they benefit personally from sharing their data with BaaS banking providers. More people use Banking Services Banking as a service does not create an additional burden on the bank. Instead, BaaS provides new lines and revenue streams. The bank offers access to data through the API and takes a commission for this. He does not care how third-party distributors will attract the audience, where they will look for funds, whether they will outperform competitors, etc. They do not need to invest in development. Their primary responsibility is to ensure that customer data is well protected from breaches. Banks get to know the needs of their audience By analyzing the performance of a third-party BaaS provider, banks can gain insight into the needs of their customers. What features do they use, what helps them manage their finances, and what annoys them? Such insights can be obtained using machine learning solutions for finance and incorporated into developing the bank’s products. Benefits for Business Non-banks, enterprises, and fintech companies that provide BaaS play the most responsible role in this game. In addition to the benefits, they may find investing in a new solution challenging, just as it can be when developing any other product. They must build a to avoid failing their idea. But despite the threats, they can still gain a lot of strength. risk management strategy Enterprises Become Bankers, not Being Bankers As payments and settlements are the most popular startup segment among American banking investors. With the fintech industry’s growth, they all see great potential in investing in banking solutions. To offer banking services themselves and circumvent banking laws, businesses prefer to act as a third party and earn money by acting as an intermediary between the financial institution and the customer. FinancesOnline states, Customer Recognition Yes, it is not easy for clients to entrust their financial data to a third-party business they have never heard of. By linking with well-known banking institutions, BaaS providers build on the bank’s reputation in customers’ eyes and quickly gain their trust. Disadvantages of Banking as a Service Competition can shrink banks’ customer base For banks, BaaS means they face the constant danger of losing some of their market share to better-serving non-banks. Usually, no one-on-one relationships If you prefer digital banking but want to interact with your financial institution in person, you generally won’t get it with BaaS accounts. Your information is less secure Because you use two companies for your banking transactions (the account offering company and the bank), your information is exposed in two ways instead of one. Banking as a Service Examples To get a better understanding of BaaS, let’s take a look at a couple of real-world applications. This list is not definitive and is growing every day, so we will analyze three options for using banking as a service: Platforms and marketplaces with a large user base can benefit significantly by offering their customers the e-wallet functionality through deposit accounts. For example, crowdfunding platforms can use a BaaS solution to create unique IBAN accounts for individual users and hit two birds with one stone. Firstly, it contributes to a better user experience as they do not need to make a bank transfer every time they make a transaction on the platform as the funds are securely stored there. Secondly, it is easier for the platform to convince customers to reinvest, significantly increasing client retention. Almost any service provider can benefit from BaaS and offer white-label payment cards to their clients. Customers take advantage of individual card programs, and businesses create an additional revenue stream. However, fintech startups are taking full advantage of BaaS services. They can use the infrastructure and functionality of banks (also known as banking software as a service) and data banks about their customers. This opens up a whole new spectrum of startup opportunities, from personal finance apps to real-time payments, from targeting niche customers to focusing on mainstream adoption. What is paramount for startups is that BaaS can save you a ton of money and at least a couple of years in business and product development. Not to mention that they would not need to have the funds to acquire a license. The earlier they enter the market, the happier their investors are. How to Choose a Banking as a Service provider? So you’ve decided to integrate your business with a financial services platform. When searching for the ideal BaaS provider candidate, we suggest considering the following: Reputation In the global network, nothing stays a secret for long. Look for reviews and testimonials to form an objective opinion. Relevance of services Take a close look at the services offered by a particular provider to ensure they meet your business requirements. Ownership of services Are the proposed APIs and solutions provided by the company or owned by third parties? This issue will become necessary as the partnership develops. Scalability Does the potential partner have the tech stack, resources, and stamina to play the long game? Will they be able to stay up-to-date as their customer base expands and business needs grow? Compatibility and speed to market How quickly and reliably can the supplier deliver the solution you need? There is one more small difference that we should mention to avoid any confusion. Top Banking as a Service Companies As BaaS gains momentum, new providers are entering the market along with platforms created by banks. While BaaS providers use a closed architecture, platforms are designed to share APIs with clients. Here are some of the leading players. The Bancorp With $6.2 billion in assets and $232 billion in annual cumulative processing volume, started as a branchless bank and is now a leader in digital financial services. The company provides private banking and technology solutions for non-banking businesses. It has been holding the number one position in prepaid card volume in the US for eight consecutive years and specializes in institutional banking and commercial lending. The Bancorp Fidor Bank This German company, founded in 2009, has gone as far as creating its own BaaS platform. It runs on a proprietary OS and is a cloud-based modular system. teams have created over 40 standardized, forward-thinking APIs that integrate seamlessly with any customer service. The Fidor mobile banking app covers everything from standard accounts and card transactions to loans and crypto investments. Fidor’s Treezor is a Paris-based banking platform as a service, a “one-stop payment solution.” Recently acquired by , thanks to their innovative expertise, the startup is accredited to provide personalized payment services to its customers. Treezor Societe Generale Group Challenges of Banking as a Service The challenges of implementing a BaaS strategy are numerous. Fortunately, related solutions pave the way for user-friendly financial products and solutions. Let’s dig deeper. Modernization of traditional banks The core systems of most traditional banks are outdated. They are incompatible with modern technology. This can be a significant problem when implementing a BaaS model, as it can interfere with third-party integration. The future of banking as a service will include a modernized architecture of traditional banks. This will help expose services, products, and processes such as APIs. Changing roles of players in the financial industry Recent research shows that traditional banks are slowly losing the “customer trust” advantage over fintech players. On the other hand, many tech companies like Apple Card enter the financial space because they have customer trust. Moreover, BaaS involves cooperation with third-party players. Naturally, there are many coincidences in terms of functionality. In addition, many companies use ‘white labeling’ when offering their products. This can confuse end customers. Given these points, the future of BaaS shows a massive shift in player responsibilities. A well-defined API strategy Opening a bank or business (middleware) via an API is no small feat. Operational processes and business opportunities must be presented optimally. However, most organizations face challenges when creating an API strategy. The main goal when creating an API strategy should be ease of integration. It should provide maximum business value by limiting the cumbersome aspects of integration. The future of the financial industry may include a global standardization of the API strategy. Considering all factors, the BaaS sector shows no signs of stopping. It would be interesting to see how technological progress will affect the BaaS model in the next decade. The Banking as a Service Future The financial sector is rapidly changing, and BaaS is paving the way for a new reality. Banks, fintech, service providers, and brands can achieve synergy by creating functional and efficient integrated solutions. In an interconnected environment, everyone will reap their respective benefits if they quickly adjust their strategy. As financial services more closely reflect consumer needs, BaaS providers will attract new customers. Better customer profiling and additional revenue streams will give merchants a well-deserved bonus. All vendors need to do is establish relationships with a few relevant merchants and manage them effectively. The benefits for the banking sector from merging with providers and brands and reaching a much wider audience are even more apparent. Conclusion As you can see, BaaS has its benefits and challenges, just like any other development case. But it is a relatively vacant niche that gives you higher chances to stand out from the rivals. If the banking industry in your country is well-developed, you can create a BaaS solution and expand your market share. Also published here .

BaaS (Banking as a Service): Everything You Need to Know

1. Forget about hardware; the real money is in software For months, headlines have fixated on Huawei's limitations in producing advanced 7nm chips, while Apple excels with its cutting-edge 3nm technology. However, this focus on hardware overlooks a critical lesson from history: software, not hardware, drives  profits. Bill Gates built the Microsoft empire not by building hardware—outsourced to IBM—but by dominating the software business. Today, Microsoft’s software business dwarfs IBM's historical combined hardware and software projects. Huawei’s HarmonyOS NEXT, already claimed to be the world’s third-largest mobile OS with over a billion installations, represents a significant milestone. While currently present mostly in China, the system has the potential to expand to other markets, particularly in the Global South. HarmonyOS could appeal to nations seeking to reduce reliance on U.S.-based technology. A large user base often translates into substantial revenue streams over time. Moreover, Huawei is working on extending its OS to personal computers under the name HarmonyOS PC, with a target release in Q3 2025. Even if this initiative gains traction solely within China, particularly in government systems, it could reduce the dominance of Microsoft Windows and Apple macOS, cutting into their lucrative revenue streams. 2. Know-How and Engineering Workforce Unlike hardware chip technology, software OS tools and expertise are widely accessible, starting with the open-source availability of Android OS. This means the necessary know-how is either readily available or easy to acquire. China also boasts a large skilled engineering workforce—reportedly four times larger than that of the U.S.—providing Huawei with ample talent at a competitive cost to develop its new OS. With sufficient time and resources, Huawei is likely to succeed in its HarmonyOS project. 3. Marketing or Reality? Reports suggest that HarmonyOS is facing some challenges. According to a media report, even the migration of China’s own WeChat app to the platform has encountered difficulties. This is not entirely surprising, as building a stable operating system is a highly complex and demanding task. Even Steve Jobs famously staged parts of his iPhone presentation during its early development stages. It required time and engineering effort for Apple to refine and perfect the product. Huawei faces a similar trajectory. If it commits to the project with enough talent, funding, and patience, HarmonyOS could mature into a serious alternative to Microsoft and Apple’s software dominance. 4 References [1] HarmonyOS [2] HarmonyOS NEXT [3] China's first fully home-grown mobile operating system HarmonyOS NEXT launched [4] https://www.huaweicentral.com/category/harmonyos/harmonyos-next/ [5] HarmonyOS NEXT becomes the world’s third major mobile OS, joining Android and iOS [6] Huawei’s HarmonyOS NEXT faces major test with WeChat: Will it pass? [7] Huawei’s China-Made 7nm Chip ‘Years Behind US’, Raimondo Says [8] In Huawei’s battle against Apple, chips are still a weakness, says analyst [9] HuaweiNext-gen Huawei PCs will ditch Windows for HarmonyOS: Chairman [10] Huawei HarmonyOS PC rumored to delay till Q3 2025 [11] HarmonyOS PC UI design allegedly surfaced on Huawei Developer website [12] The Global Distribution of STEM Graduates: Which Countries Lead the Way? [13] How Steve Jobs Faked His Way Through Unveiling the iPhone 1. Forget about hardware; the real money is in software For months, headlines have fixated on Huawei's limitations in producing advanced 7nm chips, while Apple excels with its cutting-edge 3nm technology. However, this focus on hardware overlooks a critical lesson from history: software, not hardware, drives  profits. Bill Gates built the Microsoft empire not by building hardware—outsourced to IBM—but by dominating the software business. Today, Microsoft’s software business dwarfs IBM's historical combined hardware and software projects. Huawei’s HarmonyOS NEXT , already claimed to be the world’s third-largest mobile OS with over a billion installations, represents a significant milestone. While currently present mostly in China, the system has the potential to expand to other markets, particularly in the Global South. HarmonyOS could appeal to nations seeking to reduce reliance on U.S.-based technology. A large user base often translates into substantial revenue streams over time. HarmonyOS NEXT world’s third-largest mobile OS Moreover, Huawei is working on extending its OS to personal computers under the name HarmonyOS PC , with a target release in Q3 2025 . Even if this initiative gains traction solely within China, particularly in government systems, it could reduce the dominance of Microsoft Windows and Apple macOS, cutting into their lucrative revenue streams. extending its OS to personal computers HarmonyOS PC Q3 2025 2. Know-How and Engineering Workforce Unlike hardware chip technology, software OS tools and expertise are widely accessible, starting with the open-source availability of Android OS. This means the necessary know-how is either readily available or easy to acquire. China also boasts a large skilled engineering workforce —reportedly four times larger than that of the U.S.—providing Huawei with ample talent at a competitive cost to develop its new OS. With sufficient time and resources, Huawei is likely to succeed in its HarmonyOS project. large skilled engineering workforce 3. Marketing or Reality? Reports suggest that HarmonyOS is facing some challenges. According to a media report, even the migration of China’s own WeChat app to the platform has encountered difficulties. This is not entirely surprising, as building a stable operating system is a highly complex and demanding task. Even Steve Jobs famously staged parts of his iPhone presentation during its early development stages. It required time and engineering effort for Apple to refine and perfect the product. Huawei faces a similar trajectory. If it commits to the project with enough talent, funding, and patience, HarmonyOS could mature into a serious alternative to Microsoft and Apple’s software dominance. 4 References [1] HarmonyOS HarmonyOS [2] HarmonyOS NEXT HarmonyOS NEXT [3] China's first fully home-grown mobile operating system HarmonyOS NEXT launched China's first fully home-grown mobile operating system HarmonyOS NEXT launched [4] https://www.huaweicentral.com/category/harmonyos/harmonyos-next/ https://www.huaweicentral.com/category/harmonyos/harmonyos-next/ [5] HarmonyOS NEXT becomes the world’s third major mobile OS, joining Android and iOS HarmonyOS NEXT becomes the world’s third major mobile OS, joining Android and iOS [6] Huawei’s HarmonyOS NEXT faces major test with WeChat: Will it pass? Huawei’s HarmonyOS NEXT faces major test with WeChat: Will it pass? [7] Huawei’s China-Made 7nm Chip ‘Years Behind US’, Raimondo Says Huawei’s China-Made 7nm Chip ‘Years Behind US’, Raimondo Says [8] In Huawei’s battle against Apple, chips are still a weakness, says analyst In Huawei’s battle against Apple, chips are still a weakness, says analyst [9] HuaweiNext-gen Huawei PCs will ditch Windows for HarmonyOS: Chairman HuaweiNext-gen Huawei PCs will ditch Windows for HarmonyOS: Chairman [10] Huawei HarmonyOS PC rumored to delay till Q3 2025 Huawei HarmonyOS PC rumored to delay till Q3 2025 [11] HarmonyOS PC UI design allegedly surfaced on Huawei Developer website HarmonyOS PC UI design allegedly surfaced on Huawei Developer website [12] The Global Distribution of STEM Graduates: Which Countries Lead the Way? The Global Distribution of STEM Graduates: Which Countries Lead the Way? [13] How Steve Jobs Faked His Way Through Unveiling the iPhone How Steve Jobs Faked His Way Through Unveiling the iPhone

Experts Skeptical of Huawei Silicon May Be Missing the Forest for the Trees

الخبراء المتشككون في السيليكون الخاص بشركة هواوي ربما يغفلون عن حقيقة الأمر

“Huawei Silicon”a şübhə ilə yanaşan ekspertlər ağaclar üçün meşədən məhrum ola bilərlər

Stručnjaci skeptični prema Huawei Silicijum možda nedostaje šuma za drveće

Los expertos escépticos sobre el silicio de Huawei podrían estar perdiendo de vista el bosque detrás de los árboles

מומחים הספקנים לגבי סיליקון Huawei עשויים להחמיץ את היער בשביל העצים

ファーウェイのシリコンに懐疑的な専門家は、木を見て森を見ずかもしれない

Pakar Ragu-ragu Huawei Silicon Mungkin Hilang Hutan untuk Pokok

Ditsebi tše di Belaelago Silicon ya Huawei e ka ba e Hlolwa Sethokgwa bakeng sa Dihlare

Стручњаци скептични према Хуавеи силицијуму можда недостаје шума за дрвеће

Hünärmenler Huawei Silikonyna şübheli garaýarlar, agaçlar üçin tokaýy ýitirip bilerler

Huawei Silikonuna Şüpheyle Yaklaşan Uzmanlar Ormanı Ağaçlardan Kaçırıyor Olabilir

Huawei kremniyiga shubha bilan qaraydigan ekspertlar daraxtlar uchun o‘rmon yetishmasligi mumkin

How to Build a Database From Scratch: Understanding LSM Trees and Storage Engines (Part 1)

How Decentralized Interaction Protocols Work: Analyzing VC, ZKP, and Āut’s Interaction Tree

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 2.3 Leaves Structure Until now, we have discussed how we can commit to a list of data by using a hash tree, specifically, a Merkle tree. Now let’s delve into the structure of the data we are committing to. In our commitment to data via a Merkle tree, each leaf (except the last right leaf) contains key-value pairs of data: The ’User Identifier’ is a unique identifier for each user. The ’Asset Identifier’ refers to the identifier for each asset. For example, in the Ethereum network, we consider the zero address as the identifier for ETH, and for each token, we consider their token address as the identifier. The ’amount’ is the balance the user holds of that specific asset according to the business database that wants to prove their liabilities amount. This approach to committing to our liabilities is similar to other proof of solvency approaches. However, traditionally, committing to our liabilities in this way would require us to make our total liabilities public. To prove the correctness of the sum, we would need to enlist the help of an auditor firm or use Zero-Knowledge Proofs (ZKP). But in doing so, we would have to reveal our total liabilities. The approach we’re introducing allows the total liabilities to remain private. Let’s explain how this is achieved by discussing the last right leaf of our Merkle tree: The Total Balance is the sum of the balances of all users for a specific asset (Asset1: user1 balance + user2 balance + ...). We then use a ZKP protocol to create a circuit and leverage the characteristic of verifiable computation to prove that the total sum in the last right leaf is calculated correctly by adding previous leaves related attributes and that there is no negative balance in any leaf. So now, we commit to a liabilities tree that includes all of our user liabilities. We also hold the total amount we commit to and have a proof for the correctness of the entire tree and calculation, without revealing the total amount of our liabilities. This allows us to maintain privacy while still proving our solvency. 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 2.3 Leaves Structure Until now, we have discussed how we can commit to a list of data by using a hash tree, specifically, a Merkle tree. Now let’s delve into the structure of the data we are committing to. In our commitment to data via a Merkle tree, each leaf (except the last right leaf) contains key-value pairs of data: The ’User Identifier’ is a unique identifier for each user. The ’Asset Identifier’ refers to the identifier for each asset. For example, in the Ethereum network, we consider the zero address as the identifier for ETH, and for each token, we consider their token address as the identifier. The ’amount’ is the balance the user holds of that specific asset according to the business database that wants to prove their liabilities amount. This approach to committing to our liabilities is similar to other proof of solvency approaches. However, traditionally, committing to our liabilities in this way would require us to make our total liabilities public. To prove the correctness of the sum, we would need to enlist the help of an auditor firm or use Zero-Knowledge Proofs (ZKP). But in doing so, we would have to reveal our total liabilities. The approach we’re introducing allows the total liabilities to remain private. Let’s explain how this is achieved by discussing the last right leaf of our Merkle tree: The Total Balance is the sum of the balances of all users for a specific asset (Asset1: user1 balance + user2 balance + ...). We then use a ZKP protocol to create a circuit and leverage the characteristic of verifiable computation to prove that the total sum in the last right leaf is calculated correctly by adding previous leaves related attributes and that there is no negative balance in any leaf. So now, we commit to a liabilities tree that includes all of our user liabilities. We also hold the total amount we commit to and have a proof for the correctness of the entire tree and calculation, without revealing the total amount of our liabilities. This allows us to maintain privacy while still proving our solvency. 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

Understanding Leaf Structures: How Merkle Trees Maintain Privacy in Liabilities

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

How Merkle Trees Enhance Data Integrity in Crypto Custody

The Impact of Adaptive Tree Structures on Blockchain Technology

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 9.2. Comparison with Existing Solutions In the quest to address blockchain scalability, several innovative solutions have been proposed and implemented across various platforms. Each of these solutions presents unique advantages and challenges. Below (Table 7), we provide a comparative analysis of these solutions, including our adaptive restructuring approach, to highlight their relative strengths and limitations. The comparative analysis underscores the diversity of approaches to tackling blockchain scalability, each with its unique trade-offs. Sharding and Layer 2 protocols, while promising significant throughput improvements, introduce additional layers of complexity and potential security concerns. State channels and sidechains offer more specialized solutions but are limited by their applicability and integration challenges. Our approach, adaptive restructuring of Merkle and Verkle trees, stands out by directly optimizing the underlying data structure of the blockchain. This method offers a fundamental improvement in efficiency without introducing external dependencies or significantly altering the blockchain's operational principles. While it necessitates initial efforts for restructuring and ongoing maintenance, the benefits of reduced path lengths and lower verification costs present a compelling case for its adoption. Moreover, being a relatively new concept, it opens up extensive opportunities for further research and development to fully realize its potential and address any emerging challenges. Thus, our work contributes a novel perspective to the field of blockchain research, opening new avenues for the development of more scalable and efficient blockchain systems. By addressing scalability at the data structure level, we provide a foundational solution that can be integrated with other scalability and efficiency-enhancing techniques, offering a comprehensive approach to overcoming one of the most significant barriers to blockchain adoption. 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 9.2. Comparison with Existing Solutions In the quest to address blockchain scalability, several innovative solutions have been proposed and implemented across various platforms. Each of these solutions presents unique advantages and challenges. Below (Table 7), we provide a comparative analysis of these solutions, including our adaptive restructuring approach, to highlight their relative strengths and limitations. The comparative analysis underscores the diversity of approaches to tackling blockchain scalability, each with its unique trade-offs. Sharding and Layer 2 protocols, while promising significant throughput improvements, introduce additional layers of complexity and potential security concerns. State channels and sidechains offer more specialized solutions but are limited by their applicability and integration challenges. Our approach, adaptive restructuring of Merkle and Verkle trees, stands out by directly optimizing the underlying data structure of the blockchain. This method offers a fundamental improvement in efficiency without introducing external dependencies or significantly altering the blockchain's operational principles. While it necessitates initial efforts for restructuring and ongoing maintenance, the benefits of reduced path lengths and lower verification costs present a compelling case for its adoption. Moreover, being a relatively new concept, it opens up extensive opportunities for further research and development to fully realize its potential and address any emerging challenges. Thus, our work contributes a novel perspective to the field of blockchain research, opening new avenues for the development of more scalable and efficient blockchain systems. By addressing scalability at the data structure level, we provide a foundational solution that can be integrated with other scalability and efficiency-enhancing techniques, offering a comprehensive approach to overcoming one of the most significant barriers to blockchain adoption. 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

Comparing Adaptive Merkle Trees with Sharding, Layer 2, and Other Scalability Solutions

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 9.1. Our Contribution Our primary contribution lies in the introduction of adaptive Merkle trees, a novel concept that leverages dynamic restructuring based on usage patterns to optimize path lengths and reduce the computational overhead associated with data verification and integrity checks. By applying principles from Huffman and Shannon-Fano coding to the organization of tree nodes, we ensure that frequently accessed data is more accessible, thereby reducing the average path length and associated costs. Through rigorous analysis and examples, we demonstrated the efficiency gains achievable with adaptive Merkle trees. Our algorithm for Merkle tree restructuring, detailed in Section 5, provides a systematic approach for dynamically adjusting tree structures, significantly improving upon the static nature of traditional Merkle trees. Extending our concept to Verkle trees, we showcased how adaptive restructuring could be applied to this advanced data structure, further enhancing its efficiency and making it even more suitable for large-scale blockchain applications. This application not only underscores the versatility of our approach but also its potential to contribute to the next generation of blockchain technologies. 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 9.1. Our Contribution Our primary contribution lies in the introduction of adaptive Merkle trees, a novel concept that leverages dynamic restructuring based on usage patterns to optimize path lengths and reduce the computational overhead associated with data verification and integrity checks. By applying principles from Huffman and Shannon-Fano coding to the organization of tree nodes, we ensure that frequently accessed data is more accessible, thereby reducing the average path length and associated costs. Through rigorous analysis and examples, we demonstrated the efficiency gains achievable with adaptive Merkle trees. Our algorithm for Merkle tree restructuring, detailed in Section 5, provides a systematic approach for dynamically adjusting tree structures, significantly improving upon the static nature of traditional Merkle trees. Extending our concept to Verkle trees, we showcased how adaptive restructuring could be applied to this advanced data structure, further enhancing its efficiency and making it even more suitable for large-scale blockchain applications. This application not only underscores the versatility of our approach but also its potential to contribute to the next generation of blockchain technologies. 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 Merkle Trees and Their Impact on Blockchain Scalability

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 9. Discussion In this work, we have embarked on a comprehensive exploration of optimizing tree structures within the blockchain ecosystem, addressing the critical challenge of scalability that plagues current blockchain technologies. Our investigation spans from conceptualizing the inherent problems associated with traditional Merkle trees to proposing and validating an innovative approach for adaptive restructuring of these trees to enhance efficiency and scalability in blockchain systems. The blockchain paradigm, while revolutionary, faces significant scalability challenges, primarily due to the inherent limitations of its underlying data structures and consensus mechanisms. Traditional Merkle trees, despite their widespread adoption for ensuring data integrity and facilitating efficient verifications, contribute to these scalability issues due to their static nature and the increasing cost of operations as the blockchain grows. Existing solutions to blockchain scalability, such as sharding and layer 2 protocols, offer partial remedies by distributing the workload or offloading transactions. However, these approaches often introduce complexity or compromise on decentralization and security. Our review of the state of the art highlights a gap in dynamically optimizing the data structures themselves to directly address the root causes of inefficiency. 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 9. Discussion In this work, we have embarked on a comprehensive exploration of optimizing tree structures within the blockchain ecosystem, addressing the critical challenge of scalability that plagues current blockchain technologies. Our investigation spans from conceptualizing the inherent problems associated with traditional Merkle trees to proposing and validating an innovative approach for adaptive restructuring of these trees to enhance efficiency and scalability in blockchain systems. The blockchain paradigm, while revolutionary, faces significant scalability challenges, primarily due to the inherent limitations of its underlying data structures and consensus mechanisms. Traditional Merkle trees, despite their widespread adoption for ensuring data integrity and facilitating efficient verifications, contribute to these scalability issues due to their static nature and the increasing cost of operations as the blockchain grows. Existing solutions to blockchain scalability, such as sharding and layer 2 protocols, offer partial remedies by distributing the workload or offloading transactions. However, these approaches often introduce complexity or compromise on decentralization and security. Our review of the state of the art highlights a gap in dynamically optimizing the data structures themselves to directly address the root causes of inefficiency. 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

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