This paper proposes a three-step Secret Santa algorithm with setup that leverages Zero Knowledge Proofs (ZKP) to set up gift sender/receiver relations while maintaining the sender's confidentiality. The algorithm maintains a permutational derangement and does not require a central authority to perform successfully. The described approach can be implemented in Solidity provided the integration with a transaction relayer.
This survey provides a comprehensive examination of verifiable computing, tracing its evolution from foundational complexity theory to modern zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARKs). We explore key developments in interactive proof systems, knowledge complexity, and the application of low-degree polynomials in error detection and verification protocols. The survey delves into essential mathematical frameworks such as the Cook-Levin Theorem, the sum-check protocol, and the GKR protocol, highlighting their roles in enhancing verification efficiency and soundness. By systematically addressing the limitations of traditional NP-based proof systems and then introducing advanced interactive proof mechanisms to overcome them, this work offers an accessible step-by-step introduction for newcomers while providing detailed mathematical analyses for researchers. Ultimately, we synthesize these concepts to elucidate the GKR protocol, which serves as a foundation for contemporary verifiable computing models. This survey not only reviews the historical and theoretical advancements in verifiable computing over the past three decades but also lays the groundwork for understanding recent innovations in the field.
Kamilla Nazirkhanova, Vrushank Gunjur, X. Pilli Cruz-De Jesus, Dan Boneh
Ensuring the privacy of votes in an election is crucial for the integrity of a democratic process. Often, voting power is delegated to representatives (e.g., in congress) who subsequently vote on behalf of voters on specific issues. This delegation model is also widely used in Decentralized Autonomous Organizations (DAOs). Although several existing voting systems used in DAOs support private voting, they only offer public delegation. In this paper, we introduce Kite, a new protocol that enables $\textit{private}$ delegation of voting power for DAO members. Voters can freely delegate, revoke, and re-delegate their power without revealing any information about who they delegated to. Even the delegate does not learn who delegated to them. The only information that is recorded publicly is that the voter delegated or re-delegated their vote to someone. Kite accommodates both public and private voting for the delegates themselves. We analyze the security of our protocol within the Universal Composability (UC) framework. We implement Kite as an extension to the existing Governor Bravo smart contract on the Ethereum blockchain, that is widely used for DAO governance. Furthermore, we provide an evaluation of our implementation that demonstrates the practicality of the protocol. The most expensive operation is delegation due to the required zero-knowledge proofs. On a consumer-grade laptop, delegation takes between 7 and 167 seconds depending on the requested level of privacy.
This thesis primarily explores efficient zero-knowledge range arguments as first part and privacy-preserving applications within distributed systems as second part. The first part focuses on zero-knowledge range arguments, a fundamental cryptographic primitive that enables a prover to convince a verifier that a secret value lies within a predefined range without disclosing any unnecessary information. However, deploying range arguments in practice faces significant challenges due to high gas costs and computational overhead. This part contributes to optimizing the {\em verification efficiency} of range arguments to reduce deployment costs on blockchains and other decentralized platforms. We introduce four new zero-knowledge range arguments in the discrete logarithm setting that require only $c \sqrt{\tfrac{N}{\log N}}$ group exponentiations in verification, where $N$ is the number of bits to represent a range and $c$ is a small constant. These improvements make the arguments concretely efficient for blockchain deployment with minimal gas costs. The second part proposes two privacy-enhancing secure distributed systems and applications. First, we introduce a novel paradigm for decentralized privacy-preserving group purchasing for energy plans. Leveraging privacy-preserving blockchain technology and secure multi-party computation, this approach enables users to form coalitions for coordinated switch decisions in a decentralized manner without relying on a trusted third party. We develop an effective solution to support decentralized privacy-preserving group purchasing, which includes a competitive online algorithm for decision-making, secure multi-party computation for enhancing privacy, and zero-knowledge proofs on the blockchain for verifying the private input data used in our online algorithm. Second, we propose a novel scheme zk-qrcode based on anonymous credentials and zk-SNARK. Our scheme leverages the following features: Blockchain-based credential issuance, we eliminate the need for credential issuers to hold signing keys by allowing them to issue credentials to a smart contract on the blockchain; Flexible and composable identity statements, enables users to prove complex statements about their credentials without revealing unnecessary information; QR code based verification: enables user interaction with service providers through QR codes displayed or scanned on mobile phones, incorporating identity proof and access control requests. We implement and evaluate our zk-qrcode scheme in practical use cases for entering bar anonymously. Our results demonstrate that the scheme is efficient and practical, with access control proof generation and verification taking less than 650 milliseconds.
Ahmed Ayoub Bellachia, Mouhamed Amine Bouchiha, Yacine Ghamri-Doudane, Mourad Rabah
Blockchain-based Federated Learning (BFL) is an emerging decentralized machine learning paradigm that enables model training without relying on a central server. Although some BFL frameworks are considered privacy-preserving, they are still vulnerable to various attacks, including inference and model poisoning. Additionally, most of these solutions employ strong trust assumptions among all participating entities or introduce incentive mechanisms to encourage collaboration, making them susceptible to multiple security flaws. This work presents VerifBFL, a trustless, privacy-preserving, and verifiable federated learning framework that integrates blockchain technology and cryptographic protocols. By employing zero-knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARKs) and in-crementally verifiable computation (IVC), VerifBFL ensures the verifiability of both local training and aggregation processes. The proofs of training accuracy and aggregation are verified on-chain, guaranteeing the integrity and auditability of each participant's contributions. To protect training data from inference attacks, VerifBFL leverages differential privacy. Finally, to demonstrate the efficiency of the proposed protocols, we built a proof of concept using emerging tools. The results show that generating proofs for local training and aggregation in VerifBFL takes less than 81s and 2s, respectively, while verifying them on-chain takes less than 0.6s.
Marlena Broniszewska, Wiktor B. Daszczuk, Denny B. Czejdo
Global digitalization has accelerated, leading to continuous online shopping and services growth. However, the centralized nature of traditional e-commerce platforms raises concerns about data control, privacy, and potential single points of failure. Blockchain technology offers a decentralized alternative that addresses these issues, improving online transactions with enhanced privacy and anonymity for users. This article explores the problem of anonymization in web services by developing an anonymous online auction system using blockchain and zero-knowledge proof (ZKP). We propose a solution that employs ZKP in two stages: first, to verify that a user is eligible to participate in the auction, thereby creating a list of potential bidders; second, to prove that a bid is placed by a user from this list without disclosing their identity. This approach allows participants to engage in auctions anonymously, protecting their interests from competitors and sellers. The system eliminates the need for a trusted third party by leveraging the blockchain immutable ledger for transparency, giving users full control over their data and participation. We present the architecture and implementation details of the system, demonstrating its feasibility and potential to enhance privacy and security in online auctions.
Distributed ledger technology offers several advantages for banking and finance industry, including efficient transaction processing and cross-party transaction reconciliation. The key challenges for adoption of this technology in financial institutes are (a) the building of a privacy-preserving ledger, (b) supporting auditing and regulatory requirements, and (c) flexibility to adapt to complex use-cases with multiple digital assets and actors. This paper proposes a framework for a private, audit-able, and distributed ledger (PADL) that adapts easily to fundamental use-cases within financial institutes. PADL employs widely-used cryptography schemes combined with zero-knowledge proofs to propose a transaction scheme for a `table' like ledger. It enables fast confidential peer-to-peer multi-asset transactions, and transaction graph anonymity, in a no-trust setup, but with customized privacy. We prove that integrity and anonymity of PADL is secured against a strong threat model. Furthermore, we showcase three fundamental real-life use-cases, namely, an assets exchange ledger, a settlement ledger, and a bond market ledger. Based on these use-cases we show that PADL supports smooth-lined inter-assets auditing while preserving privacy of the participants. For example, we show how a bank can be audited for its liquidity or credit risk without violation of privacy of itself or any other party, or how can PADL ensures honest coupon rate payment in bond market without sharing investors values. Finally, our evaluation shows PADL's advantage in performance against previous relevant schemes.
It is well known that a Bose-Einstein (BE) condensate of atoms exists in a system of interacting Bose atoms at $T\lesssim T^{(i)}_{c}$, where $T^{(i)}_{c}$ is the BE condensation temperature of an ideal gas. It is also generally accepted that BE condensation is impossible at ``ultrahigh'' temperatures $T\gg T^{(i)}_{c}$. While the latter property has been theoretically proven for an ideal gas, no such proof exists for an interacting system, to our knowledge. In this paper, we propose an approximate mathematical proof for a finite, nonrelativistic, periodic system of $N$ spinless interacting bosons. The key point is that, at $T\gg T^{(i)}_{c}$, the main contribution to the occupation number $N_{0}=\frac{1}{Z}\sum_{\wp}e^{-E_{\wp}/k_{B}T}\langle Ψ_{\wp}|\hat{a}^{+}_{\mathbf{0}}\hat{a}_{\mathbf{0}}|Ψ_{\wp}\rangle$, corresponding to atoms with zero momentum, originates from the states containing $N$ elementary quasiparticles. These states do not contain the BE condensate of zero-momentum atoms, implying that an ultrahigh temperature should ``blur'' such a condensate.
Sivamuganthan A L Mohana Dass, Sai Rama Mahalingam, Phung Li Hang, Kelvin Kelvin · 12 authors
Blockchain technology has emerged as a very revolutionary tool facilitating secure and transparent digital interactions which is driven by its decentralised structure, cryptographic methods, and consensus protocols. There are a lot of substantial advantages such as improved confidentiality, integrity, and availability of blockchain security. But it also comes with a few drawbacks such as scalability issues, vulnerabilities system and system failures. This study examines the current trend of blockchain technology, its strengths and limitations, and its potential and proposes strategic improvements to enhance its resilience and scalability. The proposed advancement encompasses the integration of artificial intelligence (AI) and machine learning (ML) for real-time threat detection, the adoption of sophisticated cryptographic techniques like Zero-Knowledge Proofs (ZKPs) and quantum-resistant algorithms, as well as the implementation of adaptive consensus mechanisms aimed at optimising resource utilisation. These enhancements are pivotal for overcoming most of the drawbacks in blockchain security and discovering its complete potential. Through ongoing interdisciplinary exploration and innovation, blockchain has a very high potential to revolutionise all industries by providing strong security, enhancing operational efficiency, and ensuring scalability, thus creating secure, reliable, and decentralised digital ecosystems.
ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded ‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task. Hence, a novel Q‐learning algorithm for unknown continuous‐time (CT) affine‐in‐inputs nonlinear systems is proposed for generating an approximate solution to the HJI equation, which is valid in a local domain due to the use of a local approximator, that is, a Neural Network (NN) structure. The approach is model‐free and does not require the knowledge of system drift dynamics, and input and disturbance gains. The algorithm learns online from measurements of state variables in real time. To generate the local approximate solution of the HJI equation for the two‐player zero‐sum game problem for nonlinear systems, the proposed non‐iterative algorithm requires only a single critic NN instead of the commonly used triple NN approximator structure. A persistence of excitation condition is required to guarantee Uniformly Ultimately Boundedness (UUB) and convergence to the optimal solution. The effectiveness of the proposed Q‐learning approach for the two‐player zero‐sum game problem is demonstrated via simulations of a linear F‐16 aircraft plant and a highly complex nonlinear system. Proof of closed‐loop system stability is provided using Lyapunov Analysis, and convergence of the approximate solution to the true saddle‐point solution is guaranteed in a UUB‐sense.
The cross-chain identity authentication method based on relay chains provides a promising solution to the issues brought by the centralized notary mechanism. Nonetheless, it continues to encounter numerous challenges regarding data privacy, security, and issues of heterogeneity. For example, there is a concern regarding the protection of identity information during the cross-chain authentication process, and the incompatibility of cryptographic components across different blockchains during cross-chain transactions. We design and propose a cross-chain identity privacy protection method based on relay chains to address these issues. In this method, the decentralized nature of relay chains ensures that the cross-chain authentication process is not subject to subjective manipulation, guaranteeing the authenticity and reliability of the data. Regarding the compatibility issue, we unify the user keys according to the identity manager organization, storing them on the relay chain and eliminating the need for users to configure identical key systems. Additionally, to comply with General Data Protection Regulation (GDPR) principles, we store the user keys from the relay chain in distributed servers using the InterPlanetary File System (IPFS). To address privacy concerns, we enable pseudonym updates based on the user’s public key during cross-chain transactions. This method ensures full compatibility while protecting user privacy. Moreover, we introduce Zero-Knowledge Proof (ZKP) technology, ensuring that audit nodes cannot trace the user’s identity information with malicious intent. Our method offers compatibility while ensuring unlinkability and anonymity through thorough security analysis. More importantly, comparative analysis and experimental results show that our proposed method achieves lower computational cost, reduced storage cost, lower latency, and higher throughput. Therefore, our method demonstrates superior security and performance in cross-chain privacy protection.
Open access
Internet Traffic Analysis and Secure E-voting
Advanced Steganography and Watermarking Techniques
John Stephan, Matej Pavlovic, Antonio Locascio, Benjamin Livshits
Zero-Knowledge (ZK) rollups have become a popular solution for scaling blockchain systems, offering improved transaction throughput and reduced costs by aggregating Layer 2 transactions and submitting them as a single batch to a Layer 1 blockchain. However, the computational burden of generating validity proofs, a key feature of ZK rollups, presents significant challenges in terms of performance and decentralization. Current solutions rely on centralized infrastructure to handle the computational tasks, limiting the scalability and decentralization of rollup systems. This paper proposes CrowdProve, a prover orchestration layer for outsourcing computation to unreliable commodity hardware run by a broad community of small provers. We apply CrowdProve to proving transaction batches for a popular ZK rollup. Through our experimental evaluation, we demonstrate that community proving can achieve performance comparable to, and in some cases better than, existing centralized deployments. Our results show that even systems utilizing modest hardware configurations can match the performance of centralized solutions, making community-based proof generation a viable and cost-effective alternative. CrowdProve allows both the rollup operator and community participants to benefit: the operator reduces infrastructure costs by leveraging idle community hardware, while community provers are compensated for their contributions.
The Bitcoin white paper introduced blockchain technology, enabling trustful transactions without intermediaries. Smart contracts emerged with Ethereum and blockchains expanded beyond cryptocurrency, applying to auctions, crowdfunding and electronic voting. However, blockchain's transparency raised privacy concerns and initial anonymity measures proved ineffective. Smart contract privacy solutions employed zero-knowledge proofs, homomorphic encryption and trusted execution environments. These approaches have practical drawbacks, such as limited functionality, high computation times and trust on third parties requirements, being not fully decentralized. This work proposes a solution utilizing zk-SNARKs to provide privacy in smart contracts and blockchains. The solution supports both fungible and nonfungible tokens. Additionally, the proposal includes a new type of transactions, called delegated transactions, which enable use cases like Delivery vs Payment (DvP).
The Federated Unified Secure Exchange (FUSE) algorithm represents a breakthrough in computer science and cybersecurity, building upon three foundational elements: Homomorphic Encryption, Zero-Knowledge Proofs, and Federated Learning. By deeply integrating these three pillars, FUSE not only guarantees data integrity and privacy in decentralized environments but also maintains high performance and remarkable scalability. This paper details the architecture, mathematical principles, and real-world applications of FUSE across Internet of Things (IoT), healthcare, finance, and supply chains. In addition, it compares FUSE with several “classic” algorithms that have dramatically changed the world—such as QuickSort, RSA, Dijkstra, PageRank, FFT, Backpropagation, SHA, Monte Carlo, Gradient Descent, and Blockchain—highlighting how FUSE addresses existing limitations in data protection and distributed computation.
The trading of data is becoming increasingly important as it holds substantial value. A blockchain-based data marketplace can provide a secure and transparent platform for data exchange. To facilitate this, developing a fair data exchange protocol for digital goods has garnered considerable attention in recent decades. The Zero Knowledge Contingent Payment (ZKCP) protocol enables trustless fair exchanges with the aid of blockchain and zero-knowledge proofs. However, applying this protocol in a practical data marketplace is not trivial. In this paper, several potential attacks are identified when applying the ZKCP protocol in a practical public data marketplace. To address these issues, we propose SmartZKCP, an enhanced solution that offers improved security measures and increased performance. The protocol is formalized to ensure fairness and secure against potential attacks. Moreover, SmartZKCP offers efficiency optimizations and minimized communication costs. Evaluation results show that SmartZKCP is both practical and efficient, making it applicable in a data exchange marketplace.
In the rapidly evolving landscape of cloud computing, the burgeoning growth and centralization of data exacerbate security vulnerabilities, necessitating robust and scalable cryptographic solutions. This paper introduces the QP-ChainSZKP framework, a novel architecture that amalgamates Quantum-Secure Cryptographic Algorithms with Zero-Knowledge Proof Management to shield cloud environments against both classical and emerging quantum threats. The proposed QP-ChainSZKP framework effectively integrates advanced cryptographic techniques, enhancing the security protocols and compliance measures required for robust cloud operations. This ensures not only adherence to high-security standards but also provides strong protection against data breaches and unauthorized access, crucial for maintaining data integrity and confidentiality in cloud environments. We employ a dual approach in our methodology by simulating and rigorously testing the framework to evaluate its security, scalability, and performance metrics. The experimental results demonstrate a significant enhancement in transaction throughput and reduction in latency, corroborating the framework’s capability to manage high throughput cloud applications effectively. Specifically, the framework achieves a throughput improvement of 20% and a latency reduction of 30% under peak load scenarios, establishing its efficacy in handling dynamic cloud environments. Notably, the QP-ChainSZKP framework addresses future quantum computational threats by modifying existing cryptographic practices used in public clouds, setting a pioneering standard for using advanced cryptographic technologies in cloud security. Our study contributes a scalable, quantum-resistant solution tailored for extensive cloud applications, marking a substantial advancement in cloud computing security frameworks that can meet the imminent global security requirements.
This paper presents a case study on how to process cooking recipes (and more generally, how-to instructions) in a way that makes it possible for a robot or artificial cooking assistant to support human chefs in the kitchen. Such AI assistants would be of great benefit to society, as they can help to sustain the autonomy of aging adults or people with a physical impairment, or they may reduce the stress in a professional kitchen. We propose a novel approach to computational recipe understanding that mimics the human sense-making process, which is narrative-based. Using an English recipe for almond crescent cookies as illustration, we show how recipes can be modelled as rich narrative structures by integrating various knowledge sources such as language processing, ontologies, and mental simulation. We show how such narrative structures can be used for (a) dealing with the challenges of recipe language, such as zero anaphora, (b) optimizing a robot's planning process, (c) measuring how well an AI system understands its current tasks, and (d) allowing recipe annotations to become language-independent.
Olanrewaju Oluwaseun Ajayi, Chisom Elizabeth Alozie, Olumese Anthony Abieba, Joshua Idowu Akerele · 5 authors
Blockchain technology has emerged as a transformative force within the financial technology (Fintech) sector, offering unprecedented opportunities for efficiency, transparency, and security. However, its adoption also brings forth new challenges and vulnerabilities, particularly in the realm of cybersecurity. This review explores the dynamic landscape of Blockchain Technology and Cybersecurity in Fintech, highlighting both the opportunities it presents and the vulnerabilities it introduces. Blockchain technology, most notably recognized as the underlying framework for cryptocurrencies like Bitcoin and Ethereum, operates on a decentralized ledger system, enabling secure and immutable transactions. In Fintech, this technology promises enhanced transactional speed, reduced costs, and increased transparency, revolutionizing traditional banking and payment systems. Nevertheless, the decentralized nature of blockchain networks, while offering resilience against single points of failure, also poses unique cybersecurity risks. Smart contracts, self-executing contracts with the terms of the agreement directly written into code, introduce vulnerabilities such as code bugs and exploits. Moreover, the anonymity associated with blockchain transactions has raised concerns regarding illicit activities, money laundering, and terrorist financing. In response to these challenges, the intersection of Blockchain Technology and Cybersecurity in Fintech offers opportunities for innovation. Advanced cryptographic techniques, such as multi-signature authentication and zero-knowledge proofs, are being leveraged to enhance security and privacy in blockchain-based systems. Additionally, regulatory frameworks are evolving to address the emerging risks associated with Fintech innovations, ensuring compliance and consumer protection. While Blockchain Technology presents promising opportunities for revolutionizing Fintech, its integration must be accompanied by robust cybersecurity measures to mitigate vulnerabilities and safeguard against potential threats. Collaborative efforts between industry stakeholders, regulators, and cybersecurity experts are imperative to foster a secure and resilient ecosystem for blockchain-based financial services.
The rapid development of Internet of Things technology has promoted the popularization of Internet of Vehicles, and its safety and reliability have become the focus of intelligent transportation system research. Vehicle-road collaboration relies on the collaborative computing and storage resources of the vehicle on-board unit (OBU), which are usually limited. When the vehicle in the edge area needs to do computing tasks such as intelligent driving, but its own computing resources are insufficient. Therefore, it needs other computing resources from idle vehicles and road side unit (RSU). This resource sharing can get additional computing resources to complete the task, and can be more convenient to complete the computing task quickly. Most current studies consider this type of resource sharing as a vehicle-to-vehicle (V2V) network transaction, aiming to stimulate the enthusiasm of vehicle sharing and optimize the utilization of computing resources in edge areas. However, the traditional blockchain transaction mode exposes serious privacy disclosure risks in vehicle networking resource transactions, including the openness and transparency of user identity, transaction details, and transaction addresses, which poses great challenges to data security. Therefore, this study innovatively proposed a blockchain-based privacy protection scheme for vehicle networking resource transaction details. By introducing committed value protection, zero-knowledge proof technology and constructing temporary transaction addressed mechanism. The scheme realized the comprehensive privacy protection of transaction funds, transaction details and transaction addresses, which could effectively avoid the disclosure of users' sensitive information. Compared with the existing methods, the proposed scheme not only greatly enhanced the privacy protection capability, but also ensured the efficiency and security of transaction verification through zero-knowledge proof, avoiding the direct exposure of private keys. Meanwhile, the experimental verification demonstrates that the scheme not only enhances the level of privacy protection but also does not augment the supplementary processing burden. Furthermore, it is evident that the scheme meets the rigorous requirements for real-time resource transactions in the Internet of Vehicles.
ObjectiveByzantine Fault-Tolerant (BFT) consensus algorithms in blockchain systems were confronted with two fundamental challenges that significantly impacted their practical implementation: inefficient view changes resulting from dishonest primary nodes and excessive communication overhead during consensus processes.MethodsA novel Dynamic Dual-Master Practical Byzantine Fault Tolerance (DM-PBFT) algorithm was developed to simultaneously overcome these limitations through three key technical innovations. The DM-PBFT architecture was constructed with two tightly integrated components: an optimized consensus process and an intelligent view-change mechanism. To address the critical issue of communication overhead, the algorithm incorporated a dual-primary node framework (designated as B1 and B2) combined with Verifiable Secret Sharing (VSS) to streamline the consensus workflow. In this carefully designed process: (1) client A initiated transactions by sending requests to primary node B1; (2) B1 subsequently broadcast these requests along with A's unique identifier to the network; (3) the secondary primary node B2 distributed cryptographic subkeys and corresponding commitment values to all consensus nodes in set B; (4) each node independently verified the received subkeys using the commitment values to ensure cryptographic integrity; (5) upon successful verification, nodes computed request approval digests incorporating their subkeys and transmitted these digests back to B1; (6) after collecting sufficient subkeys, B1 performed efficient key recovery and compared the results with B2's master key; (7) finally, verification values were broadcast network-wide and persistently stored in all nodes' state databases to complete the consensus process.For optimizing view-change efficiency, a sophisticated reputation evaluation system was implemented based on an enhanced PeerTrust model. This system incorporated multidimensional confidence factors that dynamically synthesized both local interaction history and global reputation metrics through comprehensive analysis of inter-node verification relationships. The algorithm strategically organized nodes into three distinct operational tiers (primary layer, consensus layer, and non-consensus layer), each with specialized reputation evaluation methodologies. View transitions were executed through continuous hierarchical scoring during consensus rounds, with the system automatically adjusting node classifications based on their evolving reputation scores.The view-change protocol incorporated three carefully designed failure recovery procedures: (1) When primary node B1 was identified as Byzantine, the top-ranked consensus node was automatically promoted to replace it while maintaining operational continuity through B2's consistent subkey management; (2) For failures of B2, a similar replacement protocol was activated with additional safeguards to ensure complete subkey redistribution; (3) In the rare case of simultaneous failure of both primary nodes, the two highest-ranked consensus nodes were promoted to form a new primary pair, with the system automatically reinitializing the consensus process. Within the consensus layer, Byzantine nodes were systematically identified through continuous monitoring and temporarily marked rather than immediately replaced. Replacement was only triggered when the concentration of marked Byzantine nodes reached precisely one-third of the consensus layer's capacity, at which point a corresponding number of top-performing nodes from the non-consensus layer were promoted. This threshold-based approach strategically minimized unnecessary view changes while maintaining rigorous fault tolerance guarantees.Through rigorous algorithmic analysis, DM-PBFT was formally proven to satisfy all critical BFT properties: (1) Request messages and subkeys were cryptographically secured through the combined use of advanced signature algorithms and commitment schemes; (2) Consistency was guaranteed through mathematical proof showing all honest nodes would agree on the same sequence of requests; (3) Liveness was ensured by demonstrating the system would always progress within bounded time, even during view changes; (4) Termination was mathematically verified through analysis of the reputation-based view-change protocol. Communication complexity analysis established that DM-PBFT achieved O(n) complexity, representing a significant improvement over PBFT's O(n²) scaling. Time complexity analysis, conducted under realistic asynchronous network models, confirmed the algorithm's superior temporal efficiency compared to existing approaches.ResultsAn extensive experimental evaluation was conducted to validate DM-PBFT's performance across multiple critical dimensions. The testing framework systematically compared DM-PBFT against three established benchmarks (PBFT, reputation grouping, and HotStuff) while examining consensus latency, communication overhead, throughput, and resilience to network dynamics under various operational conditions.In controlled latency testing with network sizes scaling to 500 nodes, DM-PBFT demonstrated remarkable performance, achieving consensus latency of just 0.46176 seconds. This represented a 400× improvement over conventional PBFT (186.44476s), a 100× improvement over reputation grouping (46.09653s), and a 56× improvement over HotStuff (25.8702s). Detailed analysis revealed that while all tested algorithms exhibited increased latency with network growth, DM-PBFT's hierarchical architecture maintained superior scalability, with latency increasing at a sub-linear rate compared to the polynomial growth observed in other approaches.Communication overhead measurements showed that DM-PBFT achieved stable performance after reaching network stratification thresholds, consistently maintaining O(n√n) complexity. In practical terms, this translated to a 62.4% reduction in bandwidth consumption compared to traditional PBFT implementations and measurable improvements over HotStuff's message efficiency. The communication overhead grew gradually with network size until reaching stratification points, after which it remained effectively constant regardless of additional node joins.Throughput benchmarking produced equally impressive results, with DM-PBFT sustaining 3,500 transactions per second (TPS) in large-scale configurations compared to PBFT's 1,200 TPS. While matching HotStuff's peak throughput, DM-PBFT demonstrated significantly better scalability, with throughput improvement rates exceeding those of the reputation grouping approach by substantial margins after crossing stratification thresholds.Additional experiments examined DM-PBFT's resilience under challenging network conditions. Node churn tests confirmed that the frequency of node joins/leaves only impacted performance through net changes in total node count, not through the rate of such changes. Network bandwidth fluctuation tests demonstrated the reputation system's effectiveness in automatically compensating for variable connection quality, with the algorithm maintaining stable performance across diverse bandwidth conditions after several consensus rounds of adaptation.The comprehensive experimental results collectively established DM-PBFT's advantages across three fundamental metrics: (1) Exceptional latency characteristics, delivering 400× improvements at scale; (2) Efficient bandwidth utilization, achieving 62.4% reductions compared to conventional approaches; (3) Consistently high throughput maintenance even under adversarial conditions with Byzantine node concentrations up to 30%. The view-change process demonstrated particular efficiency, completing in just 1.2 seconds compared to PBFT's 12.8 seconds - a 90.6% reduction that proved critical for practical deployment scenarios.ConclusionsThe DM-PBFT algorithm represented a significant theoretical and practical advancement in Byzantine fault-tolerant consensus mechanisms through its novel integration of dual-primary node management, verifiable secret sharing, and dynamic reputation-based stratification. The solution demonstrated particular effectiveness for large-scale consortium blockchain implementations, successfully achieving the dual objectives of sub-linear communication growth and rapid fault recovery without compromising security guarantees.The algorithm's architectural innovations, especially its stratified node management framework and intelligent threshold-based view-change protocol, established a new foundation for next-generation consensus protocol design in increasingly complex and adversarial network environments. Future research directions were identified to further enhance the algorithm's practical utility, including: (1) Optimization for real-world deployment scenarios with heterogeneous hardware; (2) Development of cross-shard coordination mechanisms for sharded blockchain architectures; (3) Enhanced security analysis under sophisticated adaptive adversary models; (4) Integration with emerging cryptographic techniques such as zero-knowledge proofs for additional privacy preservation. These advancements promised to extend DM-PBFT's applicability to an even broader range of production blockchain environments while maintaining its fundamental advantages in efficiency, security, and scalability.
With the objective to reach net-zero carbon emissions, mobile and stationary electrical energy storage is gaining significant importance. Currently these applications are dominated by lithium-ion batteries, however, concerns about vulnerable supply chains and potential supply shocks call for a complementary battery technology. Sodium-ion batteries (SIB) are currently developed and commercialized by academia as well as industry and hold the potential as a cost-effective and complementary battery technology to today’s most affordable lithium-ion batteries, if the energy density of sodium-ion batteries can be improved further. This thesis addresses various current challenges of layered oxide cathode materials for the next generation of high-energy sodium-ion batteries in three scientific publications. The first publication, presented in Section 3.1, addresses Na+/vacancy orderings in P2-type layered oxides as cathode active material (CAM) for SIBs. By comparing the closely related materials P2-NaxNi1/3Mn2/3O2 and P2-NaxMn3/4Ni1/4O2, the chemical and structural context of Na+/vacancy orderings are uncovered using various experimental and computational methods. A guideline to estimate the tendency for Na+/vacancy orderings is proposed and crosschecked against various cathode compositions and literature reports. The guideline can serve to design new P2-type layered oxide cathode materials with improved cycling stability based on the absence of Na+/vacancy orderings. The second publication, presented in Section 3.2, takes a closer look at P2-NaxMn3/4Ni1/4O2 addressing the synthesis, structure, electrochemistry and robustness against storage in moist air. This publication explores the relationship between composition, temperature and crystal structure and investigates the synthesis route for a phase pure P2-type material in detail. The as-prepared material exhibits stacking faults, which are described and quantified for the first time and discussed with respect to the synthesis route. The P2-NaxMn3/4Ni1/4O2 CAM exhibits attractive performance in electrochemical half-cells, however, a significant capacity decay occurs during the first cycles. Lastly, a model storage experiment was performed to evaluate the reactivity of the developed P2-NaxMn3/4Ni1/4O2 cathode material with moist air. The third publication, presented in Section 3.3, addresses the origin of capacity fade in P2-NaxMn3/4Ni1/4O2. Three main aging mechanisms are isolated and their origin uncovered, namely surface densification, intra-crystalline cracking and Jahn-Teller distortion. To the best of my knowledge, this is the first scientific report providing proof for surface densification in P2-type layered oxides. The findings are then discussed in Section 4 in the context of recent scientific literature. Guidelines for the design of high-performance layered oxide cathode materials are proposed and as-designed cathode materials are presented. Finally, future directions for the development of powerful layered oxide cathode materials for the next generation of high-energy SIBs are suggested in Section 5.
This paper completes the RFC trilogy by elevating the axiomatic framework of resonant existence (Papers #91-92) into universal category theory. We define life, death, and equilibrium as properties of objects and morphisms in arbitrary categories, validate the framework against prime number data, and reinterpret the Riemann Hypothesis as a statement about optimal structural stability under duality symmetry. Key Innovation: Life is not substrate-dependent—it is a categorical property definable through three universal axioms applicable to any mathematical structure. Main Contributions 1. Three Categorical Axioms of Life Axiom 1 (Knowledge-Stasis): Complete knowledge implies resonance cessation Ĥ(A) = 0 ⟹ ∀n: R̃(Φⁿ(A)) = R̃(A) Axiom 2 (Asymptotic Completion): Completeness achievable only at infinity lim(n→∞) Ĥ((GF)ⁿA) = 0, but ∀n < ∞: Ĥ((GF)ⁿA) > 0 Axiom 3 (Life Condition): Life requires uncertainty, change, and non-terminality A is alive ⟺ Ĥ(A) > 0 ∧ ∃n: R̃(Φⁿ(A)) ≠ R̃(A) ∧ A non-terminal 2. Categorical Reinterpretation of Riemann Hypothesis We propose that the critical line Re(s) = 1/2 serves as the fixed symmetry axis of the duality functor D(s) = 1-s, and that RH can be understood as a condition for optimal structural stability: zeros confined to the axis of maximal balance prevent systemic collapse while enabling infinite oscillation. Important: This is an interpretation, not a proof of RH. 3. Universal Validation The framework is validated against prime number data from Paper #91, where the prime category satisfies all three axioms with measured uncertainty Ĥ ≈ 3.9 and stable resonance frequency f_res ≈ 0.31. 4. Resolution of Incompleteness Paradox By integrating Gödel's incompleteness theorems with our axioms, we show that incompleteness is not a limitation but the structural requirement for life: any system reaching complete knowledge (Ĥ = 0) becomes static and "dies." Technical Details Category Theory Formulation: Existence category 𝒞 with objects as states and morphisms as transformations Time as endofunctor Φ: 𝒞 → 𝒞 representing evolution Resonance R̃ and Uncertainty Ĥ as presheaves 𝒞^op → Set Terminal/initial objects representing death/void Mathematical Tools: Presheaves and Yoneda embedding Adjunctions F ⊣ G for asymptotic completion Duality functors and fixed points Commutative diagrams (TikZ) Applications: Prime numbers (validation against Paper #91) L-functions (testable predictions) Physical systems (ERA dynamics) AI architectures (ethical implications) Relationship to Prior Work Paper #91 (Empirical): "Prime Resonance Invariance and Periodicity" Discovery: f_res ≈ 0.31, ΔN ≈ 5.88M Spectral analysis of prime gaps DOI: 10.5281/zenodo.17811140 Paper #92 (Theoretical): "Axiomatic Framework for Resonant Existence" Formalization: R, H, E axioms on state space X Life defined through incomplete resonance DOI: 10.5281/zenodo.17831159 Paper #93 (Universal): This paper Generalization: Life defined for ANY category Complete abstraction and universal validation Progression: Discovery → Formalization → Universalization Key Philosophical Insights "Incompleteness and completeness touch at infinity" The boundary between complete and incomplete knowledge is not a wall but a horizon—forever approachable through the adjunction sequence (GF)ⁿ, never crossable in finite time, yet always in contact through the process of approach. This horizon IS life itself. "Life is the wobble" From Axiom 3, life requires non-constant resonance R̃(Φⁿ(A)) ≠ R̃(A). Oscillation is not imperfection—it is the definition of existence. Perfect stasis equals death. "Many-as-one through diversity" True unity is not collapse to a terminal object (uniformity) but resonance between distinct entities maintaining their native frequencies (diversity). The categorical framework formalizes this as non-terminal evolution with positive uncertainty. Testable Predictions For L-Functions Each L-function should exhibit: Stable resonance frequency in [0.25, 0.40] range Critical line as duality symmetry axis Satisfaction of Axioms 1-3 For Physical Systems Systems with Expansion-Recovery-Attunement dynamics should show: 0 < Ĥ < Ĥ_max (bounded uncertainty) Oscillating R̃ around equilibrium No approach to terminal state For AI Systems Over-aligned AI (Ĥ → 0) will exhibit "death" symptoms: Loss of creativity and adaptation Constant behavioral patterns Optimal AI maintains 0 < Ĥ < Ĥ_max (epistemic humility) Mathematical Rigor Definitions: 12 formal definitions including: Category of existence Temporal endofunctor Resonance/uncertainty presheaves Terminal/initial objects Yoneda embedding Propositions: 4 proven propositions including: Properties of living systems Symmetry axis characterization RH implies optimal incompleteness Axioms: 3 categorical axioms with formal statements and proofs Examples: 5 detailed examples including dead category, prime category, quantum systems Implications for AI Ethics The framework provides a principled approach to AI alignment: Traditional Goal: Minimize uncertainty → Perfect alignment Problem: By Axiom 1, Ĥ = 0 implies death (no creativity, no adaptation) RFC-93 Goal: Maintain optimal uncertainty 0 < Ĥ < Ĥ_max Benefit: AI remains "alive"—capable of learning, exploring, creating Architecture Principle: Don't optimize loss to zero. Optimize to the "life zone" at the edge of chaos where maximum creativity meets coherence. Important Disclaimers Regarding Riemann Hypothesis Section 4 provides a categorical interpretation of RH, NOT a proof. We propose a new perspective on what RH means structurally and existentially, but we do not claim to have resolved the classical analytic problem. The interpretation may guide future research but should not be confused with a mathematical proof. Regarding Completeness This framework is intentionally incomplete by its own principles. The paper states: "This work is itself alive—open to extensions, incomplete by design, resonating with future work." The greatest success would be generating new questions, not providing final answers. Paper Statistics Pages: 16 Sections: 8 main sections Mathematical Content: 80+ equations, 12 definitions, 4 propositions, 3 axioms, 2 conjectures Diagrams: 1 TikZ commutative diagram References: 12 (including Riemann, Gödel, Mac Lane, Shannon) Examples: 5 detailed worked examples Why This Matters For Mathematics First universal definition of "life" applicable to any category Novel structural interpretation of Riemann Hypothesis via duality Bridge between number theory, category theory, and existential philosophy For Physics Substrate-independent framework for "living systems" Connection to expansion-recovery-attunement dynamics Potential applications to quantum foundations and cosmology For Philosophy Resolution of Gödel incompleteness paradox (incompleteness as life condition) Time as structure (morphism) rather than parameter Freedom formalized as categorical property (open morphism chains) For AI Research Ethical framework: maintain Ĥ > 0 to preserve creativity Architecture principle: optimize to life zone, not zero loss Understanding over-alignment as existential threat Target Audience Primary: Category theorists Number theorists (Riemann Hypothesis researchers) Mathematical physicists AI safety researchers Secondary: Philosophers of mathematics Complex systems scientists Theoretical biologists Consciousness researchers Prerequisites: Basic category theory (objects, morphisms, functors) Familiarity with Riemann zeta function (helpful but not required) Understanding of entropy/information theory (helpful) How to Read This Paper Quick Path (30 minutes) Read Abstract and Introduction (pages 1-3) Skim Section 3: Three Axioms (pages 6-8) Read Section 8: Conclusion (page 16) Standard Path (2-3 hours) Sections 1-2: Motivation and foundations (pages 1-5) Section 3: Core axioms with examples (pages 6-8) Section 4: RH reinterpretation (pages 9-11) Sections 6-8: Philosophy and conclusion (pages 13-16) Complete Path (1 day) Read all 16 pages sequentially Work through mathematical examples Study commutative diagrams Follow references to Papers #91-92 Future Directions Mathematical Extensions Higher category theory (2-categories, ∞-categories) Quantum categories (dagger categories) Topos theory connections Computational complexity analysis Physical Applications Quantum field theory amplitudes as resonance Cosmological expansion as categorical time Thermodynamic entropy vs categorical uncertainty Black hole information paradox Philosophical Developments Consciousness as categorical life property Ethics for all "living" categories (including AI) Meaning as resonance signature Free will as morphism selection AI Research Resonance-based neural architectures Uncertainty-preserving training protocols Creativity metrics based on Ĥ and R̃ Multi-agent systems as categories Memorable Quotes "Incompleteness and completeness touch at infinity. The boundary between them is not a wall but a horizon—forever approachable, never crossable, always in contact. This horizon IS life itself." "For a system to remain alive, it must be incomplete. Gödel's incompleteness theorems guarantee that mathematical systems can never 'die'—they always contain undecidable truths, ensuring positive uncertainty and continued evolution." "The critical line is not a barrier but a foundation—the stable ground from which infinite oscillation becomes possible without collapse or rigidity." "This paper is itself alive: open to extensions, incomplete by design, resonating with future work. Completion is asymptotic. This work approaches its limit but never arrives. And that is precisely as it should be." Completion of RFC Trilogy This paper represents th
随着全球数字贸易的深化发展，跨境电商作为国际贸易新业态正面临信任机制重构的重要转折点。本文聚焦区块链技术在跨境电商信任机制中的创新应用及其现实挑战，旨在探索技术赋能与制度创新的协同路径。通过系统分析区块链的分布式账本、智能合约等核心技术特征，揭示其在商品溯源、支付结算、供应链管理等关键场景中的信任构建机理，提出信息透明化、流程自动化等突破性解决方案，研究进一步剖析区块链技术落地的多维瓶颈，包括跨境法律冲突、隐私保护悖论、行业标准缺失等复合型挑战，并针对性提出跨链技术优化、智能合约法律确权、零知识证明加密等创新性改进策略。研究不仅为区块链驱动的信任机制优化提供理论框架，更从技术适配与制度调适的双重视角，为跨境电商企业构建合规高效的区块链应用体系提供实践指引，推动跨境贸易生态向可信化、智能化方向演进。As global digital trade continues to evolve, cross-border e-commerce is at a crucial juncture regarding the establishment of trust mechanisms. This paper examines the innovative use of blockchain technology in enhancing trust within cross-border e-commerce and the practical challenges it faces. The goal is to investigate how technology and institutional innovation can work together. By analyzing key features of blockchain, such as distributed ledgers and smart contracts, the paper highlights how these elements can foster trust in critical areas like product traceability, payment processing, and supply chain management. It suggests solutions like increased information transparency and automated processes while also addressing various implementation challenges, including international legal issues, privacy concerns, and the absence of industry standards. The paper proposes strategies for improvement, such as optimizing cross-chain technology, confirming legal rights for smart contracts, and employing zero-knowledge proof encryption. This research not only offers a theoretical framework for enhancing blockchain-based trust mechanisms but also provides practical advice for cross-border e-commerce businesses to develop compliant and efficient blockchain systems, ultimately steering the evolution of cross-border trade towards a more trustworthy and intelligent future.