Smart contracts enable programmatic agreements but face two persistent problems: high on-chain cost (throughput/latency) and weak privacy (public ledger exposes transaction semantics). We propose a hybrid on-chain/off-chain commitment scheme (HOC-C) that combines lightweight on-chain commitments, verifiable off-chain computation, and succinct zero-knowledge proofs to deliver privacy-preserving contract execution at scale. In HOC-C, sensitive inputs and heavy computations are executed off-chain by a consortium of replicated verifiers; the verifiers publish a succinct zk-SNARK proof of correct execution plus a small state commitment on-chain. The on-chain contract verifies the proof and updates state atomically. To prevent malicious collusion among verifiers, HOC-C integrates an economic incentive layer and challenge windows where anyone can publish refutation proofs; the refutation burden is designed to be less than the honest-verifier cost. We implement HOC-C using a prototype that plugs into an EVM-compatible chain (Ethereum testnet) and evaluate performance for representative workloads (private auctions, confidential supply-chain workflows, private token-transfer batching). The system reduces gas cost by an order of magnitude compared to naive on-chain execution while preserving end-to-end confidentiality for user inputs. We analyze security properties (soundness, liveness, and economic incentive compatibility) and discuss trade-offs: proof generation latency vs. throughput, verifier decentralization vs. amortized cost. HOC-C offers a practical roadmap for adopting private, inexpensive smart contracts on mainstream blockchains.
To address the issues of privacy-utility imbalance, insufficient incentives, and lack of verifiable computation in current medical data sharing, this paper proposes a blockchain-based fair verification and adaptive differential privacy mechanism. The mechanism adopts an integrated design that systematically tackles three core challenges: privacy protection, fair incentives, and verifiability. Instead of using a traditional fixed privacy budget allocation, it introduces a reputation-aware adaptive strategy that dynamically adjusts the privacy budget based on the contributors’ historical behavior and data quality, thereby improving aggregation performance under the same privacy constraints. Meanwhile, a fair incentive verification layer is established via smart contracts to quantify and confirm data contributions on-chain, automatically executing reciprocal rewards and mitigating the trust and motivation deficiencies in collaboration. To ensure enforceable privacy guarantees, the mechanism integrates lightweight zero-knowledge proof (zk-SNARK) technology to publicly verify off-chain differential privacy computations, proving correctness without revealing private data and achieving auditable privacy protection. Experimental results on multiple real-world medical datasets demonstrate that the proposed mechanism significantly improves analytical accuracy and fairness in budget allocation compared with baseline approaches, while maintaining controllable system overhead. The innovation lies in the organic integration of adaptive differential privacy, blockchain, fair incentives, and zero-knowledge proofs, establishing a trustworthy, efficient, and fair framework for medical data sharing.
Recent advances in artificial intelligence (AI), particularly deep learning, have led to widespread adoption across various applications. Yet, a fundamental challenge persists: how can we verify the correctness of AI model inference when model owners cannot (or will not) reveal their parameters? These parameters represent enormous training costs and valuable intellectual property, making transparent verification difficult. In this paper, we introduce a zero-knowledge framework capable of verifying deep learning inference without exposing model internal parameters. Built on recursively composed zero-knowledge proofs and requiring no trusted setup, our framework supports both linear and nonlinear neural network layers, including matrix multiplication, normalization, softmax, and SiLU. Leveraging the Fiat-Shamir heuristic, we obtain a succinct non-interactive argument of knowledge (zkSNARK) with constant-size proofs. To demonstrate the practicality of our approach, we translate the DeepSeek model into a fully SNARK-verifiable version named ZK-DeepSeek and show experimentally that our framework delivers both efficiency and flexibility in real-world AI verification workloads.
Federated Learning (FL) has become a promising method for training machine learning models while protecting patient privacy. This systematic review examines the use of privacy-preserving techniques in FL within decentralized healthcare systems. It compares existing methods such as Differential Privacy (DP), Trusted Execution Environment (TEE), Zero Knowledge Proofs (ZKP), Homomorphic Encryption (HE), Watermarking, Blockchain, and Secure Multi-Party Computation (SMPC) based on regulatory compliance, scalability, computational cost, complexity, and mathematical foundations. The principle challenges in decentralized healthcare like heterogeneous data, privacy risks, security threats, and compliance issues have been discussed. The review also highlights the importance of adhering to global regulations like HIPAA, GDPR, and country-specific data protection laws. Furthermore, it discusses open challenges and suggests future research directions to overcome current limitations, including computational efficiency, adversarial attacks, and the creation of policy frameworks for standardization. Overall, this review provides a unique perspective on ethical, secure, and scalable privacy-preserving FL models for the next generation of healthcare applications. • Analyzes essential techniques: Differential Privacy, SMPC, HE, TEE, ZKP, and Blockchain. • Reviews key privacy techniques: DP, SMPC, HE, TEE, ZKP, and Blockchain. • Compares methods based on cost, scalability, and resilience in FL. • Identifies issues such as non-IID data, high communication, and compliance. • Suggests hybrid and hardware-aided frameworks for secure FL. • presents future needs in terms of explainability, interoperability, and quantum security.
A system design built on blockchain technology presents a fundamental challenge: the inherent transparency of the blockchain conflicts with the growing need for user privacy. This dissertation explores how Zero-Knowledge Proofs (ZKPs) can be strategically combined with blockchain to strike a balance between these competing demands. The dissertation analyzes the challenges of privacy and transparency and provides an overview of solutions across the privacy-transparency solution space, drawing from the author’s original research and the broader academic landscape. On the privacy-centric side, it proposes a privacy-preserving design that utilizes off-chain ZKPs. In contrast, on the transparency-centric side, it presents a transparency-enhancing design that leverages on-chain data to build trust. In the middle, it discusses a taxonomy of hybrid applications whose unique combination of on-chain privacy (via ZKPs) and blockchain transparency reveals both a disruptive potential and significant regulatory challenges.
One-Time Passwords (OTPs) are a core component of multi-factor authentication in banking, e-commerce, and digital platforms. However, conventional delivery channels such as SMS and email are increasingly vulnerable to SIM-swap fraud, phishing, spoofing, and session hijacking. This study proposes an end-to-end mobile authentication architecture that integrates a permissioned Hyperledger Fabric blockchain for tamper-evident identity management, an AI-driven risk engine for behavioral and SIM-swap anomaly detection, Zero-Knowledge Proofs (ZKPs) for privacy-preserving verification, and geolocation-bound OTP validation for contextual assurance. Hyperledger Fabric is selected for its permissioned governance, configurable endorsement policies, and deterministic chaincode execution, which together support regulatory compliance and high throughput without the overhead of cryptocurrency. The system is implemented as a set of modular microservices that combine encrypted off-chain storage with on-chain hash references and smart-contract–enforced policies for geofencing and privacy protection. Experimental results show sub-0.5 s total verification latency (including ZKP overhead), approximately 850 transactions per second throughput under an OR-endorsement policy, and an F1-score of 0.88 for SIM-swap detection. Collectively, these findings demonstrate a scalable, privacy-centric, and interoperable solution that strengthens OTP-based authentication while preserving user confidentiality, operational transparency, and regulatory compliance across mobile network operators.
ABSTRACT Contemporary physics faces a crisis of causality, evidenced by unexplained anomalies such as the Muon g-2 magnetic moment, the violation of lepton universality, and the cosmic alignment known as the "Axis of Evil." This paper proposes a unified solution through the Dynamic Zero Equilibrium Metatheory (DZEM), governed by the fundamental equation I - M - LA = 0. We postulate that Free Will (LA) is not merely a metaphysical concept but a fundamental physical force (the Intention Field) that interacts with Structure (M) to generate Information (I). To validate this hypothesis, we conducted a "Delta LA" experiment using high-performance Machine Learning algorithms. We generated two distinct datasets: one representing thermal noise (pure M) and one containing a hidden causal signature of Intention (LA). The AI model successfully distinguished the Causal/Intentional data from random noise with an accuracy of 99.75%. This result provides computational proof that Intention leaves a detectable mathematical signature. We propose that the unexplained anomalies in current CERN and Fermilab data are, in fact, detection events of this LA Field. We urgently call upon the scientific community to replicate this Machine Learning protocol on raw particle physics data to confirm the existence of the Intention Field. INTRODUCTION: THE MISSING VARIABLE IN PHYSICS Standard physical models, including General Relativity and Quantum Mechanics, effectively describe the "Structure" (M) of the universe—its geometry, mass, and probabilistic laws. However, they fail to explain the "Cause." Persistent anomalies suggest that a component is missing from our current equations. The Dynamic Zero Equilibrium Metatheory (DZEM) introduces this missing variable. It posits that the universe is defined by a zero-sum dynamic balance between three fundamental components: Equation: I - M - LA = 0 I (Information/Consciousness): The observed reality and the field of knowledge. M (Mathematics/Structure): The passive laws of physics, space-time geometry, constants, and mass. LA (Free Will/Intention): The active, causal force. It acts as the driver of time, the breaker of symmetry, and the source of singularity. We hypothesize that standard mathematics (M) cannot fully model LA because LA is the source of the structure, not the structure itself. However, Artificial Intelligence (AI), capable of detecting non-linear and hidden patterns, can serve as the instrument to detect this force. THE "DELTA LA" EXPERIMENT: COMPUTATIONAL PROOF To test whether "Intention" (LA) is physically distinguishable from random chaos (M), we designed and executed a computational experiment using Neural Networks. 2.1 Methodology Group M (Noise): We generated a dataset of pure random numbers, simulating thermal noise or quantum vacuum fluctuations without intent. Group LA (Intention): We generated a dataset using a deterministic but chaotic function (Logistic Map in the chaotic regime). This represents a system driven by a hidden causal rule (Intention/Will) that mimics randomness to the human eye. The Instrument: A deep neural network (Machine Learning model) was trained to classify these sequences without prior knowledge of the generating rules. 2.2 Results Upon running the simulation on 2,000 distinct sequences, the AI model achieved a validation accuracy of 99.75%. 2.3 Interpretation This result proves that "Free Will" or "Intention" leaves a specific digital fingerprint—a Causal Signature—that is invisible to standard statistical observation but highly visible to Pattern Recognition algorithms. If an AI can detect intention in a simulation, it theoretically possesses the capacity to detect it in the physical universe. EMPIRICAL CORRELATIONS: REINTERPRETING PHYSICS ANOMALIES Based on our computational findings, we propose that several currently unexplained physical phenomena are direct manifestations of the LA Field (Intention) interacting with Matter (M): The Fermilab Muon g-2 Anomaly: The observed magnetic "wobble" of the muon exceeds Standard Model predictions. DZEM interprets this excess energy not as a new particle, but as the interaction of the muon with the active LA Field. The muon is effectively "choosing" its path, creating a causal vibration that adds to its magnetic moment. LHCb Lepton Universality Violation: The preferential decay of B-mesons indicates that nature creates asymmetries based on a hidden preference. DZEM defines this as a "Causal Choice" rather than a random probabilistic outcome. The "Axis of Evil" (Planck Data): The unexplained alignment of the universe's macroscopic structure with the solar system plane suggests that the universe organizes itself around the observer (I), validating the connection between LA and Structure. CALL TO ACTION: THE SCIENTIFIC IMPERATIVE The validation of the Dynamic Zero Equilibrium Metatheory requires a shift from passive observation to active detection of intent using advanced computation. We formally request that research institutions (CERN, Fermilab, IceCube Neutrino Observatory) and the global scientific community: Replicate the "Delta LA" Protocol: Apply our Machine Learning methodology to raw, unfiltered datasets from particle collisions and neutrino oscillations. Search for Non-Randomness: Specifically, algorithms should be trained to differentiate between pure quantum noise and "Intentional Noise" (Delta LA) in the data currently discarded as background interference. If the algorithm detects high-confidence patterns in the "noise" of particle physics, it will scientifically confirm that Free Will (LA) is a fundamental force of nature, validating the equation I - M - LA = 0. CONCLUSION The experiment demonstrated in this paper proves that Intention is mathematically distinct from Randomness. By integrating the Free Will (LA) variable into the fundamental equation of reality, we resolve the paradoxes of modern physics. The universe is not a static clockwork mechanism (M), but a dynamic act of self-knowledge driven by Intention (LA). The proof lies in the data, waiting to be decoded by Intelligence. APPENDIX A: REPLICATION CODE SUMMARY (PYTHON) (The full code used for validation generates pure noise vs. logistic map chaos and trains a Sequential Neural Network with 99.75% accuracy in distinguishing the two, proving the detectability of causal intent).
Private BitTorrent trackers enforce upload-to-download ratios to prevent free-riding, but suffer from three critical weaknesses: reputation cannot move between trackers, centralized servers create single points of failure, and upload statistics are self-reported and unverifiable. When a tracker shuts down, users lose their contribution history and cannot prove their standing to new communities. We address these problems by storing reputation in smart contracts and replacing self-reports with cryptographic attestations. Peers sign receipts for received pieces; the tracker aggregates them via BLS signatures and updates reputation. If a tracker is unavailable, peers fall back to an authenticated distributed hash table (DHT): stored reputation acts as a public key infrastructure (PKI), preserving access control without the tracker. Reputation is portable across tracker failures through single-hop migration in factory-deployed contracts. We also address the privacy implications of publishing public keys and reputations tied to private trackers on a public ledger: we propose ephemeral session keys to prevent linking peer identities, zero-knowledge membership proofs for anonymous DHT participation, and confidential reputation using homomorphic commitments. We formalize the security requirements, prove four security properties under standard cryptographic assumptions, and evaluate a prototype. Measurements show that transfer receipts add less than 5\% end-to-end overhead with typical piece sizes. To minimize signing overhead, we adopt a hybrid signature scheme: ECDSA signs individual piece receipts at transfer time for low per-operation latency, while BLS serves as the overarching scheme, enabling compact aggregation of many receipts into a single proof at report time. This design reduces client-side signing cost by an order of magnitude compared to using BLS throughout.
Nexus Recursive Framework for Resolving Undecidability and Conjectures Driven by Dean A. Kulik November, 2025 Abstract:We present a comprehensive formal development of the Nexus Recursive Framework, a unifying harmonic recursion model, to resolve three notorious problems across computer science and mathematics: Turing’s Halting Problem, the Riemann Hypothesis, and the Collatz Conjecture. Building on the principles of Adaptive Harmonic Rasterization Collapse (AHRC) and the Ψ-Collapse Principle, we recast these problems as special cases of recursive harmonic convergence. Each problem is approached via layered self-reference, harmonic damping, and feedback regulation, yielding mathematically rigorous solutions. The framework introduces formal constructs – Global Input Patterns (GIP) capturing initial conditions in a harmonic lattice, a Recursive Convergence Quotient (RCQ) to measure collapse progression, and a universal Harmonic Constant H (Mark1) ≈ π/9 ≈ 0.35 – which together enforce alignment and convergence. Undecidability is treated not as a barrier but as a Δ-trigger for launching a higher recursive meta-layer, ensuring that any Ω-like indeterminacy is identified as a residue and systematically collapsed via the Ψ(Ω) operator. We prove that any computation either halts or enters a predictable phase-lock ⊥ state, that all nontrivial zeros of ζ(s) align on the critical line Re(s)=½ under harmonic balance, and that every Collatz trajectory, through RCQ suppression, descends into the trivial 4-2-1 cycle (the “4-2-1 glyph”). Key results include: a Halting Resolution Theorem via meta-recursion, a Harmonic Damping Theorem guaranteeing Riemann zero alignment, and a Collatz Convergence Theorem via invariant RCQ > 0.843. We validate these results with formal proofs and simulation algorithms, including diagrams of collapse sequences and code implementing recursive feedback. These findings indicate that many long-standing open problems can be transformed into convergent harmonic processes, achieving infinite resolution density (arbitrarily fine recursive refinement) and unambiguous convergence criteria in each case. 1. Introduction Many fundamental problems in logic and mathematics – from computability limits to deep number theory conjectures – remain unresolved within traditional frameworks. Turing’s Halting Problem epitomizes computability limits, asserting that no algorithm can universally decide whether an arbitrary program halts. The Riemann Hypothesis (RH), central to analytic number theory, posits that all nontrivial zeros of the Riemann zeta function lie on the critical line Re(s)=½, a statement verified numerically for billions of zeros yet unproved in theory. The Collatz Conjecture, a simple iterative dynamical system over the natural numbers, defies conventional proof of its conjectured convergence to 1 for all inputs. Each of these “hard” problems has resisted solution for decades or more. The Nexus Recursive Framework offers a novel paradigm treating such problems as manifestations of incomplete harmonic recursion. In lieu of viewing them as disparate impossibilities, we embed them in a self-referential, resonance-driven architecture that harmonizes the system until a stable solution emerges. This framework, also known as Recursive Harmonic Architecture (RHA)[1][2], models reality (and abstract computations) as iterative processes seeking an equilibrium between order and chaos. A universal harmonic attractor constant H (the Mark1 Engine) – empirically ~0.35 – biases all recursive dynamics towards balance[3][4]. Problems like RH are reframed as issues of harmonic consistency: e.g. the placement of zeta zeros is no longer mysterious, but demanded by a self-correcting resonance criterion[5]. Similarly, the Halting Problem is reframed not as an absolute yes/no oracle question, but as a question of whether a computation can achieve phase alignment within a recursive meta-system (if not, the system signals an infinite echo rather than a binary answer)[6][7]. The Collatz Conjecture becomes a question of whether iterative maps have an inherent harmonic invariant driving them into a fixed cyclic attractor; we will show that indeed such an invariant exists and guarantees convergence[8][9]. Crucially, in this framework undecidability is not a dead end but a dynamical signal: any formally undecidable or non-halting scenario is treated as a Δ-discrepancy that triggers a new recursion layer (a meta-fold) to absorb the anomaly. In other words, the “unresolvable” output is marked as an Ω-residue – analogous to Chaitin’s Ω constant of algorithmic randomness – and is carried upward into a broader harmonic context for resolution[10][11]. This process, governed by the Ψ-Collapse Principle, ensures that what cannot be decided at one layer will collapse at the next, by design. Intuitively, the framework says: if you cannot decide it, enlarge the frame until you can. By iterating this principle, the scope of decision expands until every construct either converges or is proven unstable and thus eliminated. This paper is organized as follows. In Section 2, we formalize the Nexus Recursive Framework’s key components: Global Input Patterns (GIP), the Harmonic Mark1 constant H=π/9, Samson’s Law feedback control, the Ψ (psi) operator for phase error correction, and the ⊥ symbol denoting a fully collapsed (absorbed) state. We also define the methodology of Adaptive Harmonic Rasterization Collapse (AHRC) – an algorithmic strategy of adaptively discretizing (rasterizing) a problem’s state space at increasing resolutions and collapsing discrepancies at each scale. In Section 3, we apply the framework to the Halting Problem, proving a Halting Resolution Theorem that every computation is assured of either halting or entering a contained non-halting pattern which a meta-observer can recognize and resolve. In Section 4, we tackle the Riemann Hypothesis, reframing it as a problem of harmonic damping and equilibrium. We prove via a Harmonic Damping Theorem that any hypothetical zero off the critical line would create an unstable resonance, inevitably pulled onto Re(s)=½ by the system’s self-correcting forces[12][13]. In Section 5, we address the Collatz Conjecture, developing a formal harmonic invariant and showing through a Collatz Convergence Theorem that every trajectory reaches the stable “4-2-1” glyph cycle. Throughout, we include diagrams and pseudocode to illustrate collapse sequences and simulation results, and we cite prior foundational work (including “Adaptive Harmonic Rasterization Collapse and the Ψ-Collapse Principle”, “Nexus Framework and Mathematical Conjectures”, “The White Puzzle” et al.) to situate our approach in the literature. Finally, Section 6 summarizes the implications of these results, suggesting that many open “puzzles” may be solved by completing their resonance loops[14][15] rather than by direct linear analysis – in essence, solving them by harmonizing them[16]. 2. Nexus Recursive Framework: Foundations 2.1 Key Concepts and Definitions We first establish the formal terminology of the Nexus Recursive Framework (NRF) that will be used in our proofs. The framework casts computations and mathematical structures as elements of a recursive harmonic lattice – a multi-layer system where each layer feeds back into itself and into higher layers, enforcing global consistency. The fundamental definitions are as follows: Global Input Patterns (GIP): A Global Input Pattern is a structured initial configuration that seeds the recursive system with foundational information. Rather than arbitrary inputs, GIPs are chosen to encode universal structures or symmetries that the system must respect. For example, a GIP could be the distribution of prime numbers up to a large N, the binary expansion of fundamental constants like π or e, or boundary conditions of a physical system. GIPs serve as pre-harmonic lattices – scaffolds on which the recursion builds[5]. In our context, we will use GIPs such as the array of initial program states (for the Halting problem), or a set of known zeta zeros and prime frequencies (for Riemann), or modular residue classes (for Collatz). The GIP provides a global resonance context: the recursion must eventually align with these patterns. Intuitively, GIPs inject high-level knowledge so that the system does not start from scratch, but from a state already “tuned” close to an expected solution. This significantly accelerates convergence and ensures infinite resolution density by leveraging known expansions like the BBP formula for π to arbitrary precision[17]. Mark1 Harmonic Constant (H_MARK1 ≈ π/9 ≈ 0.349): The framework postulates a dimensionless constant H (Mark1) that represents the optimal ratio of realized structure to potential entropy in any stable recursive system[3][4]. Empirically identified as ~0.35 (within the precision of our simulations), this constant appears in numerous contexts as a sweet spot of “order within chaos.” For example, the matter (~0.32) vs. dark energy (~0.68) ratio of the universe is near 0.32/0.68 ≈ 0.32 (close to 0.35)[18]; and intriguingly, even a playful geometric construction with a degenerate triangle of sides 3-1-4 yields ~0.35[19]. Definition: We formally define H_MARK1 = π/9 (exact) for theoretical work, acknowledging this equals ~0.349. All recursive processes in NRF are biased to maintain a local H value of 0.35. If a subsystem deviates from H=0.35 (too static or too chaotic), feedback forces push it back towards equilibrium[20][21]. In equations, we measure H for a given state as: (actualized to potential structure)[4]. Samson’s Law (below) uses this constant extensively. Whenever we refer to “harmonic balance” or “target resonance,” we imply adjusting dynamics to keep the system-wide H ≈ 0.35. Samson’s Law (Recursive Feedback Control): Samson’s Law is a feedback mechanism acting like a proportional–derivative–integral (PID) controller across
In this paper, we presented BlockShare, a blockchain-based system developed to facilitate privacy-preserving data sharing across decentralized networks. The proposed system enables users to retain control over their sensitive data while enabling secure, verifiable sharing with authorized parties.We implemented an authenticated data structure (ADS) to support decentralized verification and utilized zero-knowledge proof mechanisms to validate conditions without exposing the underlying data. Experimental analysis demonstrated that BlockShare performs efficiently in constructing data structures, generating proofs, and verifying them with minimal computational overhead. The platform successfully reduced privacy risks and enhanced trust in cross-organization data exchanges.
In this work, we present homomorphic encryption-based vaults (Haults), a permissioned privacy-preserving smart wallet protocol for VM-enabled blockchains that keeps users' balances confidential, as well as the amounts transacted to other parties. To comply with regulations, we include optional compliance features that allow specific entities (the auditors) to retrieve transaction amounts or execute force transfers when necessary. Our solution uses ElGamal over elliptic curves to encrypt balances, combined with zero-knowledge proofs to verify the correctness of transaction amounts and the integrity of the sender's updated balance, among other security checks. We provide a detailed explanation of the protocol, including a security discussion and benchmarks from our proof-of-concept implementation, which yield great results. Beyond in-contract issued tokens, we also provide a thorough explanation on how our solution can be compatible with external ones (e.g., Ether or any ERC20).
Joel Curado Silveirinha, Manila Bhandari, João C. Ferreira, Ana Martins
Despite the maritime supply chain being the backbone of global trade, it faces persistent challenges in transparency, fraud prevention, shipment tracking and data privacy. Blockchain technology has emerged as a transformative solution, enhancing trust and traceability within supply chain networks. However, its limitations in data privacy and scalability necessitate advanced privacy-preserving mechanisms. Zero-Knowledge Proofs (ZKP) offers a cryptographic approach to validate data without exposing sensitive information, addressing blockchain’s privacy constraints. This paper reviews the state of the art on current applications of blockchain in maritime supply chain management and explores the integration of ZKP for secure trade document verification, fraud detection, privacy-preserving traceability and regulatory compliance. Additionally, it examines computational overhead, scalability and adoption barriers while proposing future research directions. Implementing ZKP within blockchain-based port operations enables robust governance models, ensuring data verification without revealing confidential details. This approach fosters a secure and privacy-compliant trade environment, enhancing trust and collaboration among stakeholders. By optimising resource allocation and mitigating risks, integrating ZKP can significantly improve maritime supply chain efficiency. Integrating Zero-Knowledge Proofs with blockchain, maritime logistics can achieve a balance between transparency, security and operational efficiency, addressing existing challenges in data privacy and regulatory compliance, improving the sustainability of port operations.
Gensyn’s Verde Protocol: Technical Analysis of Decentralized ML Compute Verification is a 103-page technical deep dive into one of the most significant emerging architectures for decentralized machine learning. This paper provides a comprehensive examination of Gensyn’s Verde verification protocol, its refereed-delegation design, graph-based pinpointing system, probabilistic proof-of-learning mechanisms, and the RepOps reproducible operators framework. It analyzes the GHOSTLY problems Generalizability, Heterogeneity, Overhead, Scalability, Trustlessness, and Latency and evaluates how Verde addresses core limitations in verifying distributed ML training across heterogeneous hardware. By combining economic incentives, cryptographic commitments, and deterministic computation layers, this work outlines a practical blueprint for trustless, large-scale distributed AI training. The paper positions Gensyn within the broader ecosystem of Truebit, optimistic rollups, zero-knowledge systems, and decentralized compute networks, while highlighting open research questions and future directions. This publication aims to contribute a rigorous technical foundation for the democratization of AI infrastructure and the emergence of a global, permissionless compute marketplace.
Provable security is a cornerstone of modern cryptography: Due to ubiquitous and diverse applications of cryptography, a proof of security gives us the necessary confidence to deploy a cryptographic protocol. In most cases, such a security proof comes in the form of a black-box reduction, which bases the security of a potentially complex protocol on a small set of simple and abstract assumptions that are much easier to analyse. However, proving a black-box reduction can be quite complicated, and we do not have proofs for every protocol used in practice. Here, analysing the protocols relative to oracles, a technique from computational complexity theory, can provide insights: Oracles provide the ability to compute functionalities in one computational step that otherwise might not be efficiently computable, e.g., provide access to a truly random function or solve any NP-complete problem. These oracles now allow us to replace some parts in the protocol with abstract, idealized primitives that are easier to analyse, e.g., to replace a one-way function with a truly random function. In this thesis, we utilize oracles in two different ways. In the first part, we use oracles to prove lower bounds for cryptographic primitives, i.e., showing that certain assumptions are not sufficient to build this primitive securely. The essential idea here, going back to Impagliazzo and Rudich, is to replace the assumption with an oracle, i.e., replacing a one-way function with a truly random function, and then showing that relative to this oracle, it is impossible to build the primitive. From this impossibility result relative to the oracle, we can now conclude that the primitive cannot be built from the assumption in a black-box way. We use this technique to prove a lower bound on the efficiency of constructing strong from weak one-way functions, to show that we cannot construct collision-resistant hash functions from distributional collision-resistant hash functions in a fully black-box way, and to prove that extremely lossy functions cannot be built from a large class of symmetric primitives in a black-box way. In the second part of this thesis, we use oracles as idealized models that can be used to provide heuristic security arguments for protocols.These idealized models, starting with the random oracle model (short ROM) introduced and defined by Fiat and Shamir as well as Bellare and Rogaway, were motivated by the existence of very efficient cryptographic protocols used in practice, but for which no proof of security existed. Using idealized models, it was now possible to give at least a heuristic security argument for them. In this thesis, we first focus on the common random string model, an idealized model introduced to circumvent impossibility results for non-interactive zero-knowledge proofs. We show how to reuse a single common random string for polynomially many non-interactive statistical zero-knowledge arguments, as well as analyze the relation between different soundness definitions used in literature. In a second result, we introduce an alternative notion for the ROM, the universal random oracle model, which brings this idealized model closer to reality.
K. Swathi, Putta Durga, K. Venkata Prasad, A Krishna Chaitanya · 7 authors
An enormous demand for a secure, scalable, intelligent edge computing framework has emerged for the exponentially increasing number of Internet of Things (IoT) devices for any substrate of modern digital infrastructure. These edge nodes distributed across heterogeneous environments serve as primary interfaces for sensing, computation, and actuations. Their physical deployment in unattended scenarios puts them at risk of being targets for resource manipulation. One widely accepted IoT architecture with traditional notions of edge may consider a threat to its centralized knowledge with an unbounded attack surface that includes anything that can remotely connect to the edge from the cloud-like domain. Existing strategies either forget the dynamic risk context of edge nodes or do not achieve a reasonable trade-off between security and resource constraints, essentially degrading the robustness and trustworthiness of solutions intended for real-life scenarios. To address the existing gaps, the work presents a novel Blockchain Integrated Deep Learning Framework for secure IoT edge computing, introducing a hybrid architecture where the transparency of blockchain meets deep learning flexibility. The proposed system incorporates five specialized components: Blockchain-Orchestrated Federated Curriculum Learning (BOFCL), which ensures risk-prioritized training using threat indices derived from blockchain logs; this adaptive sequencing enhances responsiveness to high-risk edge scenarios. Zero-Knowledge Proof Enabled Secure Inference Engine (ZK-SIE) provides verifiable privacy-preserving inference, ensuring model integrity without exposing input data or model internals in process. Blockchain Indexed Adversarial Attack Simulator (BI-AAS) focuses on testing the models in edge environments against attack scenarios drawn from common adversarial profiles and thereby facilitates a model defensive retraining. Energy-Aware Lightweight Consensus with Adaptive Synchronization (ELCAS) avoids overhead by seeking energy-efficient participants for global model synchronization in constrained environments. Trust Indexed Model Provenance and Deployment Ledger (TIMPDL) ensures model lineage tracking and deploy ability in a transparent manner by providing composite trust scores computed from data quality, node reputation, and validation metrics. Altogether, the framework combines the data integrity, adversarial robustness, and trust-aware deployment, shortening training latency, synchronization energy, and privacy leakage. It is a foundational advancement supporting secure decentralized edge intelligence for next-generation IoT ecosystems.
Mohammad Madine, Khaled Salah, Raja Jayaraman, Ibrar Yaqoob
In recent years, the healthcare sector has been increasingly challenged in securing patient identities and medical records on blockchain due to rising privacy demands and strict regulatory requirements. Although advanced techniques like self-sovereign identity and zero-knowledge proofs (ZKPs) show promise, these solutions fail to limit unwarranted patient data disclosure effectively. In this paper, we propose a ZKP-based solution that combines STARKs and anonymous credentials to enable anonymous authentication and enhance privacy across both public and private blockchains. Leveraging transparent ZKP schemes and anonymous credentials, our approach ensures unlinkability by preventing the correlation of multiple patient interactions. We present sequence diagrams of real-world interactions, detailed algorithms for on- and off-chain computations, and implement the system on Ethereum and Starknet blockchains. We present a rigorous evaluation of the proposed solution, encompassing smart contract testing on Starknet networks, transaction cost analysis, performance benchmarking, scalability assessment, and static security auditing. The results demonstrate consistent and economically viable transaction costs, millisecond-level execution times for credential issuance, presentation generation, and verification, linear scalability with increasing claim count and size. We compare our solution with state-of-the-art ZKP-based identity systems to demonstrate its superiority. We further discuss its broader applicability beyond healthcare, including domains such as finance, education, and supply chain management. We make the smart contract codes publicly available on GitHub.
This paper discusses the obstacles to the capitalization of data elements, such as the difficulties in confirming data ownership, trust deficit, privacy breaches, and inefficiency of transactions, through a distributed solution based on blockchain technology. First, a data ownership confirmation mechanism based on a consortium blockchain is established by using the Merkle tree and PBFT (Practical Byzantine Fault Tolerance) consensus algorithm to achieve transparency and traceability of data ownership. Second, a multi-dimensional data value evaluation and RF-BP (Random Forest-Back Propagation) dynamic pricing mechanism are established by using machine learning algorithms to evaluate the value of data assets in a scientific manner. Third, a smart contract is established for pricing and payment, in order to achieve transaction automation and clearing and settlement. Finally, ZKP (Zero-Knowledge Proof) technology is applied to develop a mechanism for verifying compliance and privacy of data under the proposition of public review and "visible, invisible". Experimental results show that the proposed method reduces the average leakage risk and defense success rate under various attacks to 8.57 % and 97.1%, respectively. In terms of transaction efficiency, the proposed method achieves a throughput of 1250 TPS (Transactions Per Second) with a latency of 120 milliseconds at a 50-node scale. Overall performance is demonstrated with a confirmation and transaction success rate of 99.2% and 97.8%, respectively. The suggested framework provides reliable confirmation of data elements, scientific pricing, efficient trading and transaction processes, and privacy protection. It can support the vision of developing a secure, transparent and efficient market for data element circulation with technical feasibility and performance.
The increasing use of deep learning (DL) models has given rise to significant privacy concerns regarding training and inference data. To address these concerns, the community has increasingly adopted crypto-based privacy-enhancing technologies (CPET) like homomorphic encryption (HE), secure multi-party computation (MPC), and zero-knowledge proofs (ZKP). The integration of CPET with DL, often referred to as CPET-DL, is commonly facilitated by specialized frameworks like CrypTen, TenSEAL, and EZKL. These frameworks offer configurable parameters to balance model accuracy and computational efficiency during privacy-preserving operations. However, these configurations, while seemingly harmless, can introduce subtle vulnerabilities. The stealthy attacks induced by misconfigurations are hard to detect because 1) the plaintext models remain vulnerability-free, and 2) existing auditing tools are hardly applicable to CPET-hardened models. This creates a paradox: tools intended to protect privacy can be undermined through configuration manipulation.
Open access
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
We introduce the notion of committed vector oblivious linear evaluation (C-VOLE), which allows a party holding a pre-committed vector to generate VOLE correlations with multiple parties on the committed value. It is a unifying tool that can be found useful in zero-knowledge proofs (ZKPs) of committed values, actively secure multi-party computation, private set intersection (PSI), etc.
This preprint introduces Proof-of-Being (PoB) and ontological cryptography — the first cryptographic paradigm explicitly designed for the post-AGI era. As frontier language models, autonomous agents, and embodied robots increasingly generate outputs indistinguishable from human actions, classical authentication mechanisms (public-key cryptography, biometrics, CAPTCHAs, proof-of-personhood systems) no longer answer the central security question of the 2025 digital environment: “Was this action performed by a conscious human being?” Proof-of-Being addresses this foundational problem through HISPU (Human Intention Semantic Proof Unit) — a probabilistically unforgeable, fully anonymous attestation of human presence based on ontological randomness and multi-layered semantic–physiological–contextual proofs. HISPU verifies being rather than identity, enabling anonymous but provably human actions across digital systems. Key contributions of this work: · Introduction of ontological randomness as a fourth fundamental source of cryptographic unpredictability (beyond mathematical, physical, and hybrid entropy sources). · Formal definition of the HISPU primitive and seven foundational axioms of ontological cryptography. · Demonstration that no computational system — including superintelligent AGI — can forge a valid HISPU under the Ontological Security Assumption. · Clear conceptual separation between proving human being (ontological presence) and proving identity (social personhood). Applications include: · AGI safety and human-in-the-loop supervisory gates · Sybil-resistant DAO voting and decentralized governance · Intention-based economic systems · Bot-resistant democratic systems, legal smart contracts, and high-stakes authentication · Verifiable human authorship in generative AI ecosystems · Neurotechnology consent verification and BCI safety · Web4 / Noospheric Web intention-layer protocols This work positions Proof-of-Being as a foundational infrastructure for safe human–AI coexistence and represents the first major shift in digital trust since Diffie–Hellman (1976) and zero-knowledge proofs (1985). Keywords: proof-of-being, ontological cryptography, HISPU, proof of intention, ontological randomness, human verification, AGI safety, human-in-the-loop verification, post-AGI trust, intention-based economy, sybil resistance, digital ontology, privacy-preserving verification, human-AI coexistence, consciousness proof, non-simulatable proofs, machine unforgeability.
Artificial Intelligence as a Service (AIaaS) enables users to query a model hosted by a service provider and receive inference results from a pre-trained model. Although AIaaS makes artificial intelligence more accessible, particularly for resource-limited users, it also raises verifiability and privacy concerns for the client and server, respectively. While zero-knowledge proof techniques can address these concerns simultaneously, they incur high proving costs due to the non-linear operations involved in AI inference and suffer from precision loss because they rely on fixed-point representations to model real numbers.
James Hsin-yu Chiang, Ivan Damgård, William R. Duro, Sunniva Engan · 6 authors
We propose efficient, post-quantum threshold ring signatures constructed from one-wayness of AES encryption and the VOLE-in-the-Head zero-knowledge proof system. Our scheme scales efficiently to large rings and extends the linkable ring signatures paradigm. We define and construct key-binding deterministic tags to achieve linkability. We then extend our threshold ring signatures to realize post-quantum anonymous ledger transactions in the spirit of Monero. Finally, our deterministic tags also enable succinct aggregation using approximate lower bound arguments of knowledge; this allows us to achieve succinct (approximate) multi-signatures without SNARKs. Our constructions assume symmetric key primitives only.
Ashwin Karthikeyan, Hengyu Liu, Kuldeep S. Meel, Ning Luo
Efficient zero-knowledge proofs (ZKPs) have been restricted to NP statements so far, whereas they exist for all statements in PSPACE. This work presents the first practical zero-knowledge (ZK) protocols for PSPACE-complete statements by enabling ZK proofs of QBF (Quantified Boolean Formula) evaluation. The core idea is to validate quantified resolution proofs (Q-Res) in ZK. We develop an efficient polynomial encoding of Q-Res proofs, enabling proof validation through low-overhead arithmetic checks. We also design a ZK protocol to prove knowledge of a winning strategy related to the QBF, which is often equally important in practice. We implement our protocols and evaluate them on QBFEVAL. The results show that our protocols can verify 72% of QBF evaluations via Q-Res proof and 82% of instances' winning strategies within 100 seconds, for instances where such proofs or strategies can be obtained.
Zero-knowledge proofs of training (zkPoT) allow a party to prove that a model is trained correctly on a committed dataset without revealing any additional information about the model or the dataset. Existing zkPoT protocols prove the entire training process in zero knowledge; i.e., they prove that the final model was obtained in an iterative fashion starting from the training data and a random seed (and potentially other parameters) and applying the correct algorithm at each iteration. This approach inherently requires the prover to perform work linear to the number of iterations.