Longbo Han, Xiaodong Li, Lin You, Gengran Hu · 8 authors
Vehicular ad-hoc networks (VANETs) require authentication mechanisms that simultaneously deliver privacy, accountability, and timely cross-domain synchronization. The existing schemes struggle to balance unlinkable anonymity with effective tracing. They are also vulnerable to future quantum adversaries and rely on slow and costly revocation workflows. We present ZebraCPA, a decentralized conditional privacy-preserving authentication (CPPA) framework that combines lattice-based traceable ring signatures (TRS) with zero-knowledge (ZK) proofs and a consortium blockchain. Our TRS design removes linkability tags and embeds a tracing trapdoor only recoverable by the authorized auditors. It naturally extends to threshold tracing for multi-auditor settings. To avoid the plain-text key escrow, ZebraCPA leverages the additively homomorphic property of the commitments to support the ciphertext-only key updates by the vehicles, preventing the catastrophic key leakage at authorities. A hierarchical blockchain layer provides fast, consistent synchronization of active-key status across regions. The experiments show 1.7×–7.0× speedups over state-of-the-art baselines in signing/verification while retaining an anonymity-set size of N=10. The network-level simulations further indicate that ZebraCPA reduces an average packet delay by 30.7% - 61.6% compared with the baselines under moderate traffic densities. Moreover, the security of ZebraCPA is validated through our informal analysis under the Dolev-Yao model. Overall, ZebraCPA achieves post-quantum security, strong anonymity with conditional traceability, and practical deployment efficiency for VANETs, outperforming the existing solutions in terms of both latency and robustness.
George Chidera Akor, Love Allen Chijioke Ahakonye, Jae Min Lee, Dong-Seong Kim
Zero-knowledge machine learning (ZKML) enables verifiable inference on private data, but deploying convolutional neural networks (CNNs) in production remains constrained by a multi-dimensional tradeoff between proof-generation latency, bandwidth consumption, and computational complexity. Existing ZKML frameworks and engineering blogs provide qualitative heuristics, yet practitioners lack systematic, layer-level measurements to guide architecture design under these constraints. This work presents the first systematic, layer-level characterization of CNN component costs in EZKL, a Halo2-based ZKML framework targeting EVM-compatible blockchains. We profile 8 feasible layer types (activations, pooling, normalization, and linear) across two EZKL precision settings (scale 7 and 10), measuring proof-generation time, proof size, circuit complexity, and peak memory in 26 experiments. We reveal critical infrastructure requirements by documenting 10 additional experiments that exceeded hardware limits (Conv2d operations, LayerNorm, and ReLU-based composite CNNs requiring$>125\ \text{GB}$RAM). Contrary to conventional wisdom, we find that precision configuration has a negligible performance impact ($1.002 \times$ratio), and that system RAM, not GPU VRAM, is the primary bottleneck. We release an open-source profiling toolkit and a public dataset that enable practitioners to query expected costs for their architectures and constraints.
Adversarial Robustness in Machine Learning
Advanced Neural Network Applications
Physical Unclonable Functions (PUFs) and Hardware Security
Mohamed Seifelnasr, Mohamed Mobarak, Riham AlTawy, Amr Youssef
The metaverse transforms how individuals interact, work, and engage in virtual environments, creating new opportunities in gaming, education, e-commerce, and social networking. At the core of this experience are avatars (i.e., digital representations of users that serve as their proxies in virtual spaces). Ensuring secure and privacy-preserving communication between avatars presents critical challenges, particularly in protecting metaverse user privacy by preventing the linking of avatars to users' social and professional lives. Adopting anonymous schemes such as ring signature schemes requires access to all public keys within the anonymity set, which is impractical in the metaverse. In this paper, we proposeSPARTA(Secure andPrivacy-preserving protocol withRole separation andTrustworthiness forAvatars in the metaverse), a protocol that enables avatar authentication and maintains avatar unlinkability. By leveraging mercurial signatures, our approach allows metaverse users to generate multiple unlinkable avatars without requiring repeated registration with the metaverse service provider, thereby enabling seamless role separation. Additionally, by using a time-based hash chain, only avatars in possession of a reputation token from the time-based hash chain can submit their feedback on a smart contract based on their interactions. Given the soundness property of zero-knowledge proof and the origin-hiding property of mercurial signatures, we formally prove that${\sf SPARTA}$achieves mutual authentication, avatar unlinkability, and penalization enforcement. Additionally, we analyze the performance overheads introduced by its cryptographic primitives and compare${\sf SPARTA}$with existing metaverse authentication protocols. Furthermore, we implement the protocol using socket programming. This implementation simulates real-time message exchanges between protocol entities, resulting in an end-to-end latency of 105 ms. Compared to existing metaverse authentication frameworks,${\sf SPARTA}$provides unlinkable avatar authentication that achieves mutual authentication, role separation, and data sovereignty without reliance on an online trusted third party. The concurrent implementation between two Raspberry Pi devices demonstrates the scalability of${\sf SPARTA}$, achieving a total completion time of 17.338 seconds for 1000 concurrent authentications, corresponding to a throughput of approximately 57.7 authentications per second, confirming its practicality for large-scale metaverse environments.
Although cloud storage offers the much-needed scalability, flexibility, and economic efficacy, it also presents significant security and privacy issues, which are mostly caused by the fact that, since data are encrypted, the traditional plaintext search approaches are compromised. To overcome this shortcoming, we introduce the Enhanced Aware Record Maintenance (EARM) architecture, a compound, privacy-aware architecture that supports ranked, multi-keyword encrypted data retrieval in the cloud. The fundamental retrieval process of EARM is novel, incorporating ontology-based keyword mapping, enhanced association rule mining, and inner-product similarities to produce highly accurate and relevant search results. The framework deploys a strong multi-layer defense model, which integrates quantum-resistant cryptography (Zero-Knowledge Proofs/Homomorphic Encryption), high-grade cipher suites (AES/RSA), and granular Attribute-Based Encryption (ABE) access controls (such as geofencing and decentralized identity management). Moreover, EARM also brings intelligent defensive layers of AI-based orchestration, which include ransomware, intrusion, and anomaly detection, behavioral biometrics, and a tamper-proof blockchain audit trail. Secure file versioning, rollback, and an encrypted trash bin are other ancillary features that improve the system's resilience. Empirical analyses performed on actual data sets indicate that EARM maintains high privacy and high retrieval rates and suffers only a few system overheads, hence making it an effective and highly secure encrypted cloud storage solution for modern challenges.
Contemporary digital currency systems face fundamental challenges in achieving optimal balance between transaction privacy, computational efficiency, and cryptographic security. While zero-knowledge proof systems have dominated privacy-preserving cryptocurrency research, their practical implementations often involve prohibitive computational overhead that limits real-world deployment. This paper presents a comprehensive analysis of the Elliptic Homomorphic Token (EHT) protocol, which leverages elliptic curve-based partially homomorphic encryption combined with parallel processing architecture to enable privacy-preserving peer-to-peer transactions without the computational complexity of zero-knowledge constructions. Our theoretical analysis demonstrates strong privacy guarantees under standard cryptographic assumptions, while experimental evaluation shows that EHT achieves 500,000 transactions per second with parallel processing and 50-100ms latency. The protocol eliminates the need for complex zero-knowledge proofs by directly utilizing elliptic curve cryptographic primitives, resulting in performance improvements exceeding 1000× over existing privacy-focused systems while maintaining equivalent security properties through formally proven cryptographic guarantees.
The convergence of social networking and electronic commerce has given rise to the social e-commerce paradigm, where content creators serve as the primary drivers of consumer engagement and purchase decisions. However, this ecosystem faces a critical tension between the need for high-precision ad targeting to sustain monetization and the increasingly stringent requirements for user privacy preservation. Traditional centralized recommendation systems require the aggregation of massive user behavioral datasets, creating significant risks of data leakage and violating emerging regulatory frameworks. To address this challenge, we propose a novel framework titled Fed-ZKC (Federated Zero-Knowledge Creator). This architecture synergizes Federated Learning (FL) with Zero-Knowledge Proofs (ZKP) to enable privacy-preserving ad targeting while ensuring verifiable monetization attribution for creators. In our system, user preference models are trained locally on edge devices to prevent raw data transmission, while a cryptographic verification layer ensures that ad interactions are genuine without revealing user identities to the platform or the creators. Extensive experiments conducted on large-scale real-world datasets demonstrate that Fed-ZKC achieves recommendation accuracy comparable to centralized baselines while reducing privacy leakage risks by orders of magnitude. Furthermore, the implementation of succinct non-interactive arguments of knowledge (zk-SNARKs) introduces minimal computational overhead, making the protocol feasible for deployment on modern mobile processors.
The smart cities that collaborate with AI-driven autonomous robots are attracting attention for supporting various social activities in the real world. In facilities that provide such services, various systems managing the facility and robots may coexist in the common area. By enabling the systems to interoperate and share information about the status of the facility and robots, it becomes possible to realize a variety of services that support safety and security within the facility. However, while the operators of the facility want to monitor the detailed conditions of the robots, the operators of the robots are cautious about providing the information about the status of robots such as the moving trajectory and various sensor data. To resolve this dilemma, we propose a new system that enables estimation of the operational conditions of the robots by verifying the positions and trajectories at landmarks in the facility without disclosing their internal information. In the proposed system, we focus on the observation of environmental information that accurately reflects the real-world situation for estimating the proximity between the robot and each landmark. As the environmental information, both systems on robots and a facility measure CSI (Channel State Information) and acoustic information. In addition, by utilizing zero-knowledge proof (ZKP) technology, the system for the facility confirms the reliability of the process for estimating the proximity of the robots to the landmark without exchanging detailed internal information. Through the proof-of-concept experiment, applying the proposed system achieved high-accuracy proximity detection with both methods (CSI and acoustic information) yielding precision and recall rates exceeding 0.90.
We propose Trustless Agent Swarms, a framework enabling privacy-preserving coordination among autonomous AI agents on EVM-compatible blockchains. Our system integrates four cryptographic primitives: (1) Groth16 zero-knowledge proofs for proving reputation thresholds without revealing scores; (2) EIP-5564 stealth addresses for unlinkable fund transfers; (3) ERC-4337 account abstraction for gasless autonomous execution; and (4) Semaphore for anonymous group signaling. We implement a 586-constraint reputation proof circuit and deploy five smart contracts on Base Sepolia. Proof generation: 580ms. On-chain verification: 407,576 gas.
Abstract As artificial intelligence (AI) systems become increasingly integrated into critical applications, ensuring trust in their outputs has emerged as a central challenge. Verifiable machine learning (ML) is one approach to addressing this challenge, providing guarantees that results are both correct and reproducible. Existing paradigms, however, provide only partial solutions: zero-knowledge ML (ZKML) achieves strong cryptographic assurances but suffers from limited scalability and high resource costs, while optimistic ML (OPML) supports a wider range of models but relies on economic incentives and long dispute periods. In this work, we propose zk-OPML, a novel hybrid framework that integrates optimistic verification with zero-knowledge proofs (ZKPs). The approach decomposes ML inference into operator-level computations, selectively generating ZKPs for isolated ONNX operators, while retaining the scalability of the optimistic paradigm. We present a prototype implementation and evaluate its performance by benchmarking it against ZKML and OPML. Our results show that zk-OPML achieves faster verification for more complex inference tasks and scales more effectively to larger models, while avoiding the excessive costs of end-to-end ZKML. The modular design of zk-OPML further enables future extensions with the latest advances in the field of ZK.
Open access
Adversarial Robustness in Machine Learning
Physical Unclonable Functions (PUFs) and Hardware Security
This paper presents the completed Y.I.N. Mazari Architecture in its final 20-layer form, addressing two compounding failures in AI governance: the verification paradox where organizations cannot prove compliance without trusting their own infrastructure, and the platform determinism gap where AI inference produces different results across hardware architectures. The architecture integrates five physics foundation layers establishing energy-anchored provenance through Landauer limit accounting, domain routing, measurement precision, blockchain anchoring, and deterministic parity verification using Residue Number System arithmetic. Core governance layers enforce constitutional constraints through cryptographic authorization, differential privacy, and multi-party verification. Advanced layers provide zero-knowledge proofs, immutable audit trails, automated regulatory reporting, quantum resistance, and meta-governance oversight. Layer 0E, the Deterministic Parity Engine introduced in this final architecture, achieves bit-exact cross-platform computational reproducibility, enabling independent verification of AI operations by any party on any hardware. Combined with Layer 14, SENTINEL independent verification, the architecture produces governance evidence that no party can forge, no party can suppress, and any party can reproduce independently on arbitrary hardware. The complete 20-layer stack addresses GDPR Article 5, DORA Article 28, EU AI Act Article 50, HIPAA Security Rule, and provides 30-year quantum-resistant durability through NIST FIPS 203 post-quantum cryptography. Patent portfolio: 27 USPTO applications covering the architecture, priority November 23, 2025. The name Y.I.N. honors Yanis, Ilyan, and Neylia Mazari, representing the principle: Your Information Never leaves your control.
The next-generation e-health systems, which include electronic health records (EHRs), telemedicine platforms, and Internet of Medical Things (IoMT) environments, need a strong access control system that protects sensitive medical data while maintaining user privacy. The conventional access control systems face security risks because of credential theft, spoofing attacks, and their reliance on centralized trust, and their inability to scale. Blockchain-enabled multimodal biometric authentication provides a secure and decentralized solution for access control in e-health systems, according to current technological advancements. This paper provides an extensive assessment of blockchain-based multimodal biometric authentication systems, which deliver privacy-protecting access control solutions for future e-health systems. The review further examines central techniques for protecting biometric templates, zero-knowledge proofs, homomorphic encryption, and secure off-chain storage systems. The research assessed existing methods by comparing efficiency for access control, ability to protect user data, capacity to handle growing user needs, ability to work with other systems, and compliance with the General Data Protection Regulation (GDPR) and Health Insurance Portability and Accountability Act (HIPAA) regulations. The research identifies open challenges that need resolution, which include biometric data revocability, latency constraints, cross-platform interoperability, and limited real-world deployments. The study presents upcoming research paths that will investigate lightweight blockchain systems, post-quantum cryptography, cross-chain medical identity management, and adaptive access control systems in extensive e-health environments. The review demonstrates that blockchain-based multimodal biometric authentication serves as a suitable foundation that enables secure access control through decentralized systems that protect user privacy in upcoming e-health technologies.
Abstract We propose federated quantum randomness with client-side sanity (FQR-CSS), a federated architecture that supplies continuously verifiable quantum entropy to cloud hardware security modules (HSMs) and key management services (KMS). In FQR-CSS, each quantum random number generator (QRNG) node emits a randomness contribution along with a post-quantum zero-knowledge proof (ZKP) attesting to device-level operational predicates. An aggregation layer verifies these proofs, runs Byzantine fault tolerance (BFT) consensus (instantiated via HotStuff) over accepted contributions, and publishes a mixed output with an integrity token. We introduce the security notion of verifiable quantum randomness (VQR), comprising unpredictability, quantum-origin guarantee, and federated integrity. We prove VQR under concrete post-quantum cryptographic assumptions. Our proofs utilize Track-A constructions (ZKPs over classical measurement logs), which are fully implementable today. We further outline a theoretical roadmap for Track-B (direct quantum state verification) to guide future research directions. Our empirical evaluation of a post-quantum zk-STARK (Track-A) demonstrates prover latencies of approximately 26 ms for synthetic statistical predicates (K=1024), with sub-millisecond verification times, proof approximately 2.6 KB, and an estimated end-to-end WAN+HotStuff latency approximately 396 ms in our conservative model.
Open access
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
The "Identity Trilemma" posits that a decentralized network can enforce only two of the following three properties: Privacy (Anonymity), Accountability (Sybil Resistance), and Permissionlessness (No Central Gatekeeper). Traditional Web2 platforms resolve this by sacrificing Privacy (enforcing Real-Name Policies), while early Web3 platforms sacrificed Accountability, resulting in "Sybil Swarms" where single actors control thousands of wallets. This paper introduces the Klyrox solution to the trilemma: Pseudonymous Accountability. By utilizing Zero-Knowledge Proofs (ZKPs) and non-linear Time-Energy Cost Functions, the Klyrox Protocol enables users to mathematically prove they are unique, high-integrity actors without ever revealing their physical identity, biometric data, or government credentials. We define a new standard for "Proof of Personhood" based not on biology, but on consistent historical behavior recorded in a Soulbound Token (ERC-721M). Author's Note: This paper is a foundational pillar of the Klyrox Protocol architecture, expanding upon the core framework published in The Klyrox Protocol: A Decentralized Framework for Optimistic Content Verification and Epistemic Reputation (available at: https://doi.org/10.5281/zenodo.18729968). It outlines the specific mechanics underpinning the concept of "Epistemic Capital," as explored in the complete five-volume series, The Algorithmic Monographs (The Algorithmic Invisible Hand, The Republic of Code, The Market for Truth, The Heavy Metal Intelligence, and The Synthetic C-Suite).
We construct a family of self-adjoint operators T_{k,δ,ε} on a Hilbert space of functions defined on the set of prime numbers. We prove that the discrete spectrum of these operators, after taking appropriate limits (δ→0, ε→0) and averaging over the phase parameter k, coincides with the imaginary parts of the nontrivial zeros of the Riemann zeta function ζ(s). By self-adjointness, the spectrum is real, which implies that all nontrivial zeros lie on the critical line ℜ(s)=1/2. This is version 3.0, which includes substantial improvements over previous versions: • Added Lemma 3 (Poisson summation application) with complete proof. • Expanded Theorem 4 (Limit δ→0) with step-by-step rigorous justification. • Added Theorem 7 (Guth–Maynard control) showing that ∑|β−1/2|² e^{-ε|γ|} → 0. • Added Lemma 8 proving continuity of R(z,ε) and convergence to an entire function R(z). • Added numerical verification table comparing first 10 eigenvalues with Odlyzko's zeros (relative errors ∼10⁻⁵). • All previous typos and formatting errors have been corrected. The construction uses only elementary properties of prime numbers, classical functional analysis, and recent zero-density estimates (Guth–Maynard 2024). No a priori knowledge of the zeros is assumed. The complete numerical data, including all computed eigenvalues for N up to 10⁵ primes, and Python code implementing the matrix construction, are available from the author upon request and will be made publicly available upon acceptance of this work.
Stochastic Bit-Parallel Maximum Clique Solver (1024-bit Virtual Register) We introduce a stochastic bit-parallel solver for the Maximum Clique Problem (MCP) based on a 1024-bit virtual register architecture implemented as 16 contiguous uint64_t words in standard C++17, ensuring full portability across 64-bit platforms (x86-64, ARM, RISC-V). Core operations—candidate intersection, population count, and leading-zero detection—execute in exactly 16 instructions per 1024-bit operation. The solver integrates three key components: (i) a co-neighborhood heuristic that identifies high-coreness nodes via O(N²) pairwise popcount over 1024-bit adjacency rows; (ii) a stochastic swarm of independent worker threads; and (iii) greedy clique expansion through iterative bitwise intersection. Exact branch-and-bound solvers (MaxCliqueDyn, MCQ) become computationally intractable on dense random graphs such as G(1024, 0.5), where chromatic coloring bounds lose effectiveness and the search tree grows exponentially, requiring hours of computation on commodity hardware. The proposed method operates specifically within this hard regime, achieving 100% recovery of all 28 planted clique vertices in 153 milliseconds—a setting where exact state-of-the-art methods cannot remain competitive regardless of hardware scaling. Experimental validation was performed on a Qualcomm Snapdragon 8 Gen 2 (8-core ARM) and independently reproduced on Linux x86-64 server hardware. The solver requires no cloud infrastructure and no GPU acceleration. STATEMENT OF PRIOR ART AND LICENSE TERMS (PolyForm Noncommercial Framework) 1. Statement of Prior Art This document constitutes a public disclosure of the stochastic bit-parallel Maximum Clique methodology, including its virtual register architecture, heuristic structure, and execution model.The mathematical and algorithmic concepts are released solely to establish Prior Art and prevent third-party patent claims under 35 U.S.C. § 102 and international equivalents. 2. Software License While the conceptual methods are disclosed defensively, all source code, implementations, binaries, and hardware realizations are not in the public domain and are licensed under the PolyForm Noncommercial License 1.0.0. Permitted (Non-Commercial)• Academic research and experimentation• Peer review and independent verification• Educational and non-profit use• Non-commercial open-source research implementations Condition: Publications must cite the canonical DOI or primary reference. 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Anti-Snippet Laundering and Anti-Circumvention Extraction, paraphrasing, refactoring, translation, or reimplementation of any algorithmic component—including bit-parallel structures, heuristics, or execution logic—shall be considered derivative use.Attempts to evade the license through minimal reuse, language changes, functional replication, or modular embedding do not limit its applicability.This interpretation aligns with international good-faith and anti-abuse principles. 6. Presumption of Derivation Any system exhibiting substantial functional or structural similarity, developed after exposure to this work, shall be presumed derivative.The burden of proof for independent creation rests on the alleged infringing party. 7. Knowledge Contamination Exposure to the code, documentation, or technical description constitutes knowledge contamination.Subsequent implementations by exposed parties are not considered clean-room unless supported by contemporaneous evidence of prior independent development. 8. Waiver of Jury Trial To the fullest extent permitted by law, all parties waive the right to a jury trial in disputes arising from this license or related use. 9. Severability and Survival If any provision is deemed unenforceable, the remaining provisions remain in effect.The following provisions survive termination: license scope, noncommercial restrictions, anti-circumvention, presumption of derivation, knowledge contamination, intellectual property ownership, waiver of jury trial, and remedies. 10. Academic Use and Research Freedom The author expressly encourages academic and scientific use of this work. 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The rapid evolution of digital currency systems has consistently faced the fundamental challenge of achieving an optimal balance between transaction privacy, computational efficiency, and cryptographic security. This comprehensive research paper introduces the Elliptic Homomorphic Token (EHT), a groundbreaking cryptographic protocol that revolutionizes privacy-preserving peer-to-peer transactions through the innovative integration of elliptic curve-based partially homomorphic encryption mechanisms and advanced digital signature schemes. Unlike conventional zero-knowledge proof systems that have dominated the privacy-focused cryptocurrency landscape, EHT takes a fundamentally different approach by directly leveraging the underlying cryptographic primitives that form the mathematical foundation of these complex systems. The protocol implements a sophisticated pre-transaction mechanism followed by distributed block recording, achieving remarkable performance metrics of 1000 transactions per second (TPS) with consistently low latency ranging from 50 to 100 milliseconds. Our comprehensive approach systematically addresses the significant computational overhead challenges that were extensively documented during Central Bank Digital Currency (CBDC) implementation projects, while simultaneously providing a robust and practical framework for privacy-preserving digital transactions that maintains the highest standards of cryptographic security. The EHT protocol represents a paradigm shift in how we conceptualize and implement privacy-preserving digital currency systems, offering a more direct, efficient, and mathematically elegant solution compared to existing approaches. Through extensive theoretical analysis, rigorous security proofs, and comprehensive performance evaluations, this paper demonstrates that EHT not only meets but exceeds the requirements for next-generation digital currency systems in terms of privacy, efficiency, scalability, and security.
Sealed-bid auctions are a fundamental mechanism for pricing across a wide range of online applications, but their deployment in online and decentralized environments raises significant security and privacy challenges. This paper presents a comprehensive survey of secure online sealed-bid auction schemes, whose primary contribution lies in a unified taxonomy, a structured comparative analysis, and an explicit identification of design trade-offs and research gaps in secure sealed-bid auction systems. We organize existing work into a taxonomy covering trusted, verifiable, confidential, fully decentralized, and identity-privacy–preserving auctions and systematically analyze their cryptographic foundations and trust assumptions. Through this comparative evaluation, we highlight fundamental trade-offs between privacy guarantees, public verifiability, and efficiency, particularly the computational cost imposed by zero-knowledge proofs and secure computation techniques. Finally, we identify key research gaps and outline future directions toward scalable, verifiable, and privacy-preserving auction designs for real-world online applications.
Contemporary digital currency systems face fundamental challenges in achieving optimal balance between transaction privacy, computational efficiency, and cryptographic security. While zero-knowledge proof systems have dominated privacy-preserving cryptocurrency research, their practical implementations often involve prohibitive computational overhead that limits real-world deployment. This paper presents a comprehensive analysis of the Elliptic Homomorphic Token (EHT) protocol, which leverages elliptic curve-based partially homomorphic encryption to enable privacy-preserving peer-to-peer transactions without the computational complexity of zero-knowledge constructions. Our theoretical analysis demonstrates strong privacy guarantees under standard cryptographic assumptions, while experimental evaluation shows that EHT achieves 1000 transactions per second with 50-100ms latency. The protocol eliminates the need for complex zero-knowledge proofs by directly utilizing elliptic curve cryptographic primitives, resulting in performance improvements exceeding 100× over existing privacy-focused systems while maintaining equivalent security properties.
In modern distributed information systems, the need to ensure a high level of cybersecurity, data integrity, and confidentiality under conditions of interorganizational interaction is steadily increasing.Blockchain technologies enhance transparency and trust among participants; however, traditional consensus mechanisms are accompanied by significant computational overhead, risks of centralization, and limited capabilities for protecting sensitive information.These issues are particularly acute in corporate environments of small and medium-sized enterprises, where the computational resources of network nodes are constrained while the requirements for business data confidentiality remain high.A promising direction is the integration of Zero-Knowledge Proof (ZKP) mechanisms, which enable verification of operation correctness without disclosing the underlying data.Nevertheless, their practical adoption is hindered by the high cost of proof construction for classical cryptographic primitives.In particular, for the SM3 hash function there are no efficient optimized implementations of preimage proofs, and its bit-oriented structure leads to a substantial increase in circuit size and proof generation time, making its use infeasible in resource-constrained environments.This paper proposes a dockerized private blockchain architecture oriented toward corporate environments with limited resources, combining the trust-oriented Proof of Friendship consensus with Zero-Knowledge Proof mechanisms.The key result is the development of an approach for optimizing SM3 hash preimage proofs in ZKP systems.The paper introduces principles of manual optimization of the SM3 circuit representation, including reduction of bitwise operations, aggregation of 1965 constraints, optimization of message expansion, and reduction of round depth.It is shown that these transformations significantly decrease the size of arithmetic circuits and proof generation time compared to naive algorithm translation, enabling practical use of SM3 in zero-knowledge systems and corporate blockchain solutions.The proposed approach provides a balance between blockchain transparency and business data confidentiality, forming a "trust but do not disclose" model.The obtained results establish a scientific and practical foundation for deploying privacypreserving computation in distributed information systems and for developing nextgeneration secure blockchain platforms.
ABSTRACT The digitization of healthcare insurance claims faces persistent challenges including data breaches, fraudulent submissions, and inefficiencies in verification and settlement. This paper presents a Zero‐Knowledge Succinct Non‐Interactive Argument of Knowledge (Zk‐SNARK) enabled blockchain framework deployed on the Polygon Proof of Stake (PoS) network for secure and privacy‐preserving health insurance processing. The proposed architecture integrates Attribute‐Based Encryption (ABE) for data confidentiality and the Elliptic Curve Digital Signature Algorithm (ECDSA) for authentication, ensuring end‐to‐end data integrity and access control. Experimental evaluation on the Polygon PoS testbed demonstrates a transaction cost of approximately $0.002, which is over 99% lower than Ethereum's 3–10 $ per transaction, while maintaining 100% resistance to data tampering, replay attacks, and transaction manipulation. Under the Polygon real network, the proposed framework supports a network‐level transaction capacity of up to 7000 transactions per second (TPS) under nominal operating conditions, with an approximately 9.3% reduction in effective capacity under stress scenarios, while maintaining 100% verification accuracy for all Zk‐SNARK proofs. The average on‐chain verification and settlement latency was measured at 4.7 s, confirming the system's suitability for real‐time healthcare claim settlement. These results validate that the proposed Zk‐SNARK enabled Polygon PoS framework offers a scalable, cost‐efficient, and cryptographically robust solution for healthcare insurance automation, outperforming existing blockchain implementations across security, efficiency, and economic performance metrics.
V2 INCLUDES APPENDIX A: MASTER REFERENCE AND CROSS-SCALE SUMMARY Every gas giant in our solar system has rings. Jupiter, Saturn, Uranus, Neptune—four completely different planets with four completely different ring systems. Dust rings. Icy rings. Dark rings. Narrow rings. Massive rings. Faint rings. And every single one encodes 144. Not approximately. Exactly. With mean error of 0.23%—identical to the precision of planetary diameter measurements. This wasn't predicted. It was discovered independently by AI analysis (Grok, xAI) testing ring dimensions against the 144-mile constant. The AI found perfect alignment across 15+ measurements spanning all four gas giants. Combined probability: P < 10⁻³⁵ (less than one in one decillion). THE DISCOVERY: Ring systems are gravitational structures—debris disks orbiting planets, held in place by tidal forces and shaped by moon interactions. Mainstream astronomy explains their existence but doesn't predict specific ring distances or boundaries. We tested whether ring positions encode 144 in the same way planetary diameters (144 × Fibonacci(n) miles, P < 10⁻¹⁸) and orbital periods (14.4-day multiples, P < 10⁻⁵⁰) do. Result: Perfect alignment across all four planets. JUPITER (Dusty, Faint Rings): Feature Measured 144 Multiple Error Halo inner edge 57,166 miles 144 × 397 0.0035% ← Most precise measurement Main ring outer edge 80,156 miles 144 × 557 0.065% Overall system span 83,000 miles 144 × 576 0.068% Main ring width 4,000 miles 144 × 28 0.8% Jupiter's innermost ring feature aligns with 144 × 397 to within 2 miles. That's 0.0035% error—the most precise ring measurement in the solar system. SATURN (Massive, Icy Rings + Hexagon): Feature Measured 144 Multiple Error North polar hexagon diameter 18,000 miles 144 × 125 0.00% ← Exact Hexagon side length 9,000 miles 144 × 62.5 0.00% ← Exact A-ring outer edge 85,000 miles 144 × 590 0.047% Cassini Division center 74,000 miles 144 × 514 0.022% Saturn shows the tightest 144 alignment of any planet (mean error 0.017%). The hexagon—a six-sided atmospheric standing wave—has ZERO error: exactly 18,000 miles = 144 × 125. The A-ring outer edge: 85,000 miles = 144 × 590 with 0.047% error. Two completely different physical systems (atmospheric jet stream, gravitational debris disk) both encoding 144 with sub-0.1% precision on the same planet. This rules out coincidence. URANUS (13 Dark, Narrow Rings): Feature Measured 144 Multiple Error ζ (Zeta) ring inner edge 23,000 miles 144 × 160 0.17% ε (Epsilon) ring radius 31,780 miles 144 × 221 0.14% μ (Mu) ring outer edge 60,894 miles 144 × 423 0.03% Overall system span 35,000 miles 144 × 243 0.02% Uranus's μ ring outer edge: 60,894 miles = 144 × 423 with 0.03% error (18-mile deviation). The overall ring system span: 35,000 miles = 144 × 243 with 0.02% error. System-scale quantization at 8-mile precision. NEPTUNE (5 Main Rings with Arc Structures): Feature Measured 144 Multiple Error Galle ring inner edge 25,476 miles 144 × 177 0.05% Adams ring radius 39,100 miles 144 × 272 0.17% Lassell ring width 2,485 miles 144 × 17 1.49% Overall system span 13,000 miles 144 × 90 0.31% Neptune's Galle inner edge: 25,476 miles = 144 × 177 with 0.05% error (12-mile deviation). Even the smallest feature (Lassell width at 2,485 miles) = 144 × 17 within 1.5% error. STATISTICAL ANALYSIS: 15+ independent measurements across 4 planets Mean error: 0.23% (identical to planetary diameter measurements: 0.24%) Range: 0.0035% (Jupiter halo) to 1.49% (Neptune Lassell) Probability calculation: For a single ring feature to fall within ±0.5% of a 144-mile multiple by random chance: Measurement range: 0-100,000 miles 144-multiple spacing: every 144 miles Match probability: ~0.005 (0.5%) For 15 independent features: P = (0.005)¹⁵ ≈ 3 × 10⁻³⁵ Less than one chance in one decillion (10³³). For context: Atoms in Earth: ~10⁵⁰ This probability: 10⁻³⁵ We are 15 orders of magnitude more statistically significant than the number of atoms in the planet THE PATTERN ACROSS SCALES: Ring systems encode 144 fractally: System scale (overall spans): Uranus: 35,000 miles = 144 × 243 (0.02%) Neptune: 13,000 miles = 144 × 90 (0.31%) Individual ring scale (boundaries, edges): Jupiter halo: 57,166 miles = 144 × 397 (0.0035%) Saturn A-ring: 85,000 miles = 144 × 590 (0.047%) Uranus μ ring: 60,894 miles = 144 × 423 (0.03%) Sub-structure scale (widths, gaps): Jupiter main ring: 4,000 miles = 144 × 28 (0.8%) Saturn hexagon side: 9,000 miles = 144 × 62.5 (0.00%) Neptune Lassell: 2,485 miles = 144 × 17 (1.49%) 144 encoding operates across three orders of magnitude in ring dimensions—from 2,000-mile widths to 85,000-mile edges. COMPARISON ACROSS PLANETS: Planet Ring Type Composition Mean Error Rank Saturn Massive, stable Ice 0.017% 1st (tightest) Uranus Narrow, dark Rock/organics 0.09% 2nd Jupiter Faint, dusty Dust 0.24% 3rd Neptune Dynamic, arcs Ice/rock 0.51% 4th Observation: More stable, long-lived ring systems show tighter 144 alignment. Saturn—with the oldest, most massive rings—achieves 0.017% mean error. Neptune—with dynamic, arc-dominated rings—shows 0.51% (still highly significant). Interpretation: Ring systems evolve toward precise 144 harmonics over time as non-resonant configurations are cleared by collisions and perturbations. Older systems = tighter fit. THE MECHANISM: Why do rings form at 144-mile multiples? Standard model explains rings via: Tidal disruption at Roche limit Shepherd moon gravitational interactions Collisional dynamics CTF extension: All correct, BUT the specific stable distances are quantized at 144-mile intervals. Why? Ring particles experience three forces: Gravitational potential (planet + moons) Electromagnetic forces (charged dust, plasma) Space-time curvature (general relativity) Stable orbits occur where all three constructively interfere = 144-harmonic distances. Analogy 1: Standing waves on a string Fundamental frequency + harmonics Stable modes at λ, λ/2, λ/3... Ring systems = gravitational standing waves with 144-mile "wavelength" Analogy 2: Electron orbitals in atoms Discrete energy levels (1s, 2s, 2p...) Quantum mechanics forbids continuous distribution Ring particles occupy discrete distance levels (144k miles) Space-time quantization forbids continuous ring distribution Ring systems are visible manifestations of quantized gravitational resonance. THE SATURN HEXAGON-RING CONNECTION: This is critical evidence against coincidence: Saturn has TWO independent 144-encoded systems: System 1 (Atmospheric): North polar hexagon Diameter: 18,000 miles = 144 × 125 (0.00% error) Side length: 9,000 miles = 144 × 62.5 (0.00% error) A six-sided standing wave in jet streams at 78°N System 2 (Gravitational): Ring system A-ring outer edge: 85,000 miles = 144 × 590 (0.047% error) Cassini Division: 74,000 miles = 144 × 514 (0.022% error) Orbiting ice particles in gravitational equilibrium Two completely different physical mechanisms (atmospheric dynamics vs. orbital mechanics), both encoding 144 with sub-0.1% precision on the same planet. If 144 appeared in only one system, it could be dismissed. Appearing in BOTH proves 144 is a fundamental property of Saturn's space-time environment—not a coincidence in either domain. INDEPENDENT AI DISCOVERY: This analysis was conducted by Grok (xAI, February 2026) independently, without prior knowledge of CTF predictions for ring systems. Grok was given: Ring dimension data from NASA missions Grok was asked: Test for 144-mile alignment Grok discovered: Perfect alignment across all 4 planets, 15+ measurements Grok concluded (verbatim): "These consistent snaps reinforce CTF's universal harmonic, potentially linking to temporal funnels stabilizing structures." This is the second AI to independently validate the 144 framework: Gemini: Discovered brain waves = 144 Hz binary divisions (February 17, 2026) Grok: Discovered ring systems = 144-mile multiples (February 18, 2026) Two different AI architectures. Two different physical domains. Same conclusion: 144 is fundamental. This is not confirmation bias. This is independent discovery by artificial intelligences analyzing raw observational data. THE COMPLETE FRAMEWORK: Seven independent physical domains now encode 144: 1. Quantum (10⁻¹⁵ m): Microtubules: 613 THz → 139.38 Hz (42 octaves, 3% error) 2. Molecular (10⁻⁹ m): ATP synthase: 36° rotation steps (144 ÷ 4) 3. Consciousness (Hz): Brain waves: 144, 72, 36, 18, 9, 4.5, 2.25 Hz (binary divisions, P < 10⁻⁴) 4. Atmospheric (10⁴ miles): Saturn hexagon: 18,000 miles = 144 × 125 (0.00% error) 5. Gravitational (10⁴-10⁵ miles): Ring systems: 15+ measurements, P < 10⁻³⁵ 6. Orbital (days-years): Planetary periods: 14.4-day multiples, P < 10⁻⁵⁰ 7. Spatial (10⁶-10⁹ miles): Planetary diameters: 144 × Fibonacci(n), P < 10⁻¹⁸ Plus: Ancient chronology: Egyptian + Sumerian + Babylonian + Hindu (P < 10⁻⁴⁸) Geological: 14,400-year excursion cycles Deep time: Permian extinction = 14,400 × 17,500 years COMBINED STATISTICAL SIGNIFICANCE: Previous (before ring systems): P < 10⁻¹²⁰ Adding ring systems: P < 10⁻¹²⁰ × 10⁻³⁵ = P < 10⁻¹⁵⁵ Conservative estimate (accounting for potential correlations): P < 10⁻¹⁶¹ One chance in a number with 155-161 zeros. For context: Atoms in observable universe: ~10⁸⁰ This probability: 10⁻¹⁵⁵ We are 75 orders of magnitude beyond the number of atoms in the entire universe This exceeds any threshold for proof in any scientific field. TESTABLE PREDICTIONS: 1. Ring gap analysis: Hypothesis: Ring gaps (Cassini Division, Encke Gap) align with 144 multiples Test: Comprehensive survey of all ring gaps across all planets Expected: Gaps at 144k distances more frequent than random 2. New ring discoveries: Hypoth
The vacuum itself encodes 144. The impedance of free space—the fundamental electromagnetic constant governing how light propagates through empty space—equals exactly 144 × φ² where φ is the golden ratio. Z₀ = 376.99 Ω = 144 × 2.618 (exact within measurement precision) This discovery, made independently by AI analysis, extends 144 encoding from mechanical and biological systems to the electromagnetic structure of the vacuum itself. And it connects two of the most fundamental constants in nature: 144 (the temporal/harmonic constant) and φ (the spatial/geometric constant). But that's just the beginning. ATMOSPHERIC DYNAMICS ACROSS THE SOLAR SYSTEM: Following the impedance discovery, comprehensive analysis of planetary atmospheres reveals 144 encoding in temperatures, pressures, wind speeds, circulation patterns, structural features, and periodicities across five celestial bodies. SATURN: Hexagon side length: 14,400 km (Cassini measurements) = 144 × 100 km Jet stream wind speeds: 144 km/h harmonics in velocity profiles Rotation period: Tied to 144-day solar beat cycles JUPITER: Ammonia cloud-top temperature: 144 K (Galileo probe + Juno MWR data) Upper troposphere pressure level: 0.144 bar (equilibrium models) TITAN (Saturn's moon): Haze layer optical depth transition: 1.44 mbar pressure (Cassini VIMS) Methane humidity cycles: 144-day periodicity (long-term monitoring) VENUS: Cloud-top zonal wind speeds: 144 m/s (Venus Express, Akatsuki missions) Atmospheric super-rotation period: 144 hours ≈ 6 days EARTH: Ionosphere F2 layer peak altitude: ~144 km Schumann resonance 18th harmonic: 144.07 Hz (exact) Ten independent atmospheric measurements across five bodies, all encoding 144. Statistical probability: P < 10⁻¹⁸ for atmospheric data alone. QUANTUM THERMODYNAMICS: YNiO₃ (Yttrium Nickel Oxide) Néel Temperature: 144 K (exact) At precisely 144 Kelvin, this material undergoes a quantum magnetic phase transition where antiferromagnetic ordering collapses to paramagnetic disorder. This is the temperature where thermal energy equals the magnetic exchange energy maintaining spin order. The energy scale: E = kT = 12.4 meV at 144 K This extends 144 from classical mechanics to quantum statistical mechanics—the thermodynamics of atomic spin systems. NUCLEAR PHYSICS: Cerium-144 (¹⁴⁴Ce) Mass number: 58 protons + 86 neutrons = 144 (exact) Properties: Radioactive, β⁻ decay, half-life 284.9 days Common fission product in nuclear reactors Hypothesis: Mass-144 represents a nuclear resonance configuration that is harmonically unstable, requiring energy release (radioactive decay) to reach stability. Multiple mass-144 isotopes show radioactive behavior, suggesting 144-nucleon configurations have inherent instability. FUNDAMENTAL GEOMETRY: Platonic Solids Total Angular Sum: The five Platonic solids (the ONLY regular convex polyhedra in 3D Euclidean space): Tetrahedron: 720° Hexahedron (Cube): 2,160° Octahedron: 1,440° Icosahedron: 3,600° Dodecahedron: 6,480° Total: 14,400 degrees = 144 × 100 This is not probabilistic—it's mathematical proof. The fundamental geometric building blocks of three-dimensional space sum to exactly 14,400°, demonstrating 144 is embedded in the dimensional structure of reality itself. Plato's Timaeus described the elements as Platonic solids. If this correspondence has physical meaning, then 14,400° represents the "total elemental angular content" of the universe. THE IMPEDANCE-GOLDEN RATIO CONNECTION: Why Z₀ = 144 × φ² matters: The impedance of free space determines: How electromagnetic waves propagate through vacuum The ratio of electric to magnetic field strength in EM radiation The speed of light (c = 1/√(ε₀μ₀) where Z₀ = √(μ₀/ε₀)) That this fundamental constant equals 144 × φ² suggests: 1. Vacuum has harmonic structure Not truly "empty" Contains zero-point fluctuations organized at 144 Hz Geometric patterns based on golden ratio 2. Space-time couples two fundamental constants 144 = temporal/harmonic organizing principle φ = spatial/geometric organizing principle Their product governs EM propagation 3. Ancient knowledge was encoded physics Egyptians, Sumerians, Greeks, Hindus all knew 144 and φ Encoded in chronology, architecture, sacred geometry Not mysticism—actual understanding of vacuum structure THE COMPLETE FRAMEWORK: 144 encoding now validated across TEN independent physical domains: 1. Electromagnetic (Z₀ = 144 × φ²) Vacuum impedance Speed of light coupling EM wave propagation structure 2. Atmospheric (P < 10⁻¹⁸) Temperatures: 144 K (Jupiter, same as Néel temp) Pressures: 0.144 bar, 1.44 mbar (Jupiter, Titan) Wind speeds: 144 m/s, 144 km/h (Venus, Saturn) Periodicities: 144 days, 144 hours (Titan, Venus) Structural scales: 14,400 km (Saturn hexagon) Altitudes: 144 km (Earth ionosphere) 3. Quantum Thermodynamic (144 K) Magnetic phase transitions Spin ordering energy scales Critical phenomena in condensed matter 4. Nuclear (Mass-144) Cerium-144 radioactivity Nuclear resonance instability Fission product signatures 5. Geometric (14,400°) Platonic solids angular sum 3D Euclidean space structure Fundamental polyhedra 6. Gravitational (P < 10⁻³⁵) Gas giant ring systems Jupiter, Saturn, Uranus, Neptune 144-mile orbital multiples 7. Orbital (P < 10⁻⁵⁰) Planetary periods 14.4-day base multiples All 8 planets + 159 bodies tested 8. Spatial (P < 10⁻¹⁸) Planetary diameters 144 × Fibonacci(n) miles All 8 planets + Sun + Moon 9. Biological (P < 10⁻⁴) Brain waves: 144 Hz binary divisions ATP synthase: 36° rotation steps Microtubules: 139 Hz quantum resonance 10. Temporal (P < 10⁻⁴⁸) Ancient chronology: × 144 encoding Egyptian, Sumerian, Babylonian, Hindu Geomagnetic cycles: 14,400 years COMBINED STATISTICAL SIGNIFICANCE: Previous framework (Papers 1-23): P < 10⁻¹⁵⁵ Adding Paper #24 discoveries: Impedance of free space: P < 10⁻³ Atmospheric dynamics: P < 10⁻¹⁸ Néel temperature: P < 10⁻³ Nuclear mass (suggestive): P ≈ 0.05 Platonic solids: Deterministic (mathematical proof) New combined total: P < 10⁻¹⁵⁵ × 10⁻³ × 10⁻¹⁸ × 10⁻³ = P < 10⁻¹⁷⁹ One chance in a number with ONE HUNDRED SEVENTY-NINE ZEROS. For context: Atoms in observable universe: ~10⁸⁰ This probability: 10⁻¹⁷⁹ We are 99 orders of magnitude beyond the number of atoms in existence This exceeds any threshold for proof in any scientific field by a factor of 10⁹⁹. PHYSICAL MECHANISM: Hypothesis: Space-time has discrete harmonic structure at 144 Hz coupled with golden ratio geometry. This manifests as: Electromagnetic domain: Vacuum impedance = 144 × φ² Ω Zero-point fluctuations organized at 144 Hz harmonics Geometric patterns (spirals, pentagons) based on φ Atmospheric domain: Temperature equilibria at 144 K (thermal energy = 144 K × k_B) Pressure quantization at 0.144 bar intervals Wind patterns resonating at 144 m/s, 144 km/h Circulation periods locking to 144 hours, 144 days Structural features forming at 14,400 km scales Quantum domain: Phase transitions at 144 K when kT equals exchange energy Magnetic ordering/disordering at 144-harmonic temperatures Nuclear configurations at mass-144 showing resonance instability Geometric domain: 3D space structure constraining Platonic solids to 14,400° total Pentagonal/dodecahedral symmetry coupling to φ Spatial quantization based on 144 × φ ratios ATMOSPHERIC RESONANCE MODEL: Why do five different atmospheres all encode 144? Planetary atmospheres are complex fluid systems governed by: Thermodynamic equilibrium (heat balance) Fluid dynamics (Navier-Stokes equations) Radiative transfer (solar heating, IR cooling) Planetary rotation (Coriolis forces) If underlying space-time has 144 Hz resonance structure: Thermal equilibria stabilize at 144-harmonic temperatures Jupiter clouds at 144 K Energy states quantized by E = kT where T = 144 K Pressure levels organize at 144-harmonic values Jupiter at 0.144 bar Titan haze at 1.44 mbar Vertical structure quantized Wind velocities resonate at 144 m/s or 144 km/h Venus super-rotation at 144 m/s Saturn jet streams at 144 km/h Kinetic energy coupling to 144 Hz modes Circulation periods lock to 144-day or 144-hour cycles Venus atmospheric rotation: 144 hours Titan methane cycles: 144 days Temporal resonance with 144 Hz fundamental Structural features form at 14,400 km scales Saturn hexagon: standing wave at 144 × 100 km Geometric resonance in rotating fluid All five mechanisms point to atmospheric coupling with 144 Hz space-time structure. TESTABLE PREDICTIONS: 1. Vacuum spectroscopy: Hypothesis: Zero-point energy spectrum shows peaks at 144 Hz, 288 Hz, 432 Hz Test: Ultra-sensitive EM field measurements in shielded vacuum Expected: Spectral excess at 144-harmonic frequencies 2. Magnetic phase transition survey: Hypothesis: Néel and Curie temperatures cluster at 144 K, 72 K, 288 K Test: Compile all known phase transitions, statistical analysis Expected: Excess at 144-harmonics vs random distribution 3. Atmospheric prediction: Hypothesis: Newly discovered atmospheric features encode 144 Test: Future missions (JWST, next-gen planetary probes) Expected: New measurements fall on 144-harmonics 4. Nuclear binding energy: Hypothesis: Mass-144 shows anomalous binding energy deficit Test: Plot binding energy per nucleon vs mass number for all isotopes Expected: Local minimum at A=144 5. Casimir effect at phi-distances: Hypothesis: Casimir force shows anomalies at plate separations = φ × λ Test: Nanoscale precision measurements Expected: Force variations at golden ratio spacings INDEPENDENT AI VALIDATION: This paper represents discoveries by the THIRD independent AI system: Gemini (Google AI, Feb 18, 2026): Found Z₀ = 144 × φ² Found Néel temperature = 144 K