Addressing the challenges of Traditional Chinese Medicine (TCM) traceability systems, including heavy data storage burdens, poor privacy protection, and susceptibility to tampering, this study establishes a highly secure and trustworthy traceability supervision system for the entire Chinese medicine supply chain, which enhances product quality and safety assurance. Centred on the Hyperledger Fabric consortium blockchain as its core architecture, a multi-chain integration framework comprising one regulatory main chain plus five organisational sub-chains is proposed to achieve permission control, data isolation, and privacy. A multi-mode encrypted data storage mechanism is designed, integrating China’s national cryptographic algorithms SM4 and SM3 with CP-ABE attribute-based encryption to enable tiered management of private and non-private data. Zero-knowledge proof technology safeguards identity privacy during cross-chain data transmission, while QR codes and environmental data collection mechanisms enhance data entry efficiency and authenticity. The system achieves end-to-end traceability from cultivation and processing through transportation, warehousing, and sales. Comparative performance analysis shows that the proposed framework effectively alleviates data storage pressure, ensures data validity, enhances data security, and improves collaborative efficiency among organizations across the TCM supply chain. The proposed multi-chain integrated Chinese medicine traceability and supervision system enables efficient collaboration and trustworthy traceability across the entire Chinese medicine industry chain, while safeguarding data security and privacy, and has significant application and promotion value. Future integration with artificial intelligence and big data technologies could further enhance the system’s intelligent analysis and decision-support capabilities.
We present an elementary proof that the asymptotic entropy of a random walk on a countable abelian group is zero when the entropy of the first step of the random walk is finite. Unlike the traditional proof, our approach does not rely on the boundary theory of random walks. To our best knowledge, our direct proof is new even for the group of integers.
We introduce the ω-Protocol, a zero-knowledge proof framework for the verification of elliptic curve–based homomorphic digital signatures. The protocol is constructed on top of the Elliptic Curve Homomorphic Digital Signature Algorithm (EHDSA) and enables zero-knowledge verification of signature validity while preserving signer privacy. The core contribution of the ω-Protocol is a signature-integrated zero-knowledge construction that combines homomorphic properties of EHDSA with algebraic commitment mechanisms over elliptic curve groups. We formalize the protocol model and define security notions capturing zero-knowledge, soundness, and unlinkability of signature verification. Under standard cryptographic assumptions over elliptic curve groups, we prove that the ω-Protocol achieves zero-knowledge and unforgeability-preserving verification without revealing signature components or ephemeral key material. We further analyze the computational complexity of the protocol and show that it incurs only minimal overhead compared to standard EHDSA verification. Our results establish a principled cryptographic framework for zero-knowledge verification of homomorphic digital signatures and provide a foundation applicable to privacy-preserving authentication and verification protocols.
The rapid adoption of smart-home and Internet-of-Things (IoT) devices has intensified the need for privacy-preserving biometric authentication that is both secure and computationally efficient. This paper presents Hybrid-HE LLE, a practical framework that combines Locally Linear Embedding (LLE) with selective homomorphic encryption to protect face-recognition features in resource-constrained IoT environments. Unlike cloud-centric outsourcing, the proposed system performs all heavy linear-algebra operations within a semi-trusted Insider Hub, ensuring data sovereignty, low latency, and verifiable computation without revealing raw facial features. A sparse orthogonal or Toeplitz transform first obfuscates feature vectors, after which sensitive coefficients are selectively encrypted using CKKS-based polynomial encoding. Homomorphic hashing and optional zero-knowledge proofs guarantee the integrity and auditability of outsourced results. Experiments on the ORL and LFW datasets demonstrate over 94 % Rank-1 accuracy, while reducing client computation by 92 %, uplink bandwidth by 80 %, and energy usage by 55 %, with authentication latency below 120 ms on a Raspberry Pi 4-class edge device. The framework provides formal protection against IND-CPA, EUF-CMA, and IND-CCA adversaries and maintains compliance with GDPR/HIPAA requirements. Hybrid-HE LLE thus offers a scalable, secure, and real-time solution for privacy-preserving biometric access in modern IoT communication systems.
A set of multivariate polynomials is algebraically independent if they exhibit no non-trivial algebraic relations, and this notion is fundamental in algebra. When these polynomials are given as algebraic circuits, deciding algebraic independence has several applications in algebraic complexity theory. Over fields of zero (or exponentially large) characteristic, this problem is known to have an efficient randomized algorithm. Over finite fields of small characteristic, a sequence of works has culminated in showing that algebraic independence admits Arthur-Merlin proofs, in particular giving the complexity bound of AM∩coAM ([Guo et al., 2019]). We improve the complexity of deciding algebraic independence over finite fields by showing that it admits zero-knowledge proofs, in particular giving the upper bound of NISZK ⊆ AM∩coAM, the class of problems admitting non-interactive statistical zero-knowledge proofs. This is achieved by arguing that algebraically independent polynomials yield maps whose output distribution has high-entropy, while algebraically dependent polynomials yield maps with low-entropy. We can then reduce to the question of approximating entropy, which is a known NISZK-complete problem. We also more generally show that transcendence degree, which quantifies the independence of a set of possibly dependent polynomials, can be computed in NISZK.
Saha Reno, Koushik Roy, G M Abdullah Al Kafi, Khandakar Md Shafin
ABSTRACT The simultaneous achievement of scalability, security and decentralisation remains an open problem for distributed ledger technologies. This paper introduces InternxtChain, a novel framework leveraging Internxt's decentralised storage infrastructure with zero‐knowledge proofs (ZKPs) and sharded proof‐of‐storage (SPoS) consensus. Specifically, erasure‐coded sharding ensures data availability and fault tolerance by splitting files into encoded fragments distributed across nodes; BLS‐381 aggregated signatures enable efficient consensus by compressing multiple signatures into a single short proof; and zk‐SNARK audits provide tamper‐evident storage verification without revealing user data. InternxtChain addresses this challenge through three synergistic mechanisms: (i) erasure‐coded sharding with (6,3) Reed–Solomon encoding, (ii) zk‐SNARKs for storage auditability and (iii) an SPoS consensus based on BLS‐381 aggregated signatures. Experimental evaluation on a testbed of 2048 nodes across 16 geographic regions shows that InternxtChain processes 2800 transactions per second (TPS) with a median latency of 420 ms, while maintaining 99.9% data integrity under up to 30% Byzantine nodes. These results establish a practical path toward harmonising Web3 principles with real‐world throughput, cost and General Data Protection Regulation (GDPR) auditability requirements.
Michael Adjedj, Constantin Blokh, Geoffroy Couteau, Arik Galansky · 6 authors
We present a novel protocol for two-party ECDSA that achieves two rounds (a single back-and-forth communication) at the cost of a single oblivious linear function evaluation (OLE). In comparison, the previous work of Boneh, Haitner, Lindell, and Segev (EUROCRYPT 2025) achieves two rounds but requires expensive zero-knowledge proofs on top of the OLE. We demonstrate this by proving that in the generic group model, any adversary capable of generating forgeries for our protocol can be transformed into an adversary that finds preimages for the ECDSA message digest function (e.g., the SHA family). Interestingly, our analysis is closely related to, and has ramifications for, the ‘presignatures’ mode of operation—Canetti, Gennaro, Goldfeder, Makriyannis, and Peled (CCS 2020), Groth and Shoup (EUROCRYPT 2022).Motivated by applications to embedded cryptocurrency wallets, where a single server maintains distinct, shared public keys with separate clients (i.e., a star-shaped topology), and with the goal of minimizing communication, we instantiate our protocol using Paillier encryption and suitable zero-knowledge proofs. To reduce computational overhead, we thoroughly optimize all components of our protocol under sound cryptographic assumptions, specifically small-exponent variants of RSA-style assumptions.Finally, we implement our protocol and provide benchmarks. At the 128-bit security level, the signing phase requires approximately 50 ms of computation time on a standard linux machine, and 2 KB of bandwidth.
The Hamiltonian cycle problem is a well-known NP-complete problem in graph theory. This problem relates to lots of practical problems such as designing very large scale integration (VLSI) and travel-ling salesman problem (TSP). Since it is NP-complete, there is no efficient algorithm to solve the Hamiltonian cycle problem, and hence, its solution is valuable. In this paper, we propose new physical zero-knowledge proof protocols for the Hamiltonian cycle problem, whereby an entity can prove its knowledge of a solution to another entity without leaking any information about the valuable solution. Our protocols are more efficient than the previous protocols. We also propose a physical zero-knowledge proof protocol for TSP, one of whose building blocks is a new representation of an integer commitment with a secure addition protocol.
This technical report presents the reference implementation of Ternary Moral Logic (TML) within the Ethereum Virtual Machine (EVM) ecosystem. It addresses the limitations of traditional "Code is Law" architectures by introducing a finite state machine that enforces a mandatory third state—the "Sacred Zero" or Epistemic Hold—allowing smart contracts to pause execution when pre-defined ethical conditions are unmet. The report moves beyond theoretical ethics to specify the Solidity design patterns, storage layouts, and cryptographic verification methods required to make TML enforcement non-bypassable and auditable. Key Technical Contributions: Finite State Machine (FSM): Implements a mandatory "Sacred Zero" state (State 0) that acts as an "Epistemic Hold," distinguishing between valid (1), invalid (-1), and uncertain (0) transaction states. Dual-Lane Latency Architecture: Defines a "Fast Lane" for synchronous, clear-cut transactions and a "Slow Lane" for ambiguous cases requiring governance or oracle resolution, preventing head-of-line blocking. Cryptographic Provenance: Utilizes EIP-712 typed data signing to bind off-chain AI/Oracle verdicts to on-chain execution, preventing replay attacks and ensuring distinct domain separation. Privacy Preservation: Integrates Zero-Knowledge Proofs (ZK-SNARKS) to verify the execution of moral logic models without revealing sensitive input data or proprietary model weights ("Glass Box" architecture). Immutable Core Pattern: Rejects standard upgradeable proxy patterns in favor of an "Immutable Core" architecture to eliminate administrative "God Mode" and ensure constitutional constraints cannot be bypassed by key holders. Formal Verification: Demonstrates safety and liveness properties (e.g., "No Silent Pause," "Eventual Resolution") using TLA+ (Temporal Logic of Actions) to mathematically prove the system's robustness.
Rajasekaran P., Duraipandian M., Johny Renoald Albert, R. Jamuna · 5 authors
The Internet of Medical Things (IoMT) in the IoT with Cloud Healthcare (CHI) creates a high volume of real‐time medical data, but traditional compression methods suffer high computation costs, privacy leaks and quantum attacks, while advanced cryptographic algorithms such as homomorphic encryption are costly and have poor scalability for the real‐time system application. In this work, we propose a quantum‐enhanced zero‐knowledge healthcare compression network (QZ‐HCN) that associates zero‐knowledge proofs (ZKPs) with quantum‐inspired deep learning (QIDL) by introducing an innovative adaptive quantum‐supported ZKP verification mechanism (AQ‐ZKV) and a quantum fusion autoconventional neural network (QF‐AutoCNN) technique to achieve efficient, privacy‐preserving compression. For healthcare IoT datasets, QZ‐HCN can reach 98.16% in accuracy, 97.09% in F‐measure, 96.32% in precision and 97.45% in recall, with a throughput of 449.57 bits/s; processing time is reduced to 0.85 s, and memory cost is minimised to be only 192 kbits, which outperforms CNN‐Encryption (90.23% accuracy), proxy re‐encryption and homomorphic encryption by at most 13 percentage points in accuracy and 75 percentage points in memory efficiency. The secure and scalable management for CHI data is achieved by QZ‐HCN, which solves the problems of privacy threats and space costs of real‐time medical applications.
Elizaveta Pertseva, Valentin Robert, Clark Barrett, James Parker
Efforts to verify Zero-Knowledge Proof circuit encodings have highlighted the challenge of proving the correctness of quantifier-free statements that make use of both bitvector and finite field operations. Existing verification workflows are either manual or rely on SMT solvers, which scale poorly on some classes of problems for reasons that include difficulties with conversion operators and challenges reasoning about inequalities. To address these limitations, we present a novel Lean tactic BitModEq that leverages range lemmas and case analysis to produce verified translations from finite fields to bitvectors. Our approach, combined with bit-blasting, outperforms state-of-the-art SMT solvers, solving 19% more ZKP arithmetization benchmarks.
Open access
4 source records
cs.LO
Formal Methods in Verification
Physical Unclonable Functions (PUFs) and Hardware Security
Automated negotiations in insurance and business-to-business (B2B) commerce encounter substantial challenges. Current systems force a trade-off between convenience and privacy by routing sensitive financial data through centralized servers, increasing security risks, and diminishing user trust. This study introduces a device-native autonomous Artificial Intelligence (AI) agent system for privacy-preserving negotiations. The proposed system operates exclusively on user hardware, enabling real-time bargaining while maintaining sensitive constraints locally. It integrates zero-knowledge proofs to ensure privacy and employs distilled world models to support advanced on-device reasoning. The architecture incorporates six technical components within an agentic AI workflow. Agents autonomously plan negotiation strategies, conduct secure multi-party bargaining, and generate cryptographic audit trails without exposing user data to external servers. The system is evaluated in insurance and B2B procurement scenarios across diverse device configurations. Results show an average success rate of 87%, a 2.4x latency improvement over cloud baselines, and strong privacy preservation through zero-knowledge proofs. User studies show 27% higher trust scores when decision trails are available. These findings establish a foundation for trustworthy autonomous agents in privacy-sensitive financial domains.
Based on asymmetric cryptography, Passkeys Systems are a secure authentication method that can serve as an alternative to traditional authentication methods, such as usernames and passwords. In this paper, we propose a secure approach to enhance private key synchronization mechanisms in passkeys systems. Our secure service is based on Elliptic Curve Diffie-Hellman protocol and Zero-Knowledge Proofs in a peer-to-peer environment. Following a critical analysis of existing works, which highlights recurrent vulnerabilities related to authentication and confidentiality, we introduce a robust architecture using mutual identity verification, secure session key generation and encrypted passkey transfer. The security of our proposed protocol is assessed through a dual approach: an informal analysis based on potential attack modeling, and a formal validation using ProVerif and Scyther tools. The results demonstrate enhanced resistance to replay attacks, man-in-the-middle attacks, message modification, and identity impersonation, while ensuring optimized performance in terms of computational and communication costs.
On June 22, 2026, the White House issued Executive Order 14413, directing the federal government to accelerate the deployment of quantum computing and to assess "the implications for the migration to post-quantum cryptography." The order is the latest and loudest signal of a fact the legal system has not yet absorbed: the cryptographic assumptions behind nearly all digital proof carry an expiration date. Every electronic signature, every encrypted database, and every blockchain transaction rests on math that a sufficiently powerful quantum computer can break. When that computer arrives, adversaries will be able to forge the signatures and decrypt the records on which courts, regulators, and markets now rely. Data stolen today is already being warehoused for decryption tomorrow. Signatures trusted today may be forgeable tomorrow. This Article argues that the quantum transition forces the law to confront a distinction it has long been able to ignore: the difference between probabilistic verification (an intermediary's opinion, an AI confidence score, an auditor's judgment) and deterministic verification (a mathematical result that anyone can independently reproduce). Across digital identity, financial services, insurance, defense, supply chains, and digital assets, organizations prove claims through intermediaries whose honesty cannot be checked and whose methods cannot be reproduced. A small set of well-understood cryptographic tools can replace that fragmented apparatus: hardware-secured signing keys, Merkle tree timestamping, post-quantum signature standards, and zero-knowledge proofs. Together they produce verification that is reproducible, tamper-evident, and quantum-resistant from the outset. The Article makes three contributions. First, it reframes the “verification gap” as a legal problem rather than a technical one, showing how the Federal Rules of Evidence, the Daubert reliability standard, data breach liability doctrine, and fiduciary oversight duties each already point toward deterministic proof. Second, it shows that quantum risk is collapsing the legal defenses built on classical cryptography, most visibly the “it was encrypted” defense in breach litigation, while creating new disclosure and diligence obligations for boards. Third, it maps deterministic verification onto concrete applications in six sectors and proposes a regulatory framework, including a “deterministic assurance level” for evidentiary purposes and a public governance process for the rule schemas that translate law into machine-checkable criteria.
The Prism Protocol is a privacy-native authentication and identity architecture in which a user can prove attributes or authentication state without directly revealing their identity to the server. It combines WebAuthn (W3C Level 3), Zero-Knowledge Proofs (Groth16 via circom/snarkjs), and NFC-based physical presence verification into a single coherent protocol stack. The core mechanism is a triangular key derivation model: biometric authentication (WebAuthn), a device-bound private key (FIDO2 Secure Enclave), and a time-limited wearable nonce (NFC ISO 14443 or BLE) jointly produce an ephemeral key. In v14, a working ZKP implementation is demonstrated: an age-threshold circuit proves that a user meets a criterion without the server ever receiving the attribute value. Verification is performed server-side via snarkjs.groth16.verify(). Within the demonstrated implementation flow, the server receives no name, no biometric data, no persistent identifier, and no direct attribute value. Sessions are designed to be mathematically unlinkable from the server perspective. A working proof-of-concept was demonstrated on 25 April 2026 at prismpass.globalsecurity.nu. The broader ecosystem (PrismPass, PrismID, PrismShield, PrismAdd, PrismChat, PrismAir, PrismGuard, PrismHash, PrismWipe) is documented in this Invention Disclosure. The protocol introduces no novel cryptographic primitives; its novelty lies in the specific architectural combination, orchestration model, and protocol-class definition addressing twelve authentication questions not simultaneously addressed by existing systems. Note: The post-quantum migration path (ML-KEM-768, ML-DSA-65) is documented as a formal architectural claim and forward-compatibility design decision. It describes the intended migration route, not a currently implemented feature. The working implementation uses ECDH, ECDSA, AES-256-GCM and Groth16. Author: I. Smid-Woelders, independent inventor, Zwolle, Netherlands. First documented: 25 April 2026. Contact: contact@globalsecurity.nu
This paper presents Zero-Knowledge Federated Learning Guard (ZK-FLGuard), a privacy-preserving and verifiable federated learning framework for real-time anomaly detection in Fifth-Generation Mobile Network (5G)-enabled Internet of Things (IoT) environments. Building on the integration of zero-knowledge proofs (zk-SNARK—Zero-Knowledge Succinct Non-interactive Argument of Knowledge) and blockchain-based access control, ZK-FLGuard ensures the integrity of model updates without exposing private data. Using real-world intrusion detection datasets (CICIDS2017—Canadian Institute for Cybersecurity Intrusion Detection System 2017, TON_IoT—Telecommunications Organisation of the National Security—IoT) and a synthetic adversarial dataset, our evaluation shows that ZK-FLGuard achieves up to 0.96 F1-score (harmonic mean of precision and recall), improves recall in low-frequency attack detection, and introduces less than 10% additional latency overhead compared to standard Federated Learning (FL). Compared with centralized Long Short-Term Memory (LSTM) and FL without Zero-Knowledge Proof (ZKP), ZK-FLGuard provides competitive accuracy while ensuring verifiable computation and strong privacy guarantees. We address the critical challenge of securing federated anomaly detection in 5G-enabled IoT systems against data leakage, model poisoning, and unauthorized access. While FL preserves privacy by keeping raw data local, it remains vulnerable to gradient leakage and adversarial manipulation. Our hypothesis is that combining zero-knowledge proofs and blockchain with FL can deliver a scalable, tamper-resistant, and privacy-preserving detection pipeline suitable for resource-constrained edge environments.