The integration of continuous Zero Trust Architecture (ZTA) into Segment Routing over IPv6 (SRv6) networks introduces severe performance bottlenecks and physical constraints of the Maximum Transmission Unit (MTU). Specifically, naively embedding massive Zero-Knowledge Proof (ZKP) for per-packet authentication inevitably triggers catastrophic fragmentation and disrupts stateless forwarding. To address these fundamental limitations, this paper proposes a novel session-bound zero-knowledge authorization framework tailored for SRv6 programmable data planes. Our architecture explicitly decouples heavyweight cryptographic validations from the active forwarding path. Massive ZKP payloads are processed asynchronously via payload transmission in the control plane, while the data plane enforces line-rate access control using lightweight 32-byte capability tokens encapsulated in customized SRv6 extension headers. Furthermore, to mathematically balance robust security with forwarding efficiency, we formulate the dynamic verification process as a risk-aware Partially Observable Markov Decision Process (POMDP). Using in-band network telemetry, we derive an Adaptive Threshold Verification (ATV) algorithm that yields a closed-form <inline-formula> <tex-math notation="LaTeX">$O(1)$ </tex-math></inline-formula> complexity optimal scheduling policy. Extensive evaluations demonstrate that the decoupled mechanism seamlessly resolves the MTU bottleneck, maintaining stable baseline throughput under massive concurrent sessions. Concurrently, the ATV algorithm intelligently adapts to real-time threat intensities, conserving control-plane resources during safe periods while instantaneously triggering precise re-verifications against covert and volumetric cyberattacks.
We introduce behavior-bound signatures (BBS), a signature framework in which each signature attests not only to signer authenticity but also to the satisfaction of a prescribed behavioral policy. Unlike traditional digital signatures—whose acceptance is determined by identity validity alone—BBS enforces compliance at the level of the verification predicate: a signature is accepted if and only if a zero-knowledge proof establishes that a residual function value δ(x)=∣ϕ(x)−τ∣\delta(x)=|\phi(x)-\tau|δ(x)=∣ϕ(x)−τ∣ lies below a threshold ε\varepsilonε. Thus, compliance safety is reduced to zero-knowledge soundness rather than to external monitoring or honest-majority assumptions. We formalize policy-soundness under chosen-message attacks (PS-CMA), extending EUF-CMA by requiring that no adversary can produce a valid signature for any message whose induced action violates the policy predicate. We prove that BBS achieves PS-CMA security under standard assumptions: binding of Pedersen commitments, collision resistance of Poseidon, and soundness of the underlying zero-knowledge proof system (e.g., Bulletproofs or PLONK). Our construction instantiates the policy predicate via a private structure function ϕ(x)\phi(x)ϕ(x) and enforces δ(x)<ε\delta(x)<\varepsilonδ(x)<ε through a zero-knowledge range constraint, while revealing no information about the private parameters. Sequential signatures compose into a hash-linked trajectory, enabling verifiable ordering and completeness of action sequences. We additionally define the Function Approximation Inversion Problem (FAIP) as a conjectured hardness property of the structure function, and emphasize that the security of BBS does not rely on this conjecture.
Open access
Cryptography and Data Security
Physical Unclonable Functions (PUFs) and Hardware Security
Abstract The Congo Basin, comprising the world’s second-largest tropical rainforest, presents both critical environmental challenges and unique opportunities for sustainable development. This chapter evaluates key pathways for environmentally sustainable development in the region, with an emphasis on extractive industries, renewable energy, agroforestry, biodiversity conservation, ecotourism, and climate and carbon finance. Using regional indicators such as the Fragile States Index (FSI), Human Development Index (HDI), and Environmental Performance Index (EPI), the authors highlight the structural barriers—including weak governance, institutional fragility, and extreme poverty—that constrain the region’s development trajectory. Despite these challenges, the Basin’s ecological wealth offers potential for transformative interventions. Strategies such as Reduced-Impact Logging for Climate (RIL-C), sustainable mining practices, decentralized renewable energy systems, and integrated agroforestry models are analyzed for their capacity to reduce emissions, protect biodiversity, and enhance local livelihoods. The chapter further explores the potential of REDD+ and emerging carbon market frameworks to finance conservation and climate mitigation efforts. Emphasizing the role of participatory governance, indigenous knowledge systems, and scientific innovation, the chapter underscores the necessity of context-specific, cross-sectoral approaches to operationalize sustainability in one of the planet’s most ecologically and geopolitically complex regions.
Open access
Mining and Resource Management
Economic Growth and Development
Conservation, Biodiversity, and Resource Management
Range arguments are a type of zero-knowledge proofs that aim to prove that a prover's committed value falls within a specified range for a verifier. Previously, most range arguments were constructed based on the discrete logarithm (DLOG) assumption, and hence, exponentiation operation is required for proof generation and verification. In addition, it is generally known that splitting a zero-knowledge proof protocol into a preprocessing phase and an online phase makes computation after fixing the input efficient. Still, such protocol has yet to be known for range arguments. This paper proposes an efficient range arguments protocol with a preprocessing phase. Our proposal takes a new approach by using arithmetic circuits to express the constraints that the prover must prove. The prover (resp. verifier) can generate (resp. verify) a part of proof based on multiplication and addition operations instead of exponentiation operations. Our range argument is a generic construction that does not rely on any particular mathematical assumptions, which enables us to construct a post-quantum range argument. The implementation evaluation shows that the total computation time for the prover and verifier in the online phase is efficient compared to Bulletproofs, one of the state-of-the-art range proofs. Especially, the prover computation is efficient.
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.
This study assesses whether Bitcoin’s linkage with AI equities remains robust after accounting for equity risk sentiment. To this end, the study employs the multiscale quantile‐on‐quantile correlation (MSQQC) and multiscale quantile‐on‐quantile partial correlation (MSQQPC) approaches, using daily data covering 02/01/2019–16/06/2025. The results indicate that BTC–AI comovement is strongly state‐ and frequency‐dependent rather than stable across the joint distribution or across horizons. In the high‐frequency band, dependence is weak and only intermittently significant, with localised negative regions around BTC ≈ 0.20 with AI ≈ 0.30–0.50 and BTC ≈ 0.30 with AI ≈ 0.70. In the mid‐frequency band, significance concentrates in the tails, showing negative dependence under downside stress conditions such as BTC ≈ 0.10–0.30 with AI ≈ 0.10, alongside sign changes when BTC is in upper‐tail states. In the low‐frequency band, dependence becomes broadly positive and significant across most quantile combinations, with limited decoupling when AI is highly elevated (≈ 0.80–0.90) and BTC is also in upper quantiles (≈ 0.70–0.90). Importantly, conditioning on VIX and VVIX does not materially alter these patterns, suggesting that sentiment influences segments of short‐run dependence but does not overturn the longer‐run BTC–AI linkage. The study derives policy recommendations from these findings.
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.