The article systematizes modern methods of zero-knowledge proof (ZKP). Classification features are considered: protocol interactivity, algebraic or stochastic basis, need for trusted setup, type of zero-knowledge, and proof model. Classical schemes (Fiat–Shamir, Schnorr, Blum), modern zk-SNARK and zk-STARK, as well as novel approaches – PLONK, Halo 2, Bulletproofs, lattice-based ZKPs, and machine learning proofs are described. A comparative analysis is conducted according to efficiency, proof size, generation and verification complexity. It is shown that SNARKs provide compactness but require a trusted setup, while STARKs are transparent and post-quantum secure but large. Open problems are highlighted: recursive proofs, standardization, metadata protection, and applications in machine learning. It is concluded that further research in this field is aimed at creating scalable, secure, and quantum-resistant protocols for digital technologies.
Healthcare AI needs large, diverse datasets, yet strict privacy and governance constraints prevent raw data sharing across institutions. Federated learning (FL) mitigates this by training where data reside and exchanging only model updates, but practical deployments still face two core risks: (1) privacy leakage via gradients or updates (membership inference, gradient inversion) and (2) trust in the aggregator, a single point of failure that can drop, alter, or inject contributions undetected. We present zkFL-Health, an architecture that combines FL with zero-knowledge proofs (ZKPs) and Trusted Execution Environments (TEEs) to deliver privacy-preserving, verifiably correct collaborative training for medical AI. Clients locally train and commit their updates; the aggregator operates within a TEE to compute the global update and produces a succinct ZK proof (via Halo2/Nova) that it used exactly the committed inputs and the correct aggregation rule, without revealing any client update to the host. Verifier nodes validate the proof and record cryptographic commitments on-chain, providing an immutable audit trail and removing the need to trust any single party. We outline system and threat models tailored to healthcare, the zkFL-Health protocol, security/privacy guarantees, and a performance evaluation plan spanning accuracy, privacy risk, latency, and cost. This framework enables multi-institutional medical AI with strong confidentiality, integrity, and auditability, key properties for clinical adoption and regulatory compliance.
Blockchain technology is a game-changing invention that guarantees digital transactions on decentralized networks. The vital role that cryptography plays in guaranteeing the authenticity, confidentiality, and integrity of blockchains is examined in this paper. To secure the data on the blockchain and validate transactions, we are examining fundamental cryptographic techniques like hashing, symmetric and asymmetric encryption, and digital signatures. Furthermore, advanced cryptographic solutions that have the potential to improve privacy and scalability—such as homomorphic encryption, zero-knowledge proofs, and zk-SNARKs—are being discussed. Along with reviewing consensus techniques like proof of work and proof of stake, the paper contrasts the main blockchains, including those that are still in development, like Ethereum, Solana, and Hyperledger Fabric. Through an analysis of the advantages and disadvantages of existing cryptographic implementations, the study emphasizes the necessity for additional innovation.
The article systematizes modern methods of zero-knowledge proof (ZKP). Classification features are considered: protocol interactivity, algebraic or stochastic basis, need for trusted setup, type of zero-knowledge, and proof model. Classical schemes (Fiat–Shamir, Schnorr, Blum), modern zk-SNARK and zk-STARK, as well as novel approaches – PLONK, Halo 2, Bulletproofs, lattice-based ZKPs, and machine learning proofs are described. A comparative analysis is conducted according to efficiency, proof size, generation and verification complexity. It is shown that SNARKs provide compactness but require a trusted setup, while STARKs are transparent and post-quantum secure but large. Open problems are highlighted: recursive proofs, standardization, metadata protection, and applications in machine learning. It is concluded that further research in this field is aimed at creating scalable, secure, and quantum-resistant protocols for digital technologies.
The Local Energy Market (LEM) is a key element in the energy sector's transition toward a decentralized system, enabling the integration of a growing number of small generation sources and energy storage facilities located at end-user locations.By utilizing digital energy trading platforms provided by LEMs, small consumers, producers, and prosumers actively participate in system balancing, which, among others, allows them to increase profits and energy independence.The efficiency of energy exchange in LEM is achieved by means of optimization methods that make use of sensitive participant data, such as energy consumption profiles.Therefore, ensuring privacy while simultaneously ensuring trust in the achieved optimal quantitative and qualitative results is crucial.The classic technology used in decentralized systems, i.e., blockchain, does not provide adequate scalability when transactions result from solving optimization problems.In this article, we analyze the possibilities of verifying optimization results by the use of cryptographic zero-knowledge proofs (ZKP).We explain how ZKP can support privacy and enable verification of computations without the need of repeating them for every participant.We also refer to existing ZKP implementations on LEM, while highlighting the barriers of high computational costs that prevent direct implementation of complex optimization algorithms within ZKP protocols.'To overcome these barriers, we present an approach integrating ZKP with optimality certificates, which has significant potential to increase the efficiency of
With the rapid proliferation of smart home cameras, wearable vision devices, and user-generated Consumer Internet of Things (CIoT) content, ensuring visual media authenticity, rightful ownership, and tamper detection has become increasingly challenging. We propose Chain-Visage, a blockchain-assisted framework for secure content authentication and tamper tracing in decentralized CIoT multimedia ecosystems. The termChainreflects the consortium blockchain backbone that guarantees immutable provenance, decentralized ownership management, and copyright revocation, whileVisagesymbolizes the unique visual identity of multimedia content achieved through dual-stage visual hash embedding. The proposed framework integrates Zero-Knowledge Proofs (ZKPs) for privacy-preserving ownership verification and employs optimized smart contracts to manage visual rights, provenance records, and ownership transfers efficiently. Evaluations on a large-scale dataset of over 10,000 real-world images and 3,850 video clips from diverse CIoT devices demonstrate Chain-Visage’s superior performance, achieving 97.5% traceability accuracy, 93% tamper detection sensitivity, and low verification latency even under resource-constrained environments. This work addresses a critical research gap in secure, privacy-preserving, and energy-efficient multimedia ownership control and tamper-resilient content authentication for next-generation CIoT ecosystems.
Open access
Blockchain Technology Applications and Security
Digital Media Forensic Detection
Advanced Steganography and Watermarking Techniques
Aaron Chan, Alex Ding, Frank Sicong Chen, Alan Wu · 6 authors
The rapid integration of Large Language Models (LLMs) into decentralized physical infrastructure networks (DePIN) is currently bottlenecked by the Verifiability Trilemma, which posits that a decentralized inference system cannot simultaneously achieve high computational integrity, low latency, and low cost. Existing cryptographic solutions, such as Zero-Knowledge Machine Learning (ZKML), suffer from superlinear proving overheads (O(k NlogN)) that render them infeasible for billionparameter models. Conversely, optimistic approaches (opML) impose prohibitive dispute windows, preventing real-time interactivity, while recent "Proof of Quality" (PoQ) paradigms sacrifice cryptographic integrity for subjective semantic evaluation, leaving networks vulnerable to model downgrade attacks and reward hacking. In this paper, we introduce Optimistic TEE-Rollups (OTR), a hybrid verification protocol that harmonizes these constraints. OTR leverages NVIDIA H100 Confidential Computing Trusted Execution Environments (TEEs) to provide sub-second Provisional Finality, underpinned by an optimistic fraud-proof mechanism and stochastic Zero-Knowledge spot-checks to mitigate hardware side-channel risks. We formally define Proof of Efficient Attribution (PoEA), a consensus mechanism that cryptographically binds execution traces to hardware attestations, thereby guaranteeing model authenticity. Extensive simulations demonstrate that OTR achieves 99% of the throughput of centralized baselines with a marginal cost overhead of $0.07 per query, maintaining Byzantine fault tolerance against rational adversaries even in the presence of transient hardware vulnerabilities.
In this paper we present BlockMedLedger, a decentralized patient health record management system based on blockchain and IPFS. BlockMedLedger provides solutions to the challenges of healthcare data silos, security vulnerabilities and patient ownership of their own data. The patient centric model supports patients, medical data owners, to have complete control over their own medical data, while providing an efficient process to facilitate secure sharing of the medical data with care providers initiated through smart contracts and cryptographic access controls. The system uses an Ethereum compatible blockchain to support access control decision and IPFS for decentralized encrypted storage of encrypted medical records. The implementation demonstrates good security, efficient access, retrieval and sharing of encrypted health information for health care providers and patients while meeting requirements specified in HIPAA utilizing zero-knowledge proofs and patient consent control features.
Online harassment, incitement to violence, racist behavior, and other harmful content on social media can damage social harmony and even break the law. Traditional blocklisting technologies can block malicious users, but this comes at the expense of identity privacy. The anonymous blocklisting has emerged as an effective mechanism to restrict the abuse of freedom of speech while protecting user identity privacy. However, the state-of-the-art anonymous blocklisting schemes suffer from either poor dynamism or low efficiency. In this paper, we propose $\mathsf{ShadowBlock}$, an efficient dynamic anonymous blocklisting scheme. Specifically, we utilize the pseudorandom function and cryptographic accumulator to construct the public blocklisting, enabling users to prove they are not on the blocklisting in an anonymous manner. To improve verification efficiency, we design an aggregation zero-knowledge proof mechanism that converts multiple verification operations into a single one. In addition, we leverage the accumulator's property to achieve efficient updates of the blocklisting, i.e., the original proof can be reused with minimal updates rather than regenerating the entire proof. Experiments show that $\mathsf{ShadowBlock}$ has better dynamics and efficiency than the existing schemes. Finally, the discussion on applications indicates that $\mathsf{ShadowBlock}$ also holds significant value and has broad prospects in emerging fields such as cross-chain identity management.
Nadia van Niekerk, Brink van der Merwe, Louwrens Labuschagne
In the rapidly evolving realm of blockchain technology, the pursuit of enhanced privacy, security, and scalability has propelled the exploration of cryptographic innovations. Zero-Knowledge Proofs (ZKPs) have emerged as a pivotal solution, addressing diverse challenges across decentralized applications and cryptographic systems. However, the intricate mathematical foundations of ZKPs can pose a barrier to widespread adoption. To bridge this gap, a spectrum of ZKP tools has been developed, abstracting mathematical complexities and enabling developers with varying levels of expertise to incorporate ZKPs into their projects. The exploration of the 5 W’s – Who, What, When, Where, and Why – guides developers in selecting ZKP tools aligned with their specific needs and understanding. This paper serves as a vital resource for developers entering the dynamic landscape of ZKP development. By answering crucial questions and providing nuanced insights into ZKP tools, it empowers developers to navigate this intricate domain effectively. As ZKP technology continues to evolve, our findings contribute to the ongoing dialogue surrounding its implementation, utilization and the ever-adapting toolkit shaping the future of cryptographic innovation. This paper employs a Mining Software Repositories (MSR) approach to unravel insights from the expansive landscape of ZKP development. By delving into GitHub repositories, we categorize author archetypes, discuss ZKP proof constructions, identify phases of tool development, explore the level of understanding required and examine the correlation between tool types and application purposes. Through a metrics-driven analysis, we unveil patterns in tool popularity, development trends, and historical perspectives, offering a comprehensive understanding of the ZKP tooling ecosystem.
Digital systems face not a security failure but an ontological one. Authority on the internet is implemented as code, and code is inherently simulable, reproducible, and scalable. As artificial intelligence exposes this flaw at scale, efforts to secure digital authority through identity, credentials, and probabilistic verification prove structurally insufficient. This paper argues that authority cannot ontologically originate from code, and that all code-based authority systems are therefore structurally vulnerable, regardless of implementation quality. We outline the historical origins of the error, explain why vulnerability is unavoidable in code-based authority systems, and propose a return to presence as the only non-simulable foundation for digital authority—implemented through local cryptographic proof generation that preserves privacy by architectural design. The core claim is simple: code cannot be authority. Authority must arise from being. This is not a technological decision, but an ontological one—and ontological mistakes cannot be patched. Keywords: ontological cryptography, HISPU, digital trust, code-based authority, human presence verification, cryptographic attestation, privacy-preserving architecture, cybersecurity, authentication, biometric entropy, local processing, zero-knowledge presence, environmental embedding, physical unclonability, quantum-resistant, AI safety, digital sovereignty, proof of being, presence-based authority
Traditional health data infrastructure fragments longitudinal health status into isolated clinical encounters, introduces significant self-reporting bias, and concentrates data ownership among centralized custodians.This paper proposes an institutional research lab architecture-Proof of Health-that treats verified health status as a cryptographically attestable primitive suitable for decentralized trials, data marketplaces, and risk-adjusted health contracts.The architecture integrates three core components: (1) multi-modal longitudinal data collection via remote patient monitoring (RPM), wearable sensors, and structured clinical assessments; (2) privacy-preserving verification using off-chain encrypted storage paired with on-chain attestations and zero-knowledge proofs; and (3) decentralized trial infrastructure supporting hybrid recruitment, telemedicine visits, and electronic patient-reported outcomes (ePROs).We define a standardized "Proof of Health" metric derived from biomarker trajectories, behavioral adherence logs, and imaging-derived phenotypes, versioned using FHIR interoperability standards and blockchain-based metadata provenance.The lab architecture incorporates HL7 FHIR compliance, GDPR/HIPAA-aligned consent automation via smart contracts, and risk-based remote monitoring (RBM) protocols aligned with ICH-GCP guidelines.Initial pilot studies (N = 20-50 participants per cohort) will validate the Proof of Health signal across three use cases: (1) insurance risk stratification, (2) employment wellness contracts, and (3) participation in decentralized science (DeSci) research data marketplaces.Participants retain cryptographic custody of raw data while institutions gain provably valid, tamper-evident health intelligence.We present the system architecture, methodology, preliminary endpoint definitions, and regulatory pathways for pilot and confirmatory trials.This framework aims to resolve the central tension in modern health research: enabling rigorous longitudinal science while strengthening individual data sovereignty and consent transparency.
BitBallot: Final Proposal Summary Overview This document presents the final architectural design of BitBallot, an electronic voting system engineered for legally binding public elections under explicit institutional and physical deployment assumptions. Architectural Innovation BitBallot addresses long-standing limitations of end-to-end verifiable voting by separating cryptographic enforcement from institutional responsibility. * Execution Model: Rather than relying on trusted execution environments (TEEs), specialized hardware, or application logic embedded in the consensus layer, the system enforces correctness through verifiable programs (vProgs) and zero-knowledge proofs (ZKP). Infrastructure: It utilizes a public Layer-1 blockchain solely as a neutral substrate for ordering and finality. Core Contribution: Atomic Display Integrity (ADI) The central breakthrough of BitBallot is Atomic Display Integrity (ADI)—a protocol-level security property that: Cryptographically binds voter intent, interface display, and recorded ballots. Ensures a single atomic authorization event at the moment of confirmation. Maintains integrity even under re-voting semantics. Strategic Advantage: Combined with last-vote-valid voting and terminal-complete zero-knowledge tallying, BitBallot achieves strong privacy, public verifiability, and resistance to coercion without intermediate information leakage. Practical Deployment BitBallot is purpose-built for deployment on commodity hardware within supervised polling environments. Cost & Complexity: By avoiding trusted execution environments and specialized cryptographic hardware, the system significantly reduces operational complexity and deployment costs. Security: Despite using standard hardware, it preserves rigorous security guarantees through its underlying protocol design. Conclusion Together, these design choices demonstrate that large-scale, verifiable public elections can be implemented using architectures that are both cryptographically sound and institutionally realistic.
Abstract This paper revisits Virgo, a well-known transparent zero-knowledge proof system that has been used in many subsequent studies. Through our analysis, we uncover previously overlooked limitations and several exploitable security vulnerabilities within Virgo’s zkVPD protocol design and implementation. We subsequently address these issues and improve Virgo’s zkVPD protocol. Our improvements feature simplified but more efficient VPD and zkVPD algorithms, offering enhanced support for computations over binary fields and their extension fields.
Financial institutions are currently faced with suffering never experienced before as they strive to guarantee the privacy of data and address the demands of regulation to report and cooperate in machine learning. This paper proposes PrivChain-AI, a novel blockchain-based federated learning system designed to facilitate secure and privacy-preserving financial reporting and access control. The proposed framework will integrate three key components: differential privacy, homomorphic encryption, and smart contract-based governance, enabling cooperative model training across financial institutions while preventing the leakage of sensitive information. PrivChain-AI is a hierarchical design that incorporates permissioned consensus protocols and utilises zero-knowledge proof verification to authenticate transactions. It has been demonstrated that the performance is higher than that of the actual financial data, with an outcome of 94.7% accuracy in fraud recognition at the cost of e-differentiation privacy, where ϵ = 1.0. It is 40% faster in terms of communication overhead and ensures regulatory compliance, as it features immutable audit trails. The analysis of performances reveals that a privacy preservation metric improves by 78%, and access control granularity is improved by 62% compared to the current state-of-the-art approaches. The PrivChain-AI paradigm introduced provides a new analytical model for safe, collaborative finance, meeting the highest standards and ensuring compliance with relevant regulatory jurisdictions.
The rapid growth of IoT devices in smart home environments has introduced significant challenges in ensuring secure, scalable, and efficient communication among heterogeneous devices. Centralized architectures suffer from a single point of failure, while blockchain-only solutions face high latency, limiting their use in real-time control. To address these issues, we propose a multi-layered decentralized framework that combines a consortium blockchain, a trusted off-chain coordinator, group-based zero-knowledge proofs (ZKPs), and a two-tiered access control policy (ACP) architecture. The consortium blockchain provides an immutable ledger for device identities and foundational, coarse-grained ACP enforcement through smart contracts, ensuring tamper-proof trust. For privacy-preserving mutual authentication, a group-based ZKP protocol enables collective device authorization without revealing sensitive keys. The off-chain coordinator complements this by enforcing dynamic security mechanisms, including fine-grained ACPv2 checks—such as rate limits, time-of-day restrictions, and device telemetry—in addition to anomaly detection for behavioral risk assessment. This proposed hybrid structure achieves both immutability and high efficiency over traditional methods. A performance evaluation highlighted the framework’s efficiency by demonstrating that the core ZKP verification for a 500-device group can be completed in just 190 ms. The framework drastically reduces on-chain costs, with critical access control policy transactions consuming only 82,748 gas—a reduction of over 90% compared to benchmarked on-chain systems. The complete end-to-end workflow, from user request to secure session establishment, has a latency bound of approximately 3s. Formal security verification with the BAN and AVISPA tools validates resilience against common attacks, including man-in-the-middle, replay, and impersonation, while static analysis using the Slither framework confirms the absence of critical vulnerabilities in the smart contract code. By combining an immutable on-chain foundation with intelligent, dynamic off-chain enforcement, our proposed framework provides a uniquely resilient, scalable, and adaptive security solution for modern smart home systems.
Damilare E. Bakare, Adekemi Olawunmi Amoo, Mary T. Onifade
The health insurance sector has been facing many challenges recently, such as fraudulent activities in insurance claims, data breaches, and high transaction costs, particularly with existing systems built on the Ethereum network, which negatively affect its efficiency and effectiveness.These challenges undermine the trust and financials of insurance providers while compromising the privacy of the patient's health records.To address this issue, this study proposes a conceptual framework that uses zero-knowledge proof within the blockchain system and is deployed on the Polygon Network for its low transaction fees and higher throughput.The proposed model allows the verification of an insurance claim without revealing sensitive patient health records, ensuring privacy while preventing fraudulent activities.In this conceptual design, the hospital can issue verifiable proof of treatment, appointment, and bill that shows the validity of the insurance claim without revealing the underlying health record to the insurer.This study, therefore, contributes to supporting research in decentralized applications for healthcare insurance by presenting a conceptual model and comprehensively analyzing the feasibility, rather than a full-scale implementation.It also emphasizes the need to preserve privacy in sensitive domains and the potential benefits of blockchain and ZKP integration.In conclusion, the research's findings show that, in theory, integrating ZKP with blockchain technology can enhance healthcare insurance processes in terms of reliability, efficiency, privacy, and security.However, further research and practical development are required to realize and evaluate a fully operational system.
Digital product passports outline information about a product’s lifecycle, circularity, and sustainability-related data. Sustainability data contains claims about carbon footprint, recycled material composition, ethical sourcing of production materials, etc. Also, upcoming regulatory directives require companies to disclose this type of information. However, current sustainability reporting practices face challenges, such as greenwashing, where companies make incorrect claims that are difficult to verify. There is also a challenge of disclosing sensitive production information when other stakeholders, such as consumers or other economic operators, wish to verify sustainability claims independently. Zero-knowledge proofs (ZKPs) provide a cryptographic system for verifying statements without revealing sensitive information. The goal of this research paper is to explore ZKP cryptography, trust models, and implementation concepts for extending DPP capability in privacy-aware reporting and verification of sustainability claims in products. To achieve this goal, first, formal representations of sustainability claims are provided. Then, a data matrix and trust model for generating proofs are developed. An interaction sequence is provided to show different components for various proof generation and verification scenarios for sustainability claims. Lastly, the paper provides a circuit template for the proof generation of an example claim and a credential structure for their input data validation. The proposed approach is assessed using a scenario-based evaluation to check the performance metrics for data credential verification and proof generation for verifying material composition in a product.
Open access
2 source records
Physical Unclonable Functions (PUFs) and Hardware Security
An open question recently posed by Fawzi and Ferme [IEEE Transactions on Information Theory 2024], asks whether non-signaling (NS) assistance can increase the capacity of a broadcast channel (BC). We answer this question in the affirmative, by showing that for a certainK-receiver BC model, called Coordinated Multipoint broadcast (CoMP BC) that arises naturally in wireless networks, NS-assistance provides multiplicative gains in both capacity and degrees of freedom (DoF), even achievingK-fold improvements in extremal cases. Somewhat surprisingly, this is shown to be true even for 2-receiver broadcast channels that are semi-deterministic and/or degraded. In a CoMP BC,Bsingle-antenna transmitters, supported by a backhaul that allows them to share data, act as oneB-antenna transmitter, to send independent messages toKreceivers, each equipped with a single receive antenna. A fixed and globally known connectivity matrix specifies for each transmit antenna, the subset of receivers that are connected to (have a non-zero channel coefficient to) that antenna. Besides the connectivity, there is no channel state information at the transmitter. The receivers have perfect channel knowledge. We show that NS-assistance has no DoF advantage in a fully connected CoMP BC. The DoF region is fully characterized for a class of connectivity patterns associated with tree graphs, for which the classical sum-DoF value is shown to be the number of leaf nodes, while the NS-assisted sum-DoF value is the total number of all (non-root) nodes. For arbitrary connectivity patterns, the sum-capacity with NS-assistance is bounded above and below by the min-rank and triangle number of the connectivity matrix, respectively, leading to matching bounds in many cases, e.g., if min(B,K) ≤ 6. While translations to Gaussian settings are demonstrated, for simplicity most of our results are presented under noise-free, finite-field (Fq) models. Converse proofs for classical DoF are found by adapting the Aligned Images bounds to the finite field model. Converse bounds for NS-assisted DoF/capacity extend the same-marginals property to the BC with NS-assistance available to all parties. Beyond the BC setting, even stronger (unbounded) gains in capacity due to NS-assistance are established for certain ‘communication with side-information’ settings, such as the fading dirty paper channel.
This paper presents zero knowledge proofs, their cryptographic significance and applications. It presents a basic classification: interactive and noninteractive zero knowledge proofs. It presents and compares three protocols of non-interactive zero knowledge proofs: ZK-SNARK, ZK-STARK and Bulletproofs. It presents the quadratic residue problem and proofs it with both interactive and non-interactive zero knowledge proofs. The non-interactive protocol used to prove the quadratic residue problem is ZK-SNARK. The proof is implemented in the Python programming language, using python-snark library.
With the rapid development of geological blockchains and Internet of Things-based data acquisition technologies, massive amounts of heterogeneous data are constantly emerging. However, this data is stored in a distributed manner across different organizational or business blockchains. Data sharing among multiple geological blockchains faces numerous challenges, either exposing sensitive data during verification or lacking effective authorization mechanisms. Therefore, how to achieve fine-grained access control and privacy protection across multiple blockchains has become a critical issue that must be addressed in geological data sharing. In this paper, we propose GeoCross, a cross-chain geological data sharing framework that enables fine-grained authorization management and privacy protection. First, GeoCross provides a hierarchical hybrid encryption mechanism that uses symmetric encryption for geological data protection and ciphertext-policy attribute-based encryption to enable flexible cross-chain access policies. Second, we integrate a Groth16-based zero-knowledge proof mechanism, which allows a chain to verify the existence, integrity, and accessibility of off-chain data without revealing the content. Furthermore, we introduce a Reputation-based Non-interactive Relay node Selection protocol (RNRS), which enhances the trustworthiness and fairness of cross-chain routing. Finally, we implement GeoCross in a multi-chain Hyperledger Fabric environment and evaluate its performance under real-world workloads. Results show that Groth16 verification requires only three bilinear pairings, achieving a throughput of up to 390 tps on a single chain and 1550 tps in a concurrent multi-chain environment. Even with 50% malicious nodes, the RNRS protocol still maintains a success rate of over 91%. These results demonstrate that GeoCross provides an efficient and practical solution for secure and privacy-preserving cross-chain geological data sharing.
Secure electronic voting (e-voting) systems have become an essential component of modern democratic processes, demanding strong guarantees of privacy, integrity, verifiability, and resistance to coercion. Homomorphic commitment schemes, which integrate the properties of commitment schemes with homomorphic encryption, provide a promising approach to meeting these requirements by enabling computations on encrypted or committed data without revealing the underlying information. This capability allows secure vote tallying while preserving voter anonymity. This paper presents a comprehensive review of homomorphic commitment schemes within secure voting infrastructures, focusing on key security models such as privacy, verifiability, coercion resistance, and robustness against malicious adversaries. It also examines optimization techniques, including batching, threshold cryptography, and blockchain integration, which enhance system efficiency and scalability. Furthermore, emerging paradigms such as post-quantum cryptography and decentralized systems are discussed for their potential impact on voting protocols. The study highlights advancements in cryptographic primitives, zero-knowledge proofs, and distributed ledger technologies, while providing a comparative analysis of multiple research contributions. The findings indicate that although homomorphic commitment schemes significantly enhance transparency and privacy, challenges related to computational complexity, scalability, and real-world implementation persist, suggesting the need for lightweight, quantum-resistant, and hybrid secure voting solutions. , , , ,