Zero-knowledge range proofs (ZKRPs) allow a prover to convince a verifier that a secret value lies in a given interval. ZKRPs have numerous applications: from anonymous credentials and auctions, to confidential transactions in cryptocurrencies. At the same time, a plethora of ZKRP constructions exist in the literature, each with its own trade-offs. In this work, we systematize the knowledge around ZKRPs. We create a classification of existing constructions based on the underlying building techniques, and we summarize their properties. We provide comparisons between schemes both in terms of properties as well as efficiency levels, and construct a guideline to assist in the selection of an appropriate ZKRP for different application requirements. Finally, we discuss a number of interesting open research problems.
Javier José Díaz Rivera, Muhammad Afaq, Wang‐Cheol Song
As network systems advance and become more sophisticated, the associated security challenges grow more complex. The zero trust model emerges as a new paradigm to address this, significantly emphasizing robust and continuous identity verification. Multi-factor authentication (MFA) methods have become crucial for enhancing authentication security within this framework. Additionally, the integration of blockchain technology is increasingly recognized for its potential to strengthen identity trustworthiness further, complementing the zero trust approach by providing a more secure and transparent identity verification process. However, privacy concerns remain, especially in public blockchain environments where personal data is vulnerable to inadvertent exposure. Also, using centralized servers for authentication, even in systems integrated with blockchain, presents the risk of creating single points of failure. This paper introduces a privacy-preserving MFA system that harnesses the decentralized capabilities of blockchain technology to enable a Distributed Authentication Mechanism (DAM) as a network of authenticators for enhancing the reliability of the authentication process. This system utilizes blockchain-based Zero-Knowledge Proofs (ZKP) as a privacy mechanism to prove the knowledge of a One-Time Password (OTP). This approach not only ensures the authenticity of the proof authenticity but also confirms the identity of the prover. In the final stage of the MFA process, non-transferable, non-fungible tokens (NFTs) are employed as authentication tokens for identity verification. Our experimental results and comparative security analyses suggest a relevant contribution to secure, private, and dependable MFA framework research.
Autonomous decision-making in decentralized multi-agent systems (MAS) poses significant challenges related to security, scalability, and privacy. This paper introduces an innovative architecture that integrates Decentralized Identifiers (DIDs), Zero-Knowledge Proofs (ZKPs), Hyperledger Fabric blockchain, OAuth 2.0 authorization, and the Command Query Responsibility Segregation (CQRS) pattern to establish a secure, scalable, and privacy-focused framework for MAS. The use of DIDs and ZKPs ensures secure, self-sovereign identities and enables privacy-preserving interactions among autonomous agents. Hyperledger Fabric provides an immutable ledger, ensuring data integrity and facilitating transparent transaction processing through smart contracts. The CQRS pattern, combined with event sourcing, optimizes the system’s ability to handle high volumes of read and write operations, enhancing performance and scalability. Practical applications are showcased in Smart Grids, Healthcare Data Management, Secure Internet of Things (IoT) Networks, and Supply Chain Management, highlighting the architecture’s ability to address industry-specific challenges. This integration offers a robust solution for ensuring trust, verifiability, and scalability in distributed systems while preserving the confidentiality of agents.
Zero-knowledge proof (ZKP) systems have surged attention and held a fundamental role in contemporary cryptography. Zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) protocols dominate the ZKP usage, implemented through arithmetic circuit programming paradigm. However, underconstrained or overconstrained circuits may lead to bugs. The former refers to circuits that lack the necessary constraints, resulting in unexpected solutions and causing the verifier to accept a bogus witness, and the latter refers to circuits that are constrained excessively, resulting in lacking necessary solutions and causing the verifier to accept no witness. This article introduces a novel approach for pinpointing two distinct types of bugs in ZKP circuits. The method involves encoding the arithmetic circuit constraints to polynomial equation systems and solving them over finite fields by the computer algebra system . The classification of verification results is refined, greatly enhancing the expressive power of the system. A tool, AC 4 , is proposed to represent the implementation of the method. Experiments show that AC 4 demonstrates an increase in the solved rate, showing a 36.7% improvement over Picus and CIVER, and a slight improvement over halo2-analyzer, a checker for halo2 circuits. Within a solvable range, the checking time has also exhibited noticeable improvement, demonstrating a magnitude increase compared to previous efforts.
Kuznetsov, Oleksandr, Anton Yezhov, Vladyslav Yusiuk, Alexandr Kuznetsov
Zero-knowledge proofs (ZKPs) have emerged as a promising solution to address the scalability challenges in modern blockchain systems. This study proposes a methodology for generating and verifying ZKPs to ensure the computational integrity of cryptographic hashing, specifically focusing on the SHA-256 algorithm. By leveraging the Plonky2 framework, which implements the PLONK protocol with the FRI commitment scheme, we demonstrate the efficiency and scalability of our approach for both random data and real data blocks from the NEAR blockchain. The experimental results show consistent performance across different data sizes and types, with the time required for proof generation and verification remaining within acceptable limits. The generated circuits and proofs maintain manageable sizes, even for real-world data blocks with a large number of transactions. The proposed methodology contributes to the development of secure and trustworthy blockchain systems, where the integrity of computations can be verified without revealing the underlying data. Further research is needed to assess the applicability of the approach to other cryptographic primitives and to evaluate its performance in more complex real-world scenarios.
Open access
3 source records
Cryptography and Data Security
Blockchain Technology Applications and Security
Advanced Steganography and Watermarking Techniques
Camilla Fioravanti, Christoforos N. Hadjicostis, Gabriele Oliva
Networked Control Systems (NCS) are pivotal for sectors like industrial automation, autonomous vehicles, and smart grids. However, merging communication networks with control loops brings complexities and security vulnerabilities, necessitating strong protection and authentication measures. This paper introduces an innovative Zero-Knowledge Proof (ZKP) scheme tailored for NCSs, enabling a networked controller to prove its knowledge of the dynamical model and its ability to control a discrete-time linear time-invariant (LTI) system to a sensor, without revealing the model. This verification is done through the controller's capacity to produce suitable control signals in response to the sensor's output demands. The completeness, soundness, and zero-knowledge properties of the proposed approach are demonstrated. The scheme is subsequently extended by considering the presence of delays and output noise. Additionally, a dual scenario where the sensor proves its model knowledge to the controller is explored, enhancing the method's versatility. Effectiveness is shown through numerical simulations and a case study on distributed agreement in multi-agent systems.
Aušrys Kilčiauskas, Antanas Bendoraitis, Eligijus Sakalauskas
One of the main trends for the monitoring and control of business processes is to implement these processes via private blockchain systems. These systems must ensure data privacy and verifiability for the entire network here denoted by ‘Net’. In addition, every business activity should be declared to a trusted third party (TTP), such as an Audit Authority (AA), for tax declaration and collection purposes. We present a solution for a confidential and verifiable realization of transactions based on the Unspent Transaction Output (UTxO) paradigm. This means that the total sum of transaction inputs (incomes) $In$ must be equal to the total sum of transaction outputs (expenses) $Ex$, satisfying the balance equation $In=Ex$. Privacy in a private blockchain must be achieved through the encryption of actual transaction values. However, it is crucial that all participants in the network be able to verify the validity of the transaction balance equation. This poses a challenge with probabilistically encrypted data. Moreover, the inputs and outputs are encrypted with different public keys. With the introduction of the AA, the number of different public keys for encryption can be reduced to two. Incomes are encrypted with the Receiver’s public key and expenses with the AA’s public key. The novelty of our realization lies in taking additively-multiplicative, homomorphic ElGamal encryption and integrating it with a proposed paradigm of modified Schnorr identification providing a non-interactive zero-knowledge proof (NIZKP) using a cryptographically secure h-function. Introducing the AA as a structural element in a blockchain system based on the UTxO enables effective verification of encrypted transaction data for the Net. This is possible because the proposed NIZKP is able to prove the equivalency of two ciphertexts encrypted with two different public keys and different actors. This integration allows all users on the Net to check the UTxO-based transaction balance equation on encrypted data. The security considerations of the proposed solution are presented.
AI and zero-knowledge proofs (ZKPs) may revolutionize cryptographic protocol privacy, as this research shows. The report examines how AI may improve ZKP efficiency, scalability, and security and identifies developing AI-driven privacy-preserving technologies across sectors. The study reviews secondary data from peer-reviewed journals, technical reports, and conference proceedings. Key results show that AI automates proof creation, optimizes verification procedures, and identifies weaknesses, allowing innovative architectures like federated learning mixed with ZKPs for safe, collaborative AI training. The research shows AI's potential to improve privacy in banking, healthcare, and secure identity management. However, concerns about the computational needs of the AI model, explainable systems, and interoperability persist. The policy implications highlight standardization, security framework improvements, and research to solve these shortcomings. The policy should also support openness and accountability in AI-driven cryptography systems to build confidence and acceptance. This paper shows how AI might transform privacy-preserving cryptographic methods and how to overcome their existing limitations to maximize their promise.
Privacy and auditability have been conflicting design requirements for blockchainbased distributed ledgers since the inception of the field.As purpose-built blockchains with permissioned consensus and client access are developing in a broad and diverse range of industries, a specific form of this dichotomy is emerging: the need to audit the handling of regulated on-ledger financial assets, such as central bank digital currencies, while preserving the privacy and confidentiality of transactions as much as possible.This paper proposes a novel, privacy-preserving, noninteractive-zero-knowledge-proof-based protocol for a blockchain-based distributed ledger, to prove conformance with fundamental compliance requirements to external auditing parties.We present an extendable implementation and demonstrate the practicality of the approach.
Abstract Building trust in modern business and in social interactions is a critical need as our networks continue to grow and as we engage deeply with unknown people and companies from various parts of the planet. Zero-Knowledge (ZK) technology is a powerful enabler of this trust. It allows a person to demonstrate they know something, have something, or can do something without revealing the actual information or process. We describe the fundamental concepts of cryptography and ZK, their use and limitations, and discuss how ZK technology can be used from a personal as well as a business perspective.
Alexandr Kuznetsov, Alex Rusnak, Anton Yezhov, Dzianis Kanonik · 6 authors
Blockchain technology has emerged as a revolutionary tool in ensuring data integrity and security in digital transactions. However, the current approaches to data verification in blockchain systems, particularly in Ethereum, face challenges in terms of efficiency and computational overhead. The traditional use of Merkle Trees and cryptographic hash functions, while effective, leads to significant resource consumption, especially for large datasets. This highlights a gap in existing research: the need for more efficient methods of data verification in blockchain networks. Our study addresses this gap by proposing an innovative aggregation scheme for Zero-Knowledge Proofs within the structure of Merkle Trees. We develop a system that significantly reduces the size of the proof and the computational resources needed for its generation and verification. Our approach represents a paradigm shift in blockchain data verification, balancing security with efficiency. We conducted extensive experimental evaluations using real Ethereum block data to validate the effectiveness of our proposed scheme. The results demonstrate a drastic reduction in proof size and computational requirements compared to traditional methods, making the verification process more efficient and economically viable. Our contribution fills a critical research void, offering a scalable and secure solution for blockchain data verification. The implications of our work are far-reaching, enhancing the overall performance and adaptability of blockchain technology in various applications, from financial transactions to supply chain management.
Aditya Pathak, Irfan Al‐Anbagi, Howard J. Hamilton
Authentication in low-latency Internet of Things (IoT) networks must satisfy three requirements, namely, high security and privacy preservation, high scalability, and low authentication time. These requirements arise because devices in IoT networks must operate in a secure and scalable manner despite being limited in computational resources. Existing authentication mechanisms focus on the security and privacy of IoT networks but neglect the importance of scalability and authentication time. Therefore, existing authentication mechanisms are unscalable and unsuited to low-latency IoT networks. With a focus on increasing scalability and reducing the authentication time while providing high security and privacy preservation in low-latency IoT networks, we propose a mutual authentication mechanism called Zero-Knowledge Proof-based Privacy-Preserving Mutual Authentication (Z-PMA) for IoT networks. The Z-PMA mechanism utilizes a combination of a zero-knowledge proof, an incentive mechanism, and a permissioned blockchain to provide secure, privacy-preserving, scalable, low-latency authentication for IoT networks. We develop a new approach to address the trade-off between the three requirements for authentication mechanisms for low-latency IoT networks that has the potential to improve the overall performance of these networks. A permissioned blockchain is incorporated in the approach to provide secure and immutable data storage using its distributed and unforgeable ledger. Our experimental results show that the Z-PMA mechanism reduces authentication time than existing state-of-the-art authentication mechanisms, while providing high security and privacy preservation as well as high scalability.
In the rapidly advancing domain of smart manufacturing, securing data integrity and preventing unauthorized access are critical challenges. This study introduces a novel approach that synergizes anomaly detection techniques with Zero-Knowledge Proofs (ZKPs) to fortify the security framework of smart manufacturing systems. Our methodology employs a combination of data preprocessing, including statistical imputation and data smoothing, alongside advanced anomaly detection using classification methods and neural networks, particularly focusing on deep learning architectures. The detected anomalies undergo verification through zk-SNARKs, a specialized ZKP scheme, ensuring a robust validation process without compromising data confidentiality. Our findings reveal a notable enhancement in the accuracy of anomaly detection, achieving detection rates of approximately 95% for temperature fluctuations and 90% for pressure irregularities, with a significant reduction in false positives. This performance is markedly superior to traditional methods and aligns closely with the highest efficacy rates reported in contemporary studies. Moreover, the utilization of ZKPs for anomaly verification demonstrated a 98% success rate, ensuring the secure and private verification of anomalies. The integration of anomaly detection with ZKPs presents a significant leap forward in addressing the security vulnerabilities inherent in smart manufacturing. This study not only showcases the effectiveness of our approach in enhancing data security and integrity but also sets a benchmark for future research in creating more resilient and trustworthy industrial operations.
Self-sovereign identity models and decentralized, blockchain-based identity management can prevent digital ecosystem data breaches and misuse, the study finds. As digital services proliferate and personal data becomes more valuable, central database-based identity systems expose users to single-point failures, unauthorized access, identity theft, and large-scale breaches. This paper analyzes how decentralized IDs, verifiable credentials, and cryptographic verification reduce middlemen, enable selective disclosure, and promote identity governance privacy. Important academic, industrial, and technical contributions show that blockchain anchors credentials in distributed ledgers rather than institutional repositories, improving authentication, traceability, and tamper resistance while limiting undesired access. Immutable audit trails, user-controlled credentials, and reduced central authority dependency have been touted, but empirical performance data, scalability, interoperability, and comparative evaluations of public and permissioned blockchain environments are lacking. These findings explain self-sovereign identity architecture, which lets trusted authority issue credentials but users store and control them directly through digital wallets utilizing cryptographic proofs instead of database lookups. Users can control or withdraw data sharing while maintaining identity. Transparency, limited disclosure, and contextual data presentation prevent cross-platform tracking and increase user autonomy. The research shows how zero-knowledge proofs and predicate-based validation verify credentials without disclosing sensitive data, protecting privacy. Birthdates and locations are not needed to verify age- and location-based limits. SSI master key-derived domain-specific identities reduce correlation hazards and prevent service surveillance. Consent-based sharing, selective disclosure, and cryptographic compartmentalization decrease data collection and profiling. Decentralised blockchain verification maintains credentials usable when the issuer is offline, preventing service disruptions and third-party participation.
The paper elucidates the fundamental concepts of blockchain technology and its essential parameters, delving into the contemporary scalability challenges faced by blockchain networks. It studies existing directions and compares well-known protocols to propose the solution for the blockchain scalability problem. The main goal of this research is to propose a promising method to solve the scalability problem in blockchain technology. This proposed solution should be universal and applicable in different systems. We chose zero-knowledge proof technology as a promising direction for detailed study. We used protocols, based on this technology, to develop a validation system for a linked chain of blocks. Presented experimental results substantiate the prospects of this direction for solving the scalability problems of modern blockchain systems. The relevance of the chosen topic is determined by the mass introduction of blockchain systems in various areas of human life. As it happens to every network, the volume of information that must be continuously processed increases. This challenge demands to develop solutions to improve systems, making them flexible in working with millions of users. At the same time, it is still important to maintain the security and confidentiality of the information and keep the decentralized organization of the data exchange process in the updated systems. Therefore, in the modern blockchain industry, the predominant challenge revolves around discovering models and methods to overcome the scalability hurdle, facilitating the widespread implementation of blockchain applications on a full scale.
Liqun Chen, Changyu Dong, Christopher J. P. Newton, Yalan Wang
Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it extremely challenging to design a group signature scheme on top of them. It is even more challenging if we want a group signature scheme suitable for real-world applications, one that can support large groups and require few trust assumptions. Our scheme is based on MPC-in-the-head non-interactive zero-knowledge proofs, and we specifically design a novel hash-based group credential scheme, which is rooted in the SPHINCS+ signature scheme but with various modifications to make it MPC (multi-party computation) friendly. The security of the scheme has been proved under the fully dynamic group signature model. We provide an implementation of the scheme and demonstrate the feasibility of handling a group size as large as 2 60 . This is the first group signature scheme from symmetric primitives that supports such a large group size and meets all the security requirements.
Byeongchan Park, Se‐Young Jang, Seok-Yoon Kim, Youngmo Kim
Due to the Corona-19 pandemic phenomenon, various video service platforms that provide OTT (Over The Top) services such as 'Netflix' have achieved rapid growth.OTT platforms that provide such video content do not disclose the viewing time of the content watched by users due to various issues such as personal information protection, so stakeholders are conducting third-party research on usage patterns.While an objective and reliable third-party method of investigating usage patterns is needed, efforts to protect personal information are also needed in the process.The information required for viewership surveys to investigate usage patterns only requires information about what content is used and to what extent, and does not require personal information about users.In this paper, we propose a method to generate and verify the generated usage information by de-identification using zero-knowledge proof protocol when a user selects a specific OTT platform and uses content through an OTT player agent that provides OTT services.
Conventionally, organizations have used Privileged Access Management (PAM) techniques to secure, control, and monitor access to their critical information and resources. The PAM concepts have envisioned designing protocols that help protect user accounts that are deemed to have access to sensitive data ?the most valuable asset of a business. While in the past these techniques have proven vital to data protection and security, the onset of increasingly sophisticated technologies and more determined malicious actors warrants a change of data control and privacy strategies. It becomes impossible to secure a system to achieve 100 percent efficiency. Any system that is attached to the internet is vulnerable to cyberattacks. Hackers have numerous ways to compromise systems if traditional boundary security mechanisms are deployed. Detecting an intrusion in such a setup becomes increasingly challenging if an attacker successfully breaches that boundary layer of defense. Since traditional authentication and authorization might not be reliable in network systems, the zero - knowledge proof model comes in handy. Adding the zero - knowledge proof to the PAM to authenticate users or members and disclose or anonymize them through decentralized identifiers helps in solving the identification and privacy protection problem. We propose a PAM and zero - knowledge proof - inspired approach to address the authentication, data security, and privacy concerns. A zero - knowledge proof is a method that allows the prover to prove to the verifier that they know a certain information without disclosing it.
Federated learning (FL) has emerged as an alternative to traditional machine learning in scenarios where training data is sensitive. In federated learning, training is held at end devices, and thus data does not need to leave users devices. However, most approaches to federated learning rely on a central server to coordinate the learning process which, in turn, introduces its own security and privacy problems. We propose Federify, a decentralized federated learning framework based on blockchain which employs homomorphic encryption and zero knowledge proofs to provide security, privacy, and transparency. The scheme preserves the confidentiality of both the data used for training and the local models using homomorphic encryption. zkSNARKs are used to provide security by verifying the contributions from the different agents, and transparency of both the learning process and the incentive mechanism is achieved by delegating coordination into a smart contract in a public blockchain. We have also implemented, deployed, and evaluated a proof of concept of our framework, to demonstrate its viability both in terms of computational resources needed and cost to train in a public generic blockchain such as Ethereum.
Federated learning is a privacy-preserving machine learning framework where multiple data owners collaborate to train a global model under the orchestra of a central server. The local training results from trainers should be submitted to the central server for model aggregation and update. Busy central server and malicious trainers can introduce the issues of a single point of failure and model poisoning attacks. To address the above issues, the trusty decentralized federated learning (called TrustDFL) framework has been proposed in this paper based on the zero-knowledge proof scheme, blockchain, and smart contracts, which provides enhanced security and higher efficiency for model aggregation. Specifically, Groth 16 is applied to generate the proof for the local model training, including the forward and backward propagation processes. The proofs are attached as the payloads to the transactions, which are broadcast into the blockchain network and executed by the miners. With the support of smart contracts, the contributions of the trainers could be verified automatically under the economic incentive, where the blockchain records all exchanged data as the trust anchor in multi-party scenarios. In addition, IPFS (InterPlanetary File System) is introduced to alleviate the storage and communication overhead brought by local and global models. The theoretical analysis and estimation results show that the TrustDFL efficiently avoids model poisoning attacks without leaking the local secrets, ensuring the global model’s accuracy to be trained.