Despite its popularity, the nature of solar energy is highly uncertain and weather dependent, affecting the business viability and investment of solar energy generation, especially for household users. To stabilize the income from solar energy generation, there have been limited traditional options, such as using energy storage to pool excessive solar energy in off-peak periods or financial derivatives from future markets to hedge energy prices. In this paper, we explore a novel idea of "parametric solar energy insurance", by which solar panel owners can insure their solar energy generation based on a verifiable geographically specific index (surface solar irradiation). Parametric solar energy insurance offers opportunities of financial subsidies for insufficient solar energy generation and amortizes the fluctuations of renewable energy generation geographically. Furthermore, we propose to leverage blockchain and remote sensing (satellite imagery) to provide a publicly verifiable platform for solar energy insurance, which not only automates the underwriting and claims of a solar energy insurance policy, but also improves its accountability and transparency. We utilize the state-of-the-art succinct zero-knowledge proofs (zk-SNARK) to realize privacy-preserving blockchain-based solar energy insurance on real-world permissionless blockchain platform Ethereum.
Blockchain is the foundation of all cryptocurrencies, while machine learning (ML) is one of the most popular technologies with a wide range of possibilities. Blockchain may be improved and made more effective by using ML. Even though blockchain technology uses encryption to safeguard data, it is not completely reliable. Various elements, including the particular use case, the type of data, and legal constraints can determine whether it is suitable for keeping private and sensitive data. While there may be benefits, it is important to take into account possible hazards and abide by privacy and security laws. The blockchain itself is secure, but additional applications and layers are not. In terms of security, ML can aid in the development of blockchain applications. Therefore, a critical investigation is required to better understand the function of ML and blockchain in enhancing security. This study examines the current situation, evaluates the articles it contains, and presents an overview of the security issues. Despite their existing limitations, the papers included from 2012 to 2022 highlighted the importance of ML’s impact on blockchain security. ML and blockchain can enhance security, but challenges remain; advances such as federated learning and zero-knowledge proofs are important, and future research should focus on privacy and integration with other technologies.
Robotics systems of all types are revolutionizing a wide variety of industries—transportation, manufacturing, and even healthcare—and yet, many essential ingredients for robotics systems in the real world are not technologically ready for deployment. Currently, robots lack the protocols and standards required to be safe and secure outside factories. In an attempt to close this gap, recent research has demonstrated the security benefits of combining robotics systems with blockchain-based and related technologies (e.g., smart contracts, zero-knowledge proofs, Merkle trees). In this perspective article, I argue that blockchain-based robotics is starting to provide innovative solutions (e.g., secure data sharing, consensus mechanisms, and new interaction methods) to urgent problems of robot security. I list the most important takeaways so far from this emerging field of research that I helped establish together with a growing community. I close the article by discussing the implications of the security challenges that the robotics research community is facing, and possible ways for us to move forward.
Omid Mir, Daniel Slamanig, Balthazar Bauer, René Mayrhofer
Anonymous credentials (ACs) systems are a powerful cryptographic tool for privacy-preserving applications and provide strong user privacy guarantees for authentication and access control. ACs allow users to prove possession of attributes encoded in a credential without revealing any information beyond them. A delegatable AC (DAC) system is an enhanced AC system that allows the owners of credentials to delegate the obtained credential to other users. This allows to model hierarchies as usually encountered within public-key infrastructures (PKIs). DACs also provide stronger privacy guarantees than traditional AC systems since the identities of issuers and delegators can also be hidden. In this paper we present a novel DAC scheme that supports attributes, provides anonymity for delegations, allows the delegators to restrict further delegations, and also comes with an efficient construction. Our approach builds on a new primitive that we call structure-preserving signatures on equivalence classes on updatable commitments (SPSEQ-UC). The high-level idea is to use a special signature scheme that can sign vectors of set commitments, where signatures can be extended by additional set commitments. Signatures additionally include a user's public key, which can be switched. This allows us to efficiently realize delegation in the DAC. Similar to conventional SPSEQ, the signatures and messages can be publicly randomized and thus allow unlinkable delegation and showings in the DAC system. We present further optimizations such as cross-set commitment aggregation that, in combination, enable efficient selective showing of attributes in the DAC without using costly zero-knowledge proofs. We present an efficient instantiation that is proven to be secure in the generic group model and finally demonstrate the practical efficiency of our DAC by presenting performance benchmarks based on an implementation.
Bruno Pereira, José Manuel Torres, Pedro Sobral, Rui S. Moreira · 6 authors
Since its appearance in 2008, blockchain technology has found multiple uses in fields such as banking, supply chain management, and healthcare. One of the most intriguing uses of blockchain is in voting systems, where the technology can overcome the security and transparency concerns that plague traditional voting systems. This paper provides a thorough examination of the implementation of a blockchain-based voting system. The proposed system employs cryptographic methods to protect voters’ privacy and anonymity while ensuring the verifiability and integrity of election results. Digital signatures, homomorphic encryption (He), zero-knowledge proofs (ZKPs), and the Byzantine fault-tolerant consensus method underpin the system. A review of the literature on the use of blockchain technology for voting systems supports the analysis and the technical and logistical constraints connected with implementing the suggested system. The study suggests solutions to problems such as managing voter identification and authentication, ensuring accessibility for all voters, and dealing with network latency and scalability. The suggested blockchain-based voting system can provide a safe and transparent platform for casting and counting votes, ensuring election results’ privacy, anonymity, and verifiability. The implementation of blockchain technology can overcome traditional voting systems’ security and transparency shortcomings while also delivering a high level of integrity and traceability.
Traditional Insurance, a popular approach of financial risk management, has suffered from the issues of high operational costs, opaqueness, inefficiency and a lack of trust. Recently, blockchain-enabled "parametric insurance" through authorized data sources (e.g., remote sensing and IoT) aims to overcome these issues by automating the underwriting and claim processes of insurance policies on a blockchain. However, the openness of blockchain platforms raises a concern of user privacy, as the private user data in insurance claims on a blockchain may be exposed to outsiders. In this paper, we propose a privacy-preserving parametric insurance framework based on succinct zero-knowledge proofs (zk-SNARKs), whereby an insuree submits a zero-knowledge proof (without revealing any private data) for the validity of an insurance claim and the authenticity of its data sources to a blockchain for transparent verification. Moreover, we extend the recent zk-SNARKs to support robust privacy protection for multiple heterogeneous data sources and improve its efficiency to cut the incurred gas cost by 80%. As a proof-of-concept, we implemented a working prototype of bushfire parametric insurance on real-world blockchain platform Ethereum, and present extensive empirical evaluations.
We introduce the notion of \emph{traceable mixnets}. In a traditional mixnet, multiple mix-servers jointly permute and decrypt a list of ciphertexts to produce a list of plaintexts, along with a proof of correctness, such that the association between individual ciphertexts and plaintexts remains completely hidden. However, in many applications, the privacy-utility tradeoff requires answering some specific queries about this association, without revealing any information beyond the query result. We consider queries of the following types: a) given a ciphertext in the mixnet input list, whether it encrypts one of a given subset of plaintexts in the output list, and b) given a plaintext in the mixnet output list, whether it is a decryption of one of a given subset of ciphertexts in the input list. Traceable mixnets allow the mix-servers to jointly prove answers to the above queries to a querier such that neither the querier nor a threshold number of mix-servers learn any information beyond the query result. Further, if the querier is not corrupted, the corrupted mix-servers do not even learn the query result. We first comprehensively formalise these security properties of traceable mixnets and then propose a construction of traceable mixnets using novel distributed zero-knowledge proofs (ZKPs) of set membership and of a statement we call reverse set membership. Although set membership has been studied in the single-prover setting, the main challenge in our distributed setting lies in making sure that none of the mix-servers learn the association between ciphertexts and plaintexts during the proof. We implement our distributed ZKPs and show that they are faster than state-of-the-art by at least one order of magnitude.
Platooning technologies enable trucks to drive cooperatively and automatically, providing benefits including less fuel consumption, greater road capacity, and safety. To establish trust during dynamic platooning formation, ensure vehicular data integrity, and guard platoons against potential attackers in mixed fleet environments, verifying any given vehicle’s identity information before granting it access to join a platoon is pivotal. Besides, due to privacy concerns, truck owners may be reluctant to disclose private vehicular information, which can reveal their business data to untrusted third parties. To address these issues, this is the first study to propose an aggregated zero-knowledge proof and blockchain-empowered system for privacy-preserving identity verification in truck platooning. We provide the correctness proof and the security analysis of our proposed authentication scheme, highlighting its increased security and fast performance. The platooning formation procedure is re-designed to seamlessly incorporate the proposed authentication scheme, including the 1st catch-up and cooperative driving steps. The blockchain performs the role of verifier within the authentication scheme and stores platooning records on its digital ledger to guarantee data immutability and integrity. In addition, the proposed programmable access control policies enable truck companies to define who is allowed to access their platoon records. We implement the proposed system and perform extensive experiments on the Hyperledger platform. The results show that the blockchain can provide low latency and high throughput, the aggregated approach can offer a constant verification time of 500 milliseconds regardless of the number of proofs, and the platooning formation only takes seconds under different strategies. The experimental results demonstrate the feasibility of our design for use in real-world truck platooning.
Kelsey Merrill, Zachary Newman, Santiago Torres-Arias, Karen Sollins
Software repositories, used for wide-scale open software distribution, are a significant vector for security attacks. Software signing provides authenticity, mitigating many such attacks. Developer-managed signing keys pose usability challenges, but certificate-based systems introduce privacy problems. This work, Speranza, uses certificates to verify software authenticity but still provides anonymity to signers using zero-knowledge identity co-commitments. In Speranza, a signer uses an automated certificate authority (CA) to create a private identity-bound signature and proof of authorization. Verifiers check that a signer was authorized to publish a package without learning the signer's identity. The package repository privately records each package's authorized signers, but publishes only commitments to identities in a public map. Then, when issuing certificates, the CA issues the certificate to a distinct commitment to the same identity. The signer then creates a zero-knowledge proof that these are identity co-commitments. We implemented a proof-of-concept for Speranza. We find that costs to maintainers (signing) and end users (verifying) are small (< 1 ms), even for a repository with millions of packages. Techniques inspired by recent key transparency systems reduce the bandwidth for serving authorization policies to 2 KiB. Server costs in this system are negligible. Our evaluation finds that Speranza is practical on the scale of the largest software repositories. We also emphasize practicality and deployability in this project. By building on existing technology and employing relatively simple and well-established cryptographic techniques, Speranza can be deployed for wide-scale use with only a few hundred lines of code and minimal changes to existing infrastructure. Speranza is a practical way to bring privacy and authenticity together for more trustworthy open-source software.
Federated learning (FL) allows multiple parties to cooperatively learn a federated model without sharing private data with each other. The need of protecting such federated models from being plagiarized or misused, therefore, motivates us to propose a provable secure model ownership verification scheme using zero-knowledge proof, named FedZKP. It is shown that the FedZKP scheme without disclosing credentials is guaranteed to defeat a variety of existing and potential attacks. Both theoretical analysis and empirical studies demonstrate the security of FedZKP in the sense that the probability for attackers to breach the proposed FedZKP is negligible. Moreover, extensive experimental results confirm the fidelity and robustness of our scheme.
Zhiqiang Du, W. Jiang, Chenguang Tian, Xiaofeng Rong · 5 authors
Cloud computing is a disruptive technology that has transformed the way people access and utilize computing resources. Due to the diversity of services and complexity of environments, there is widespread interest in how to securely and efficiently authenticate users under the same domain. However, many traditional authentication methods involve untrusted third parties or overly centralized central authorities, which can compromise the security of the system. Therefore, it is crucial to establish secure authentication channels within trusted domains. In this context, we propose a secure and efficient authentication protocol, HIDA (Hyperledger Fabric Identity Authentication), for the cloud computing environment. Specifically, by introducing federated chain technology to securely isolate entities in the trust domain, and combining it with zero-knowledge proof technology, users’ data are further secured. In addition, Subsequent Access Management allows users to prove their identity by revealing only brief credentials, greatly improving the efficiency of access. To ensure the security of the protocol, we performed a formal semantic analysis and proved that it can effectively protect against various attacks. At the same time, we conducted ten simulations to prove that the protocol is efficient and reliable in practical applications. The research results in this paper can provide new ideas and technical support for identity authentication in a cloud environment and provide a useful reference for realizing the authentication problem in cloud computing application scenarios.
Raúl Casanova-Marqués, Joaquín Torres-Sospedra, Jan Hajný, Michael K. Gould
The increasing popularity of wearable-based Collaborative Indoor Positioning Systems (CIPSs) has led to the development of new methods for improving positioning accuracy. However, these systems often rely on protocols, such as iBeacon, that lack sufficient privacy protection. In addition, they depend on centralized entities for the authentication and verification processes. To address the limitations of existing protocols, this paper presents a groundbreaking contribution to the field of wearable-based CIPSs. We propose a decentralized Attribute-based Authentication (ABA) protocol that offers superior levels of privacy protection, untraceability, and unlinkability of user actions. Unlike existing protocols that rely on centralized entities, our approach leverages decentralized mechanisms for authentication and verification, ensuring the privacy of user location data exchange. Through extensive experimentation across multiple platforms, our results demonstrate the practicality and feasibility of the proposed protocol for real-world deployment. Overall, this work opens up new avenues for secure and privacy-preserving wearable-based CIPSs, with potential implications for the rapidly growing field of Internet of Things (IoT) applications.
Philipp G. Haselwarter, Exequiel Rivas, Antoine Van Muylder, Théo Winterhalter · 9 authors
State-separating proofs (SSP) is a recent methodology for structuring game-based cryptographic proofs in a modular way, by using algebraic laws to exploit the modular structure of composed protocols. While promising, this methodology was previously not fully formalized and came with little tool support. We address this by introducing SSProve, the first general verification framework for machine-checked state-separating proofs. SSProve combines high-level modular proofs about composed protocols, as proposed in SSP, with a probabilistic relational program logic for formalizing the lower-level details, which together enable constructing machine-checked cryptographic proofs in the Coq proof assistant. Moreover, SSProve is itself fully formalized in Coq, including the algebraic laws of SSP, the soundness of the program logic, and the connection between these two verification styles. To illustrate SSProve, we use it to mechanize the simple security proofs of ElGamal and pseudo-random-function–based encryption. We also validate the SSProve approach by conducting two more substantial case studies: First, we mechanize an SSP security proof of the key encapsulation mechanism–data encryption mechanism (KEM-DEM) public key encryption scheme, which led to the discovery of an error in the original paper proof that has since been fixed. Second, we use SSProve to formally prove security of the sigma-protocol zero-knowledge construction, and we moreover construct a commitment scheme from a sigma-protocol to compare with a similar development in CryptHOL. We instantiate the security proof for sigma-protocols to give concrete security bounds for Schnorr’s sigma-protocol.
Pedagogical ergonomics deals with the issues of rationalization of teacher's work and students' learning. The subject of pedagogical ergonomics is "human - educational environment". In recent years the educational environment has changed significantly under the influence of the process of its digitalization. It changes the psychology of teachers and students, gives rise to a number of safety issues and new aspects in the ergonomics of the educational process - its efficiency, rationality, safety, which remain little-studied. This article examines the use of artificial intelligence, zero-knowledge proof technology and machine learning in education from the perspective of basic principles of ergonomics - performance, efficiency, comfort of educational work, its safety. The article shows that digitalization of the educational environment helps to solve a number of problems of pedagogical ergonomics and serves to improve the quality of education and its accessibility for all. At the same time, the problems of using artificial intelligence in education are also noted. The possibilities of zero-knowledge proof technology that can help to reduce the risks of digitalization of the educational environment are considered.
We proposed a new construction for contract wallets, smart contract applications that allow users to control their crypto assets. Users can manipulate their crypto assets by simply sending emails with no need to manage keys. These emails are verified using zero-knowledge proof (ZKP) along with their attached digital signatures that the sender domain server (SDS) generates according to DomainKeys Identified Mail. Unless the SDS forges the emails, the crypto assets remain secure in the proposed system. Moreover, the existing SDSs can be used as is by outsourcing additional work to a third party that is not necessarily trusted. The system supports various functions to manipulate crypto assets. We produced a tool for variable-regex mapping (VRM) that enables developers to build a new function without ZKP skills. For example, using the tool, we built a demo application where users can exchange crypto assets via Uniswap only with emails. The published version of this paper is available at https://doi.org/10.1109/ICBC56567.2023.10174932.
While the Internet of things brings convenience to people's lives, it will also bring people hidden worries about data security. As an important barrier to protect data security, identity authentication is widely used in the Internet of things. However, it is necessary to protect users' identity privacy while authenticating their identity. Anonymous authentication technology is often used to solve the contradiction between legitimacy and privacy in the authentication process. The existing anonymous authentication scheme has many problems in practical application such as the inability to achieve complete anonymity, the high computational complexity of the algorithm, and the corruption of the central authority. Aiming at the privacy of authentication, we propose Zero-Cerd, a self-blindable anonymous authentication system based on blockchain and dynamic accumulator. The self-blinding properties of the credential enable the users themselves to generate a new validly pseudonymous credential. With the help of zero-knowledge proof technology, users can prove the validity of their credentials without disclosing any information. Security analysis shows that our scheme has achieved the expected security objectives. Compared with the existing schemes, our scheme has the advantages of complete anonymity and high efficiency, and is more suitable for IoT applications with privacy protection requirements.
In recent years, permissionless blockchains have gained significant attention for their ability to secure and provide transparency in transactions. The development of blockchain technology has shifted from cryptocurrency to decentralized finance, benefiting millions of unbanked individuals, and serving as the foundation of Web3, which aims to provide the next generation of the internet with data ownership for users. The rise of NFTs has also helped artists and creative workers to protect their intellectual property and reap the benefits of their work. However, privacy risks associated with permissionless blockchains have become a major concern for individuals and institutions. The role of blockchain in the transition from Web2 to Web3 is crucial, as it is rapidly evolving. As more individuals, institutions, and organizations adopt this technology, it becomes increasingly important to closely monitor the new risks associated with permissionless blockchains and provide updated solutions to mitigate them. This paper endeavors to examine the privacy risks inherent in permissionless blockchains, including Remote Procedure Call (RPC) issues, Ethereum Name Service (ENS), miner extractable value (MEV) bots, on-chain data analysis, data breaches, transaction linking, transaction metadata, and others. The existing solutions to these privacy risks, such as zero-knowledge proofs, ring signatures, Hyperledger Fabric, and stealth addresses, shall be analyzed. Finally, suggestions for the future improvement of privacy solutions in the permissionless blockchain space shall be put forward.
As digital payments become increasingly ubiquitous, concerns over data privacy and transaction security have intensified, prompting the need for privacy-preserving payment architectures. This study explores the design, implementation, and evaluation of payment systems that ensure confidentiality, integrity, and anonymity without compromising transactional efficiency or regulatory compliance. It examines key technologies such as homomorphic encryption, secure multiparty computation, zero-knowledge proofs, and blockchain-based mechanisms that enable secure payment verification and data sharing with minimal exposure of sensitive user information. Furthermore, it highlights privacy-enhancing frameworks integrated into mobile wallets, digital identity systems, and decentralized finance (DeFi) platforms. Through comparative analysis of centralized and decentralized payment models, the paper identifies trade-offs between scalability, transparency, and privacy assurance. The findings underscore that hybrid architectures—combining cryptographic privacy layers with compliance-enabling audit trails—represent the most viable approach for future financial ecosystems. Ultimately, privacy-preserving payment architectures not only safeguard user trust but also support regulatory adaptability and sustainable innovation in the evolving landscape of digital finance.
Smart contracts self-executing code deployed on blockchain platforms have revolutionized the way digital agreements are formed and executed. Despite their decentralized nature and deterministic logic, vulnerabilities in code and execution environments can compromise their security. Cryptography is pivotal in safeguarding the integrity, authenticity, and confidentiality of smart contract operations. This paper explores cryptographic techniques that enhance smart contract trustworthiness, including digital signatures, zero-knowledge proofs, and verifiable computation. We assess how these methods reinforce security, compare frameworks across criteria like scalability and auditability, and present best practices for secure smart contract development
Cristina Vilchez Moya, Juan Ramón Bermejo Higuera, Juan Ramón Bermejo Higuera, Javier Bermejo Higuera · 6 authors
The problem of digital identity acquires more relevance every day in the eyes of a society that spends more and more time connected to the Internet. It has evolved throughout its history to reach a decentralized model known as Self-Sovereign Identity (SSI), which finds its natural tools in the blockchain technology and Zero-Knowledge Proofs (ZKPs). ZKPs, in this context, allow users to prove that their credentials are legitimate without revealing more information than is strictly necessary, and constitute one of the most promising areas of applied cryptography. In this work, an application is developed for the study of Zero-Knowledge Proof methods and, specifically, in their application for authentication in public-private key encryption systems. It focuses on the study of three ZKP protocols (Feige-Fiat-Shamir, Guillou-Quisquater, and Schnorr, which rely on the problems of large number factorizations and discrete logarithms for security) in the practical use-case where a prover wants to demonstrate knowledge of a private key for a public key without revealing the key itself. The application allows the user to modify the necessary parameters in each method to achieve a better understanding of their role in their safety and efficiency. Several types of attacks are carried out against the above-mentioned protocols to analyze their degree of security and what recommendations can be made to improve it.
Abstract Blockchain and Decentralized Applications (DApps) are increasingly important for creating trust and transparency in data storage and computation. However, on-chain transactions are often costly and slow. To overcome this challenge, off-chain nodes can be used to store and compute data. Unfortunately, this introduces the risk of untrusted nodes. To address this, authenticated data structures have been proposed, however, this ignores the compute of data from the raw data. We tackle this challenge by introducing zk-Oracle, which provides an efficient and trusted compute and storage off-chain. There is a challenge in using zero-knowledge proofs (zk-proof for short), which is the large proof generation time. We aim to overcome it with novel designs in zk-Oracle. zk-Oracle builds on zk-proofs technologies to achieve two goals. First, the computation of data structures from raw data and the corresponding proof generation is improved in terms of performance. Second, the verification on-chain is inexpensive and fast. Our experiments show that we can speed up zk-proof generation by up to $$550 \times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>550</mml:mn> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> faster than the baseline method.
Xin Liu, Xiaomeng Liu, Naixue Xiong, Dan Luo · 6 authors
With the rapid development of cloud computing and other modern technologies, collaborative computing between data is increasing, and privacy protection and secure multi-party computation are also attracting more attention. The emergence of cloud computing provides new options for data holders to perform complex computing problems and to store images; however, data privacy issues cannot be ignored. If a graphic is encrypted and stored in the cloud, the cloud server will perform confidential similar matching when the user searches. At present, most research on searchable encryption is focused on text search, with few schemes researched on how to finish the graphic search. To solve this problem, this paper proposes a secure search protocol based on graph shape under the semi-honest model. Using the cut-choose method and zero-knowledge proof, further designs of the anti-malicious attack graphic similarity judgment system (AAJS) based on the Paillier encryption algorithm, can achieve the secure search and matching of the graph while resisting malicious adversary attacks. The proposed protocol’s security is proved by the real/ideal model paradigm. This paper conducts performance analysis and experimental simulation on the existing scheme and the experiments demonstrate that the system achieves high execution efficiency.
In this paper, we propose a physical protocol to verify the first nonzero term of a sequence using a deck of cards. The protocol lets a prover show the value of the first nonzero term of a given sequence to a verifier without revealing which term it is. Our protocol uses $Θ(1)$ shuffles, which is asymptotically lower than that of an existing protocol of Fukusawa and Manabe which uses $Θ(n)$ shuffles, where $n$ is the length of the sequence. We also apply our protocol to construct zero-knowledge proof protocols for three well-known logic puzzles: ABC End View, Goishi Hiroi, and Toichika. These protocols enables a prover to physically show that he/she know solutions of the puzzles without revealing them.
Abstract Fair exchange is a challenging problem for two mutually distrusting players. It is widely known that fair exchange is impossible without a trusted third party (TTP). However, relying on a single TTP can cause a single-point failure. An intuitive idea is to adopt multiple TTPs to distribute trust. This paper constructs a two-party optimistic fair exchange (OFE) protocol using decentralized ciphertext-policy attribute-based encryption (CP-ABE), achieving decentralized TTPs. This is achievable because decentralized CP-ABE ciphertext supports a nested access control policy. A nested access control policy fits perfectly in a fair exchange protocol which contains multiple roles (i.e. players and TTPs). Further, we apply non-interactive zero knowledge proofs to prove the well-formedness of ciphertexts, so as to enforce players to follow the protocol specification honestly. Consequently, we construct an OFE protocol in which each player’s operations are publicly verifiable without revealing secret information. Also, we obtain decentralized TTPs with optimism (i.e. the TTPs are involved only when arbitration is required), autonomy (i.e. the TTPs do not need to interact with each other), statelessness (i.e. the TTPs do not need to store data for the exchange protocol) and verifiability (i.e. the TTPs are publicly verifiable). Compared with previous work, our protocol assumes only a public communication channel and each party’s operations are publicly verifiable. Besides, it achieves a favorable $O(n)$ verification complexity in the normal case, where $n$ is the number of TTPs. Finally, we present a proof-of-concept implementation to demonstrate the feasibility.