Zero-Knowledge Proofs (ZKPs) are a rapidly growing technique for privacy-preserving and verifiable computation.ZKPs enable one party (a prover: P) to prove to another (a verifier: V) that a statement is true or correct without revealing any additional information.This powerful capability has led to ZKPs being applied and proposed for application in blockchain technologies, verifiable machine learning, and electronic voting.However, ZKPs have yet to see widespread, ubiquitous adoption due to the exceptionally high computational complexity of the proving process.Naturally, there has been recent work to accelerate ZKP primitives and protocols using GPUs and ASICs.However, the protocols considered so far face one of two challenges: they require a trusted setup for each new application or generate large proofs with high verification costs, limiting their applicability in scenarios with numerous verifiers or strict verification time constraints.HyperPlonk is a state-of-theart ZKP protocol that supports both one-time, universal setup and small proof sizes/verification costs expected by publicly verifiable, consensus-based systems (e.g., blockchain).While HyperPlonk's setup and verifier properties are highly desirable, the proving phase is costly.A HyperPlonk prover must compute on large bitwidths (e.g., 255-381b) and polynomials (e.g., of degree 2 24 ), employs computationally (e.g., MSM) and bandwidth (e.g., SumCheck) intensive kernels, and the complete protocol comprises many steps, each constituting distinct kernels.We present an accelerator, zkSpeed, to
The seminal work of Goldreich and Krawczyk (SIAM Journal on Computing) shows that any constant-round public-coin interactive proof for languages not in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">B</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> </mml:mrow> </mml:mrow> </mml:math> cannot be black-box zero knowledge. Their result says nothing, however, about proofs (or arguments) of knowledge for languages in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">B</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> </mml:mrow> </mml:mrow> </mml:math>. As a special case, their work leaves open the question of whether Schnorr's protocol for proving knowledge of discrete logarithms in cyclic groups is black-box zero knowledge. In this work we focus on the zero knowledge of proofs of knowledge, centering on Schnorr's protocol as a prominent example. We prove two lower bounds, ruling out two different classes of simulators through which Schnorr's protocol can be proven zero knowledge: We prove that if a relation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℛ</mml:mi> </mml:mrow> </mml:math> has a public-coin interactive proof of knowledge that is black-box zero knowledge and this protocol is compatible with the Fiat-Shamir transform in the random oracle model, then <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℛ</mml:mi> </mml:mrow> </mml:math> must be efficiently searchable. As an immediate corollary, we deduce that Schnorr's protocol cannot be black-box zero knowledge in groups in which discrete log is hard. We define a new class of simulators for Schnorr's protocol, which we call generic simulators. A generic simulator is one that works in any cyclic group, and does not use the representation of the specific group in which Schnorr's protocol is instantiated. We prove that Schnorr's protocol cannot have generic simulators. As an additional contribution, we generalize the original lower bound of Goldreich and Krawczyk, to prove that a language not in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="sans-serif">B</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> <mml:mi mathvariant="sans-serif">P</mml:mi> </mml:mrow> </mml:mrow> </mml:math> cannot have an interactive proof (not necessarily of knowledge) that is both black-box zero knowledge and compatible with the Fiat-Shamir transform in the random oracle model. In conjunction with recent works, this extends the Goldreich-Krawczyk lower bound to public-coin protocols that are not constant-round but have round-by-round soundness, including the parallel repetition of any public-coin interactive proof.
Michele Orrù, George Kadianakis, Mary Maller, Greg Zaverucha
A fundamental challenge in zero-knowledge proof systems is implementing operations that are “foreign” to the underlying constraint system, in that they are arithmetic operations with a different modulus than the one used by the proof system. The modulus of the constraint system is a large prime, and common examples of foreign operations are Boolean operations, field arithmetic, or public-key cryptography operations. We present novel techniques for efficiently embedding such foreign arithmetic in zero-knowledge, including (i) equality of discrete logarithms across different groups; (ii) scalar multiplication without requiring elliptic curve operations; (iii) proving knowledge of an AES encryption. Our approach combines rejection sampling, sigma protocols, and lookup protocols. We implement and provide concrete benchmarks for our protocols.
Justin A. Drake, Dmitry Khovratovich, Mikhail Kudinov, Benedikt Wagner
With the threat posed by quantum computers on the horizon, systems like Ethereum must transition to cryptographic primitives resistant to quantum attacks. One of the most critical of these primitives is the non-interactive multi-signature scheme used in Ethereum's proof-of-stake consensus, currently implemented with BLS signatures. This primitive enables validators to independently sign blocks, with their signatures then publicly aggregated into a compact aggregate signature. In this work, we introduce a family of hash-based signature schemes as post-quantum alternatives to BLS. We consider the folklore method of aggregating signatures via (hash-based) succinct arguments, and our work is focused on instantiating the underlying signature scheme. The proposed schemes are variants of the XMSS signature scheme, analyzed within a novel and unified framework. While being generic, this framework is designed to minimize security loss, facilitating efficient parameter selection. A key feature of our work is the avoidance of random oracles in the security proof. Instead, we define explicit standard model requirements for the underlying hash functions. This eliminates the paradox of simultaneously treating hash functions as random oracles and as explicit circuits for aggregation. Furthermore, this provides cryptanalysts with clearly defined targets for evaluating the security of hash functions. Finally, we provide recommendations for practical instantiations of hash functions and concrete parameter settings, supported by known and novel heuristic bounds on the standard model properties.
Suhyeon Lee, Euisin Gee, Najmeh Soroush, Muhammed Ali Bingol · 5 authors
Simple commit-reveal beacons are vulnerable to last-revealer strategies, and existing descriptions often leave accountability and recovery mechanisms unspecified for practical deployments. We present Commit-Reveal$^2$, a layered design for blockchain deployments that cryptographically randomizes the final reveal order, together with a concrete accountability and fallback mechanism that we implement as smart-contract logic. The protocol is architected as a hybrid system, where routine coordination runs off chain for efficiency and the blockchain acts as the trust anchor for commitments and the final arbiter for disputes. Our implementation covers leader coordination, on-chain verification, slashing for non-cooperation, and an explicit on-chain recovery path that maintains progress when off-chain coordination fails. We formally define two security goals for distributed randomness beacons, unpredictability and bit-wise bias resistance, and we show that Commit-Reveal$^2$ meets these notions under standard hash assumptions in the random-oracle model. In measurements with small to moderate operator sets, the hybrid design reduces on-chain gas by more than 80% compared to a fully on-chain baseline. We release a publicly verifiable prototype and evaluation artifacts to support replication and adoption in blockchain applications.
An E-voting framework utilizing decentralized technology can establish a secure and transparent environment for elections, where voters can confidently cast their ballots knowing that their votes are final and untampered with. Blockchain's decentralized structure ensures that votes are recorded accurately, preventing interference from external actors. In a protected Evoting framework, each vote becomes part of an immutable, distributed ledger, allowing for peer-to-peer validation of transactions. This ensures that each voice counts as the only, unchanging record. The results can be reported immediately as soon as the voting process is completed. Voting is a critical process carried out in democratic societies, usually through secret voting documents or other similar methods. However, traditional voting systems are often plagued by problems such as voting manipulation, low turnout and logistics challenge. To solve these problems, we propose implementation of decentralized voting platforms that offer advanced security, efficiency and confidence in the election process
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2 source records
Internet Traffic Analysis and Secure E-voting
Blockchain Technology Applications and Security
Advanced Steganography and Watermarking Techniques
Distributed Ledger Technologies (DLTs), including Blockchain, have revolutionized financial systems by offering decentralized, transparent, and secure mechanisms for data management and transactions. However, for these systems to maintain integrity and protect sensitive financial data, robust cryptographic techniques are essential. Cryptography ensures data confidentiality, authenticity, integrity, and non-repudiation, which are critical for the security of financial transactions in DLTs. This article examines the role of cryptographic protocols such as hashing, digital signatures, asymmetric encryption, and zero-knowledge proofs in safeguarding distributed ledgers. Furthermore, we explore their applications in securing financial transactions, preventing fraud, ensuring compliance, and enhancing the overall reliability of DLTs in financial systems. The discussion also delves into the challenges of cryptographic security in the face of emerging threats and the potential impact of quantum computing on existing cryptographic protocols.
The protection of personal privacy has become a paramount issue in the field of data science, with its significance continuously rising. Differential privacy technology has garnered significant attention for its effectiveness in preserving individual privacy. However, the implementation of differential privacy relies on a degree of trust in the entities or individuals executing the algorithms. This paper proposes an innovative solution: a verifiable differential privacy mechanism based on zero-knowledge proofs. This approach integrates differential privacy with zero-knowledge proof technology to not only verify the correctness of the differential privacy techniques but also enhance the transparency and reliability of the algorithms. Additionally, we have designed a publicly verifiable data release scheme that integrates commitment mechanisms and range proofs, ensuring that the range of published data noise does not exceed predetermined thresholds, thereby ensuring the utility of the data. Compared to other verifiable differential privacy solutions, our approach is unique in that it does not rely on the number of participants but is solely dependent on the precision of the data. This means that our computational cost will not increase with the addition of more participants. Finally, we conducted a performance evaluation of the solution, which only took 700ms to complete a single verification. On average, there was a 6% reduction in expectation and a 40% reduction in variance, demonstrating the enhancement of its data utility and the feasibility and effectiveness in practical applications.
This article presents a comprehensive framework for implementing privacy-preserving credit card reward systems using Secure Multi-Party Computation (SMPC) technologies. Traditional reward architectures require extensive sharing of sensitive transaction data across multiple entities, creating significant privacy risks, security vulnerabilities, and regulatory compliance challenges. It leverages cryptographic advances to enable card issuers, payment networks, and merchant partners to collaborate on reward calculations,fraud detection, and personalized offers without revealing sensitive transaction details to one another. The article explores the evolution of privacy-preserving technologies in financial systems, comparing Fully Homomorphic Encryption, Zero-Knowledge Proofs, and SMPC approaches. A detailed case study of a travel rewards program implementation demonstrates how this framework ensures data remains protected throughout the entire process while maintaining the performance characteristics necessary for production deployment. The system provides comprehensive privacy protection, enhances fraud detection capabilities through secure collaboration, and facilitates compliance with evolving privacy regulations.Performance evaluations confirm the practical viability of the article, with minimal latency impact, strong scalability characteristics, and robust security guarantees. It contributes to the growing field of privacy-enhancing technologies for financial services and offers a viable solution to balance analytical utility with privacy protection in consumer-facing applications.
This paper presents the translation of regulatory smart contracts written in RegLang into MedTiny, a component-based modeling language tailored for the development and verification of reliable systems. RegLang, a domain-specific language for embedding regulatory requirements in smart contracts, is limited by its users' expertise in smart contract development and formal verification. To address this, we propose an automated code generation method that translates RegLang contracts into MedTiny, enabling domain experts to utilize MedTiny's verification capabilities and modular system architecture. By leveraging MedTiny's toolchain and SMT solvers, we detect redundancies and conflicts in regulations early in the development cycle, helping domain experts avoid introducing unintended behaviors. This approach not only preserves the original specifications of RegLang contracts but also improves overall system reliability by integrating comprehensive verification capabilities. A case study illustrates the practical benefits of this translation, supporting complex rule-based contract management and mitigating the risks associated with regulatory changes.
In this work, we address the evolutionary computation in programmable cryptography on blockchain technologies for the first time in the literature. For that, we propose a novel privacy-preserving and decentralized protocol ([email protected]) where the evolutionary computation model is public while the user inputs/outputs (i.e. the current and next populations) are private. The protocol relies on the transitions between the public-domain (i.e. contract-domain) and the private-domain (i.e. evolutionary-domain) to be secure. We perform an experimental study using two popular benchmark problems to measure the blockchain gas consumption, zero-knowledge proof generation/verification times and zero-knowledge proof size.
Open access
Blockchain Technology Applications and Security
Advanced Steganography and Watermarking Techniques
Multi-Party Computation (MPC), as a distributed computing paradigm, is considered to be a potential solution for providing privacy-preserving for applications following the client-server model. However, traditional MPC solutions cannot satisfy the publicly verifiable requirement of the client-server model. In this paper, we propose a blockchain-based verifiable MPC solution using Pedersen's threshold secret sharing and Lifted ElGamal encryption. We first build a data distribution method using Pedersen's threshold secret sharing and symmetric encryption to protect the privacy of inputs while ensuring robustness. Then, we propose a result processing algorithm using Lifted ElGamal encryption to safeguard the privacy of the outputs. Finally, we employ non-interactive zero-knowledge proof and Pedersen commitment to publicly verify the correctness of the encrypted outputs in the smart contract, enabling the detection of malicious parties. Theoretical analysis indicates that the proposed method can publicly verify the correctness of outputs without revealing plain-text inputs and outputs, which satisfy the privacy-preserving requirements of the client-server model. Experimental evaluations have demonstrated that our proposed approach is efficient regarding computation overhead, communication overhead, and response time in the output verification phase while achieving stronger privacy and robustness.
Farhana Javed, Engin Zeydan, Josep Mangues‐Bafalluy, Kapal Dev · 5 authors
As edge computing gains prominence in Internet of Things (IoTs), smart cities, and autonomous systems, the demand for real-time machine intelligence with low latency and model reliability continues to grow. Federated Learning (FL) addresses these needs by enabling distributed model training without centralizing user data, yet it remains reliant on centralized servers and lacks built-in mechanisms for transparency and trust. Blockchain, a type of Distributed Ledger Technologies (DLTs) can fill this gap by introducing immutability, decentralized coordination, and verifiability into FL workflows. This article presents current standardization efforts from 3GPP, ETSI, ITU-T, IEEE, and O-RAN that steer the integration of FL and blockchain in IoT ecosystems. We then propose a blockchain-based FL framework that replaces the centralized aggregator, incorporates reputation monitoring of IoT devices, and minimizes overhead via selective on-chain storage of model updates. We validate our approach with IOTA Tangle, demonstrating stable throughput and block confirmations, even under increasing FL workloads. Finally, we discuss architectural considerations and future directions for embedding trustworthy and resource-efficient FL in emerging 6G networks and vertical IoT applications. Our results underscore the potential of DLT-enhanced FL to meet stringent trust and energy requirements of next-generation IoT deployments.
Sang-Hyeon Park, Jeonghyuk Lee, Seunghwa Lee, Jung Hyun Chun · 8 authors
Merging Internet (web2) identities with blockchain (web3) identities is increasingly important for enhancing user experience and ensuring regulatory compliance. However, conventional solutions that map web2 identities to web3 accounts often lead to privacy concerns and fragmented identifiers across networks. To address these challenges, we propose a new identity scheme named Address Abstraction (AA), which redefines blockchain address and signing systems while preserving key properties: uniqueness, immutability, and privacy-preservation. This approach eliminates the limitations of chain-specific identity systems, enabling users to interact with multiple blockchains using their web2 certificates and unified identifiers. This chain-agnostic identifier also promotes cross-chain compatibility. We further present Zero-Knowledge Address Abstraction (zkAA), an implementation of AA that uses zero-knowledge proofs to uphold AA's core properties. Additionally, a proof aggregation technique combines multiple proofs into one, achieving approximately 5.5 times gas cost savings during verification in real-world scenarios. As of August 2024, zkAA with proof aggregation incurs an additional cost of only $0.66 per transaction on Ethereum.
Background: Even while traditional Raft is effective at leader election and log replication, it is not appropriate for sensitive applications like supply chains, financial systems, or healthcare because it lacks built-in privacy safeguards. Materials and Methods: A privacy-preserving Raft consensus method is proposed to solve the privacy issues that occur when private information is transferred between nodes in a distributed system such as a blockchain. Raft itself, by default, does not provide any steps toward ensuring data confidentiality during consensus. By employing privacy-preserving cryptographic techniques like homomorphic encryption and zero-knowledge proofs, nodes can reach consensus while keeping sensitive data private. Results: Traditional Raft performs much better in scenarios where performance matters, while Privacy-Perving Raft works better in a sensitive application to privacy (the average of write throughput is 5% lower than that of traditional Raft) and CPU is 40-60%. Conclusion: Based on the gained privacy by some computational costs, it will be valid to draw the conclusion that this works for privacy-sensitive applications within decentralized systems with these performance and security analyses.
In response to the issues of high transaction transparency and regulatory difficulties in blockchain account-model transactions, this paper presents a supervised blockchain anonymous transaction model based on certificateless signcryption aimed at ensuring secure blockchain transactions while minimizing both computational and communication overhead. During the transaction process, this approach utilizes certificateless public key signcryption without bilinear pairs to generate anonymous user identities, achieving strong anonymity of user identities and confidentiality of transaction amounts. It employs the Paillier homomorphic encryption algorithm to update transaction amounts and uses the FO commitment-based zero-knowledge proof scheme to validate transaction legality. Additionally, adopting a publicly verifiable secret threshold sharing scheme for hierarchical regulatory authority reduces the security risk of a single regulator storing the regulatory key. This model not only meets the privacy and timely update requirements of account-based blockchain transactions but also effectively regulates abnormal transactions. Rigorous security analysis and proofs demonstrate that this model possesses excellent anonymity, traceability, forward security, and backward security. When compared to similar schemes, the computational cost is reduced by at least 33.18%, effectively fulfilling the requirements for security.
With the emergence of illegal behaviors such as money laundering and extortion, the regulation of privacy-preserving cryptocurrency has become increasingly important. However, existing regulated privacy-preserving cryptocurrencies usually rely on a single regulator, which seriously threatens users’ privacy once the regulator is corrupt. To address this issue, we propose a linkable group signature against malicious regulators (ALGS) for regulated privacy-preserving cryptocurrencies. Specifically, a set of regulators work together to regulate users’ behavior during cryptocurrencies transactions. Even if a certain number of regulators are corrupted, our scheme still ensures the identity security of a legal user. Meanwhile, our scheme can prevent double-spending during cryptocurrency transactions. We first propose the model of ALGS and define its security properties. Then, we present a concrete construction of ALGS, which provides CCA-2 anonymity, traceability, non-frameability, and linkability. We finally evaluate our ALGS scheme and report its advantages by comparing other schemes. The implementation result shows that the runtime of our signature algorithm is reduced by 17% compared to Emura et al. (2017) and 49% compared to KSS19 (Krenn et al. 2019), while the verification time is reduced by 31% compared to Emura et al. and 47% compared to KSS19.
Muhammad Firdaus, Harashta Tatimma Larasati, Kyung Hyune-Rhee
Healthcare data is often fragmented across various institutions due to its highly sensitive and private nature. In this sense, hospitals and clinics maintain electronic health records (EHRs) independently; hence, valuable data is siloed within individual organizations, preventing comprehensive analysis that could benefit from diverse data sources. Federated learning (FL) addresses these challenges by enabling the training of a shared global model using data distributed across multiple institutions without moving the data from its source. By leveraging FL, healthcare institutions can combine their data assets to improve predictive analytics, personalized medicine, and overall healthcare outcomes, ultimately benefiting patients and the healthcare system. However, the current FL model with a central server presents several challenges within healthcare, including the risk of malicious attacks, regulatory compliance, and privacy vulnerabilities. To overcome these issues, this paper introduces the FL framework with blockchain and homomorphic encryption (HE). Our framework aims to minimize the role of the central server, enable collaborative model training across healthcare organizations, and enhance data security and privacy. In this sense, blockchain ensures the integrity and transparency of the process, while homomorphic encryption ensures that the data remains private. This framework can potentially enable institutions to enrich medical knowledge while securely keeping patient data collaboratively and facilitating healthcare analytics in practical settings.
Blockchain technology is rapidly evolving, with scalability remaining one of its most significant challenges. While various solutions have been proposed and continue to be developed, it is essential to consider the blockchain trilemma -- balancing scalability, security, and decentralization -- when designing new approaches. One promising solution is the zero-knowledge proof (ZKP)-based rollup, implemented on top of Ethereum. However, the performance of these systems is often limited by the efficiency of the ZKP mechanism. This paper explores the performance of ZKP-based rollups, focusing on a solution built using the Hardhat Ethereum development environment. Through detailed analysis, the paper identifies and examines key bottlenecks within the ZKP system, providing insight into potential areas for optimization to enhance scalability and overall system performance.
A Decentralized Identifier (DID) empowers an entity to prove control over a unique and self-issued identifier without relying on any identity provider. The public key material for the proof is encoded into an associated DID document (DDO). This is preferable shared via a distributed ledger because it guarantees algorithmically that everyone has access to the latest state of any tamper-proof DDO but only the entities in control of a DID are able to update theirs. Yet, it is possible to grant deputies the authority to update the DDO on behalf of the DID owner. However, the DID specification leaves largely open on how authorizations over a DDO are managed and enforced among multiple deputies. This article investigates what it means to govern a DID and discusses various forms of how a DID can be controlled by potentially more than one entity. It also presents a prototype of a DID-conform identifier management system where a selected set of governance policies are deployed as Smart Contracts. The article highlights the critical role of governance for the trustworthy and flexible deployment of ledger-anchored DIDs across various domains.
Zeta Avarikioti, Eleftherios Kokoris Kogias, Ray Neiheiser, Christos Stefo
The security of many Proof-of-Stake (PoS) payment systems relies on quorum-based State Machine Replication (SMR) protocols. While classical analyses assume purely Byzantine faults, real-world systems must tolerate both arbitrary failures and strategic, profit-driven validators. We therefore study quorum-based SMR under a hybrid model with honest, Byzantine, and rational participants. We first establish the fundamental limitations of traditional consensus mechanisms, proving two impossibility results: (1) in partially synchronous networks, no quorum-based protocol can achieve SMR when rational and Byzantine validators collectively exceed $1/3$ of the participants; and (2) even under synchronous network assumptions, SMR remains unattainable if this coalition comprises more than $2/3$ of the validator set. Assuming a synchrony bound $Δ$, we show how to extend any quorum-based SMR protocol to tolerate up to $1/3$ Byzantine and $1/3$ rational validators by modifying only its finalization rule. Our approach enforces a necessary bound on the total transaction volume finalized within any time window $Δ$ and introduces the \emph{strongest chain rule}, which enables efficient finalization of transactions when a supermajority of honest participants provably supports execution. Empirical analysis of Ethereum and Cosmos demonstrates validator participation exceeding the required $5/6$ threshold in over $99%$ of blocks, supporting the practicality of our design. Finally, we present a recovery mechanism that restores safety and liveness after consistency violations, even with up to $5/9$ Byzantine stake and $1/9$ rational stake, guaranteeing full reimbursement of provable client losses.
Machine Learning (ML) in distributed environments increasingly deals with sensitive data (like healthcare or financial records) that cannot be centrally stored or processed due to privacy concerns. Federated Learning (FL) addresses this by enabling model training across decentralized devices, but faces significant challenges including system reliability, node failures, and trust issues among participants. Traditional FL approaches often rely on centralized coordinators, creating single points of failure and potential security vulnerabilities. This paper presents a novel approach to FL that leverages smart contracts, blockchain, and decentralized storage to enhance the traceability and reliability of the learning process. Our proposed system architecture is fully decentralized, eliminating single points of failure and promoting cooperation through a rewarding mechanism. Unlike previous approaches that neglect node fault tolerance, we introduce a smart contract based scheme for managing node failures and electing the aggregator node. The presence of the smart contract, executed on a decentralized permissioned blockchain, provides reliability guarantees and eliminates the need for costly distributed algorithms in terms of message exchange. An experimental study is conducted to evaluate various aspects of the FL system. We present results related to the accuracy and effectiveness of the FL system on ML models. We also examine the performance related to the distribution of the weights of the ML model based on the use of IPFS. Furthermore, we analyze the performance of the smart contract in terms of gas consumption. Lastly, we investigate the impact of failures combined with incentive policies and aggregator election algorithms on the FL system. Our findings demonstrate the viability of the proposed approach, paving the way for more robust, reliable, and efficient FL systems.
Federated Learning (FL) has emerged as a promising paradigm in distributed machine learning, enabling collaborative model training while preserving data privacy. However, despite its many advantages, FL still contends with significant challenges -- most notably regarding security and trust. Zero-Knowledge Proofs (ZKPs) offer a potential solution by establishing trust and enhancing system integrity throughout the FL process. Although several studies have explored ZKP-based FL (ZK-FL), a systematic framework and comprehensive analysis are still lacking. This article makes two key contributions. First, we propose a structured ZK-FL framework that categorizes and analyzes the technical roles of ZKPs across various FL stages and tasks. Second, we introduce a novel algorithm, Verifiable Client Selection FL (Veri-CS-FL), which employs ZKPs to refine the client selection process. In Veri-CS-FL, participating clients generate verifiable proofs for the performance metrics of their local models and submit these concise proofs to the server for efficient verification. The server then selects clients with high-quality local models for uploading, subsequently aggregating the contributions from these selected clients. By integrating ZKPs, Veri-CS-FL not only ensures the accuracy of performance metrics but also fortifies trust among participants while enhancing the overall efficiency and security of FL systems.
Anne Broadbent, Alex B. Grilo, Nagisa Hara, Arthur Mehta
In a proof of knowledge (PoK), a verifier becomes convinced that a prover possesses privileged information. In combination with zero-knowledge proof systems, PoKs play an important role in security protocols such as in digital signatures and authentication schemes, as they enable a prover to demonstrate possession of certain information (such as a private key or a credential), without revealing it. A PoK is formally defined via the existence of an extractor, which is capable of reconstructing the key information that makes a verifier accept, given oracle access to any accepting prover. We extend this concept to the setting of a single classical verifier and multiple quantum provers and present the first statistical zero-knowledge (ZK) PoK proof system for problems in QMA. To achieve this, we establish the PoK property for the ZK protocol of Broadbent, Mehta, and Zhao (TQC 2024), which applies to the local Hamiltonian problem. More specifically, we construct an extractor which, given oracle access to a provers' strategy that leads to high acceptance probability, is able to reconstruct the ground state of a local Hamiltonian. Our result can be seen as a new form of self-testing, where, in addition to certifying a pre-shared entangled state, the verifier also certifies that a prover has access to a quantum system, in particular, a ground state; this indicates a new level of verification for a proof of quantumness.