Cloud computing allows clients with limited computational resources to offload computations to more powerful remote servers. In this paradigm, homomorphic encryption (HE) schemes enable a server to run any computation on a client's encrypted data. These schemes are widely used in cloud computing protocols such as delegated computing, two-party secure computation, and zero-knowledge proofs. Quantum homomorphic encryption (QHE) aims to achieve the objectives of HE with quantum data and quantum circuits, enabling cloud quantum servers to compute on encrypted quantum data uploaded by clients. In this work, we consider a scenario where a client has access to a quantum “encryption/decryption device”, which allows the encryption, transmission, reception, and decryption of quantum states, but not universal quantum computation. In this setting, we provide a proof-of-concept software simulation of quantum homomorphic encryption. Our code implements the “EPR scheme” of Broadbent and Jeffery, which allows for the execution of universal quantum circuits by the server at the cost of requiring shared EPR pairs between the client and server. Our implementation explores the near-term viability of the EPR scheme. Perhaps unsurprisingly, our experiments indicate that the additional cost of homomorphic circuit evaluation is minor in comparison to the simulation cost of the quantum operations. Our simulation toolkit is implemented in Python and is open-source.
Data privacy has become a severe concern due to the substantial growth in data gathering and processing, driven by the widespread adoption of cloud computing and cryptocurrency. Zero-Knowledge Proof (ZKP) has emerged as a promising cryptographic protocol for ensuring data privacy. However, ZKP suffers from high computational costs, making it excessively slow when implemented in software. To identify performance bottlenecks in the ZKP protocol, existing research has focused on CPU performance evaluation at the architecture level, considering factors such as execution time and memory consumption. Nevertheless, ZKP protocols have distinct memory and computing needs at each stage, these studies lack detailed CPU performance analyses necessary to improve ZKP performance and promote wider adoption.In this paper, we provide a comprehensive performance analysis of widely used ZKP libraries on CPUs. We perform four different analyses to characterize the CPU microarchitecture, memory, code, and scalability performance of the ZKP protocol on different CPUs. Our analysis reveals that the ZKP protocol performs differently on different CPUs, emphasizing the need for microarchitecture-specific analysis and optimizations. We evaluate loads and stores, last level cache (LLC) misses per kilo instructions (MPKI), and maximum memory bandwidth utilization of ZKP. We observe the proving stage consumes the highest memory bandwidth (25Gbps). We identify the functions that consume the most CPU time in each stage of the ZKP protocol and categorize each stage as compute, control-flow, or data-flow intensive. Also, we identify the proving stage as the most scalable with the potential to be sped up by parallel computation. These findings provide valuable insights for designing future ZKP accelerators, leading to more efficient and scalable ZKP implementations.
Haotian Yang, Pujie Jing, Zihan Wu, Lu Liu · 5 authors
The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.
In this paper, we propose a smart contract-based multi-candidate self-tallying voting scheme in order to guarantee the privacy of ballots in the case of multiple candidates. This scheme uses the ElGamal cryptosystem to ensure the security of the ballots, and combines it with a Distributed Encryption algorithm to make the voting scheme have self-tallying features, and guarantees the correctness of the intermediate data through zero-knowledge proofs. The experimental results show that the scheme improves the voting efficiency without compromising the security.
Identity-based threshold signature (IDTHS) allows a threshold number of signers to generate signatures to improve the deterministic wallet in the blockchain . However, the IDTHS scheme cannot determine the identity of malicious signers in case of misinformation . To solve this challenge, we propose an identity-based threshold (multi) signature with private accountability (for short AIDTHS) for privacy-preserving blockchain . From the public perspective, AIDTHS is completely private and no user knows who participated in generating the signature. At the same time, when there is a problem with the transaction, a trace entity can trace and be accountable to the signers. We formally define the syntax and security model of AIDTHS. To address the issue of identifying malicious signers, we improve upon traditional identity-based threshold signatures by incorporating zero-knowledge proofs as part of the signature and leveraging a tracer holding tracing keys to identify all signers. Additionally, to protect the privacy of signers, the signature is no longer achievable by anyone, which requires a combiner holding the keys to produce a valid signature. We give a concrete construction of AIDTHS and prove its security. Finally, we implement the AIDTHS scheme and compare it with existing schemes. The key distribution algorithm of AIDTHS takes 13.04 ms and the signature algorithm takes 34.60 μ s . The verification algorithm takes 1 s , which is one-third of the time the TAPS scheme uses.
R. Shashidhara, Renju Chirakarotu Nair, Pavan Kumar Panakalapati
ABSTRACT Blockchain technology has revolutionized data sharing and storage, yet maintaining privacy and security while ensuring transparency and immutability remains a significant challenge. This research addresses this challenge by investigating the promising solution of Zero‐Knowledge Proofs (ZKPs), which allow for validation without revealing additional information. Unlike previous studies that focus on specific ZKP types or limited performance metrics, this article provides a comprehensive analysis of multiple ZKP technologies, along with their distinct features and blockchain applications. We evaluate ZKP tools such as snarkjs, ZoKrates, and Circom, focusing on key factors including proof size, trusted setup, prover time, verifier time, and scalability. A detailed case study on the Ethereum blockchain demonstrates the practical implementation and performance of ZKPs, effectively bridging the gap between theoretical analysis and real‐world applications. Furthermore, we explore how ZKPs can significantly enhance scalability in blockchain applications. By proposing innovative ZKP use cases and addressing current challenges, this article not only provides a comprehensive understanding of ZKP technologies but also outlines potential future research directions, making a significant impact on the field of blockchain privacy and security.
A Zero-Knowledge Proof basically is a protocol between two parties, the Prover and the Verifier, that allows the Prover to convince the Verifier about the truthness of a non trivial statement without revealing any additional information. Zero Knowledge Proofs have found a lot of practical applications covering most of the protocols concerning about data privacy and protocol verification. Examples of that are anonymous cash or electronic voting. The possibility to have real quantum computers with a reasonable size in a near future is forcing the cryptographic community to devise new methods to provide security that resist quantum attacks. Most of the zero-knowledge protocols used nowadays are based on computational problems like the discrete logarithm problem that can no longer be considered hard, since there are known efficient ways to solve them with quantum algorithms. Cryptographic research about the quantum security of zero knowledge proofs started nearly 20 years ago in a very theoretical approach, but not many papers on that topic appeared since then. The goal of this thesis is writing a survey including the main concepts about quantum secure zero-knowledge protocols, the state-of-the-art both from the theoretical and practical approaches, and an exploration of their potential application areas. The survey will be a good starting document for further students willing to do research in this topic.
Private set intersection (PSI) has important application value, however, current quantum PSI protocols are either unsuitable for multi-party scenarios or inefficient. Recently, Imran (arXiv: 2303.17196v3 , 2023) proposed two quantum secure multi-party greatest common divisor (GCD) protocols that can be used for PSI, but with the downside of information leakage and resource consumption. In this paper, we propose a novel quantum secure multi-party GCD protocol that has higher security and lower complexity. To hide privacy, each party randomly selects a coefficient within a range determined by his input integer, and with the assistance of a semi-honest third party TP, all parties secretly calculate the linear combination of their inputs under these coefficients. Once enough linear combinations are collected, TP calculates the GCD of these combinations, which is equal to the GCD of all input integers. To verify the honesty of participants, a quantum zero-knowledge proof sub-protocol is designed. Analysis shows that our GCD protocol is correct and has security against malicious attacks. Moreover, its complexity is polynomial level and lower than Imran’s. Furthermore, we demonstrate the scalability of our GCD protocol in private set operations, such as private set intersection, private set intersection cardinality, private multi-set intersection, etc.
The increased use of artificial intelligence generated content (AIGC) among vast user populations has heightened the risk of private data leaks. Effective auditing and regulation remain challenging, further compounding the risks associated with the leaks involving model parameters and user data. Blockchain technology, renowned for its decentralized consensus mechanism and tamper-resistant properties, is emerging as an ideal tool for documenting, auditing, and analyzing the behaviors of all stakeholders in machine learning as a service (MLaaS). This study centers on biometric recognition systems, addressing pressing privacy and security concerns through innovative endeavors. We conducted experiments to analyze six distinct deep neural networks, leveraging a dataset quality metric grounded in the query output space to quantify the value of the transfer datasets. This analysis revealed the impact of imbalanced datasets on training accuracy, thereby bolstering the system's capacity to detect model data thefts. Furthermore, we designed and implemented a novel Bio-Rollup scheme, seamlessly integrating technologies such as certificate authority, blockchain layer two scaling, and zero-knowledge proofs. This innovative scheme facilitates lightweight auditing through Merkle proofs, enhancing efficiency while minimizing blockchain storage requirements. Compared to the baseline approach, Bio-Rollup restores the integrity of the biometric system and simplifies deployment procedures. It effectively prevents unauthorized use through certificate authorization and zero-knowledge proofs, thus safeguarding user privacy and offering a passive defense against model stealing attacks.
On 30 April, Regulation (EU) 2024/1183 amending Regulation (EU) 910/2014 as regards establishing the European Digital Identity Framework, known as eIDAS 2.0, was published in the Official Journal of the European Union. This amendment introduces zero-knowledge proof (ZKP) privacy-enhancing technologies to support two key innovations: the European Digital Identity Wallet (EUDIW) and the electronic attestations of attributes ((Q)EAA). In parallel, the European Digital Identity Wallet Architecture and Reference Framework (EUDIW ARF) provide a common set of standards and best practices for the technical implementation of eIDAS 2.0. This paper analyses how the EUDIW can rely on ZKPs since neither the eIDAS 2.0 Regulation nor the EUDIW ARF does so. We propose a software product regime for the cryptographic derivation of data in a ZKP format through three mutually compatible regulatory options: zero-knowledge issuance by default through the EUDIW, through a software product extension of the EUDIW, or a private standalone wallet. These schemes provide the legal basis for the secure use of ZKPs, ensure effective compliance with the GDPR, and contribute to the debate on the value that electronic ledgers introduced by eIDAS 2.0 bring to digital identity.
UAVs are increasingly being used in various domains, from personal and commercial applications to military operations. Ensuring the security and trustworthiness of UAV communications is crucial, and blockchain technology has been explored as a solution. However, privacy remains a challenge, especially in public blockchains. In this work, we propose a novel approach utilizing zero-knowledge proof techniques, specifically zk-SNARKs, which are non-interactive cryptographic proofs. This approach allows UAVs to prove their authenticity or location without disclosing sensitive information. We generated zk-SNARK proofs using the Zokrates tool on a Raspberry Pi, simulating a drone environment, and analyzed power consumption and CPU utilization. The results are promising, especially in the case of larger drones with higher battery capacities. Ethereum was chosen as the public blockchain platform, with smart contracts developed in Solidity and tested on the Sepolia testnet using Remix IDE. This novel proposed approach paves the way for a new path of research in the UAV area.
This study explores the balance between data privacy and regulatory compliance in blockchain-based financial systems, focusing on privacy-enhancing technologies (PETs) such as Zero-Knowledge Proofs (ZKPs) and multiparty computations (MPCs). Through a comprehensive methodology combining literature review, comparative analysis, and empirical testing on the Ethereum test network, the research reveals significant trade-offs. Implementing ZKPs increased transaction times from 5 seconds to 12 seconds and gas fees from 0.02 ETH to 0.05 ETH, while computational load rose by 60%, highlighting the impact on scalability and efficiency. Chi-Square tests and regression analysis uncovered notable algorithmic biases, with low-value accounts experiencing 15% fewer transaction approvals and small mining pools receiving 20% fewer rewards than larger counterparts. Additionally, MPCs, while offering robust privacy, increased communication overhead by 35%, posing scalability challenges. The study recommends adopting a tiered privacy approach, implementing basic privacy measures for low-sensitivity transactions, and advanced technologies like ZKPs for high-sensitivity transactions while optimizing ZKPs to reduce their computational burden and enhance transaction speeds, and integrating artificial intelligence to detect and mitigate algorithmic biases in blockchain systems. Future research should also explore hybrid privacy solutions that combine the strengths of different PETs, such as ZKPs and MPCs, to achieve both robust privacy and high efficiency. Furthermore, investigating quantum-resistant cryptographic methods is crucial to safeguarding blockchain systems against emerging threats. These insights provide valuable guidance for financial institutions, blockchain developers, and policymakers, promoting the development of blockchain-based financial systems that optimize data privacy while maintaining system performance and regulatory compliance.
Imagine a digital bank where you want to prove to your friend that you have enough money to buy a gift without showing your entire bank statement. Zero-Knowledge Proofs allow you to verify your account balance without revealing any details about your transactions or other balances. This paper explains how ZKPs works in blockchain technology to protect privacy while ensuring transactions are valid. It covers the basics of ZKPs, different types like zk-SNARKs and zk-STARKs. The paper also discusses the technical challenges of using ZKPs, such as how it affects performance and storage, and suggests future improvements for making ZKPs more efficient and widely applicable.
This paper proposes a new global model aggregation method based on using zero-knowledge federated learning (ZKFL). The purpose is to secure horizontal or P2P federated machine learning systems with shorter aggregation times, higher model accuracy, and lower system costs. We use a model parameter-sharing Chord overlay network among all client hosts. The overlay guarantees a trusted sharing of zero-knowledge proofs for aggregation integrity, even under malicious Byzantine attacks. We tested over popular datasets, Fashion-MNIST and CIFAR10, to prove the new system protection concept. Our benchmark experiments validate the claimed advantages of the ZKFL scheme in all objective functions. Our aggregation method can be applied to secure both rank-based and similarity-based aggregation schemes. For a large system with over 200 clients, our system takes only 3 seconds to yield high-precision global machine models under the ALIE attacks with the Fashion-MNIST dataset. We have achieved up to 85% model accuracy, compared to only 3%$\sim$45% accuracy observed with federated schemes without protection. Moreover, our method demands a low memory overhead for handling zero-knowledge proofs as the system scales greatly to a larger number of client nodes.
Xudong Zhu, Haoqi He, Zhengbang Yang, Yi Deng · 6 authors
Zero-knowledge proof (ZKP) is a cryptographic primitive that enables a prover to convince a verifier that a statement is true, without revealing any other information beyond the correctness of the statement itself. Due to its powerful capabilities, its most practical type, called zero-knowledge Succinct Non-interactive ARgument of Knowledge (zkSNARK), has been widely deployed in various privacypreserving applications such as cryptocurrencies and verifiable computation. Although state-of-the-art zkSNARKs are highly efficient for the verifier, the computational overhead for the prover is still orders of magnitude too high to warrant use in many applications. This overhead arises from several time-consuming operations, including large-scale matrix-vector multiplication (MUL), number-theoretic transform (NTT), and especially the multi-scalar multiplication (MSM) which constitutes the largest proportion. Therefore, further efficiency improvements are needed.In this paper, we focus on comprehensive optimization of running time and storage space required by the MSM algorithm on GPUs. Specifically, we propose a novel, modular and adaptive parameter configuration technique—elastic MSM to enable us to adjust the scale of MSM according to our own wishes by performing a corresponding amount of preprocessing. This technique enables us to fully unleash the potential of various efficient parallel MSM algorithms. We have implemented and tested elastic MSM over three prevailing parallel Pippenger algorithms on GPUs. Across various preprocessing space limitations (across various MSM scales), our constructions achieve up to about 1.90×, 1.08× and 1.36× (2.58×, 1.39× and 1.91×) speedup versus three state-of-the-art parallel Pippenger algorithms on GPUs, respectively.From another perspective, elastic MSM could also be regarded as a preprocessing technique over the well-known Pippenger algorithm, which is modular and could be used to accelerate almost all the most advanced parallel Pippenger algorithms on GPUs. Meanwhile, elastic MSM provides an adaptive trade-off between the running time and the extra storage space needed by parallel Pippenger algorithms on GPUs. This is the first preprocessing technique to retain the improved MSM computation brought by preprocessing under varying storage space limitations. Specifically, across various preprocessing space limitations (across various MSM scales), our constructions achieve up to about 192× and 223× (159× and 174×) speedup versus two state-ofthe- art preprocessing parallel Pippenger algorithms on GPUs, respectively.
We initiate the study of relativistic zero-knowledge quantum proof of knowledge systems with classical communication, formally defining a number of useful concepts and constructing appropriate knowledge extractors for all the existing protocols in the relativistic setting which satisfy a weaker variant of the special soundness property due to Unruh (EUROCRYPT 2012). We show that there exists quantum proofs of knowledge with knowledge error 1/2 + negl(η) for all relations in NP via a construction of such a system for the Hamiltonian cycle relation using a general relativistic commitment scheme exhibiting the fairly-binding property due to Fehr and Fillinger (EUROCRYPT 2016). We further show that one can construct quantum proof of knowledge extractors for proof systems which do not exhibit special soundness, and therefore require an extractor to rewind multiple times. We develop a new multi-prover quantum rewinding technique by combining ideas from monogamy of entanglement and gentle measurement lemmas that can break the quantum rewinding barrier. Finally, we prove a new bound on the impact of consecutive measurements and use it to significantly improve the soundness bound of some existing relativistic zero knowledge proof systems, such as the one due to Chailloux and Leverrier (EUROCRYPT 2017).
Zero Knowledge Proofs (ZKPs) are cryptographic security techniques that allow secure data exchange without revealing secret information. This research study investigates and analyzes efficiency factors, robustness features, applicability, and uses, along with challenges for the implementation of these techniques, which are most important to achieving higher security. We categorize ZKPs techniques into three types: interactive, non-interactive, and succinct non-interactive arguments of knowledge (SNARKs). Different authors have examined prominent models such as zkSNARK, Ligero, Bulletproofs, Hyrax, Aurora, and Libra. Libra stands out for its outstanding efficiency, requiring a one-time trusted setup depending on the input size. The study explores various challenges in ZKPs to enhance their robustness. To solve problems like the trusted setup dilemma and quantum computing attacks, the research suggests making progress by integrating different models, improving efficiency, looking into new mathematical problems, creating more advanced cryptographic tools, and studying lattice-based cryptography for better security. The results highlight the need to overcome constraints and improve ZKPs security and effectiveness in practical setups to enhance their efficiency, and they will direct future research for privacy, security, and integrity in a variety of applications.
With the help of artificial intelligence, the large amount of data generated by Internet of Things (IoT) has unleashed significant value. Federated learning is emerging as a novel paradigm which can be applied to solve the privacy issues caused by analyzing IoT data. However, traditional federated learning protocols are vulnerable to inference and poisoning attacks. Various solutions have been proposed to enhance data privacy and robustness. Nonetheless, most of these solutions are usually centralized and rely on unrealistic security assumptions. Furthermore, the recently proposed blockchain-based decentralized solutions generally incur high costs, which is unaffordable for resource-constrained IoT devices. In this article, we propose a practical secure federated learning system named PrSeFL. We utilize blockchain to decentralize the federated learning process so that the security assumptions are easier to achieve in practice. To preserve data privacy, we implement secure multiparty computation-based secure aggregation in blockchain environment. To guarantee practical robustness, we enforce norm constraints on the masked updates via zero-knowledge proof. Moreover, we propose a modified dynamic accumulator which is utilized to realize lightweight anonymous authentication of users. Simulation results show that, compared with state-of-the-art systems, PrSeFL has superior performance on authentication and model training. And the advantage of PrSeFL becomes more significant as the number of users grows.
With the rapid development of Zero-Knowledge Proofs (ZKPs), particularly Succinct Non-Interactive Arguments of Knowledge (SNARKs), benchmarking various ZK tools has become a valuable task. ZK-friendly hash functions, as key algorithms in blockchain, have garnered significant attention. Therefore, comprehensive benchmarking and evaluations of these evolving algorithms in ZK circuits present both promising opportunities and challenges. Additionally, we focus on a popular ZKP application, privacy-preserving transaction protocols, aiming to leverage SNARKs' cost-efficiency through "batch processing" to address high on-chain costs and compliance issues. To this end, we benchmarked three SNARK proving systems and five ZK-friendly hash functions, including our self-developed circuit templates for Poseidon2, Neptune, and GMiMC, on the bn254 curve within the circom-snarkjs framework. We also introduced the role of "sequencer" in our SNARK-based privacy-preserving transaction scheme to enhance efficiency and enable flexible auditing. We conducted privacy and security analyses, as well as implementation and evaluation on Ethereum Virtual Machine (EVM)-compatible chains. The results indicate that Poseidon and Poseidon2 demonstrate superior memory usage and runtime during proof generation under Groth16. Moreover, compared to the baseline, Poseidon2 not only generates proofs faster but also reduces on-chain costs by 73% on EVM chains and nearly 26% on Hedera. Our work provides a benchmark for ZK-friendly hash functions and ZK tools, while also exploring cost efficiency and compliance in ZKP-based privacy-preserving transaction protocols.
Daniele Friolo, Geoffrey Goodell, D. R. Toliver, Hazem Danny Nakib
This article builds upon the protocol for digital transfers described by Goodell, Toliver, and Nakib, which combines privacy by design for consumers with strong compliance enforcement for recipients of payments and self-validating assets that carry their own verifiable provenance information. We extend the protocol to allow for the verification that reissued assets were created in accordance with rules prohibiting the creation of new assets by anyone but the issuer, without exposing information about the circumstances in which the assets were created that could be used to identify the payer. The modified protocol combines an audit log with zero-knowledge proofs, so that a consumer spending an asset can demonstrate that there exists a valid entry on the audit log that is associated with the asset, without specifying which entry it is. This property is important as a means to allow money to be reissued within the system without the involvement of system operators within the zone of control of the original issuer. Additionally, we identify a key property of privacy-respecting electronic payments, wherein the payer is not required to retain secrets arising from one transaction until the following transaction, and argue that this property is essential to framing security requirements for storage of digital assets and the risk of blackmail or coercion as a way to exfiltrate information about payment history. We claim that the design of our protocol strongly protects the anonymity of payers with respect to their payment transactions, while preventing the creation of assets by any party other than the original issuer without destroying assets of equal value.
Blockchain technologies have introduced a compelling paradigm for a new understanding of security through decentralized networks and consensus mechanisms. However, they need all data to be public, which may be unacceptable for use cases such as biometric data processing or sensitive monetary transactions. Therefore, confidentiality is identified as a need in blockchain. Additionally, blockchain can contribute to confidential applications by providing publicly verifiable mechanisms, therefore enhancing security. This work presents a framework for cost-effective and publicly verifiable confidential computations in blockchain, by relying on secure multi-party computation committees and zero-knowledge proofs. Our framework supports arbitrary computations on confidential data enforced by smart contracts. Additionally, staking, incentives, and cheat identification are provided as solutions to enhance trust. We also provide a technical solution to embed secure multi-party computations within smart contracts by using the Promise programming pattern. Finally, a cost analysis is provided to justify the feasibility of the framework compared to other solutions.
Vid Keršič, Martin Domajnko, Sašo Karakatič, Muhamed Turkanović
Z vse pogostejšo uporabo interneta in migracijo storitev iz fizičnega sveta v digitalni, postajajo vprašanja o varnosti, zasebnosti in digitalnem lastništvu osebnih podatkov vse pogostejša. Ena izmed ključnih tehnologij, ki omogoča razvoj rešitev na tem področju, so ničelno spoznavni dokazi (ang. zero-knowledge proofs, ZKP). ZKP so kriptografski protokoli, pri katerih dokazovalec dokaže pravilnost poljubne trditve preveritelju, ne da bi pri tem razkril dodatne informacije ali svoje podatke. V članku predstavimo ZKP protokole in njihove razlike, s posebnim poudarkom na dveh najpogostejših družinah protokolov: zk-SNARK in zk-STARK. Njihovo uporabno vrednost prikažemo na področju samo-upravljane in decentralizirane identitete ter na področju strojnega učenja. Pri decentralizirani identiteti ZKP omogočajo deljenje podatkov brez razkritja zasebnih informacij, medtem ko pri strojnem učenju omogočajo preverljivost izhodov modelov. To pomeni, da lahko uporabnik preveri, ali je bil za generiranje napovedi dejansko uporabljen pravilno izbran model.