Succinct Non-interactive Arguments Research Articles

Enhancing Unmanned Aerial Vehicle Security: A Zero-Knowledge Proof Approach with Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge for Authentication and Location Proof.

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.

Uni/multi variate polynomial embeddings for zkSNARKs

AbstractA zero-knowledge proof is a cryptographic primitive that enables a prover to convince a verifier the validity of a mathematical statement (an NP statement) without revealing any secret inputs to the verifier. A special case, called zero-knowledge Succinct Non-interactive ARgument of Knowledge (zkSNARK) is particularly designed for arithmetic circuit proof systems which have important applications in blockchain privacy. The major computations in this type of zkSNARK proofs with post-quantum security are polynomial evaluations and Lagrange interpolations over finite fields. Given a sequence over a finite field, in the field of coding and sequences research, we understand that there are two representations of the sequence, one is a univariate polynomial and the other, a multivariate polynomial. This is exactly what is done in those zero-knowledge proof systems to transform the proof of a R1CS relation to evaluate uni/multi variate polynomials at some random points in the finite field. In this paper, we present a comparative analysis on how to convert a rank 1 constrained satisfiability (R1CS) system (more general than a circuit system) into a polynomial equality and provide analysis on the concrete complexities of provers, proof sizes and verifiers. We use two concrete zkSNARK schemes, i.e., Polaris, univariate polynomial encodings and Spartan, multivariate polynomial encodings, as examples to show our analysis. Secondly, we propose to select interpolating sets as subfields instead of affine spaces of a large field for Lagrange interpolation. This new method has improved the performance of R1CS encodings largely. We comment that post-quantum secure zkSNARKs yield post-quantum digital signatures with security only depending on symmetric-key schemes. Some open problems are proposed at the end of the paper.

Cross-Blockchain Communication Using Oracles With an Off-Chain Aggregation Mechanism Based on zk-SNARKs

The closed architecture of prevailing blockchain systems renders the usage of this technology mostly infeasible for a wide range of real-world problems. Most blockchains trap users and applications in their isolated space without the possibility of cooperating or switching to other blockchains. Therefore, blockchains need additional mechanisms for seamless communication and arbitrary data exchange between each other and external systems. Unfortunately, current approaches for cross-blockchain communication are resource-intensive or require additional blockchains or tailored solutions depending on the applied consensus mechanisms of the connected blockchains. Therefore, we propose an oracle with an off-chain aggregation mechanism based on Zero-Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) to facilitate cross-blockchain communication. The oracle queries data from another blockchain and applies a rollup-like mechanism to move state and computation off-chain. The zkOracle contract only expects the transferred data, an updated state root, and proof of the correct execution of the aggregation mechanism. The proposed solution only requires constant 378 kgas to submit data on the Ethereum blockchain and is primarily independent of the underlying technology of the queried blockchains.

SublonK: Sublinear Prover PlonK

We propose SublonK --- a new succinct non-interactive argument of knowledge (SNARK). SublonK is the first SNARK that achieves both a constant proof size and prover runtime that grows only with the size of the ``active part'' of the executed circuit (i.e., *sub-linear* in the size of the entire circuit) while being *black-box in cryptography*. For instance, consider circuits encoding conditional execution, where only a fraction of the circuit is exercised by the input. For such circuits, the prover runtime in SublonK grows only with the exercised execution path. Our new construction builds on PlonK [Gabizon-Williamson-Ciobotaru, EPRINT'19], a popular state-of-the-art practical zkSNARK, and preserves all its great features --- constant size proofs, constant time proof verification, a circuit-independent universal setup, and support for custom gates and lookup gates. Our techniques are useful for a wide range of applications that involve a circuit executing k steps, where at each step, a (possibly different) s-sized segment is executed from a choice of n segments. Our prover cost for such circuits is O(ks(log (ks) + log(n))). Finally, we show that our improvements are not purely asymptotic. Specifically, we demonstrate the concrete efficiency of SublonK using zkRollups as an example application. Based on our implementation, for parameter choices derived from rollup contracts on Ethereum, n =8, k = 128, s= 2^{16}, the SublonK prover is approximately 4.8x faster than the PlonK prover, and proofs in SublonK are 2.4KB and can be verified in under 50ms.

A Blockchain-Based Privacy Preserving Intellectual Property Authentication Method

With the continuous advancement of information technology, a growing number of works, including articles, paintings, and music, are being digitized. Digital content can be swiftly shared and disseminated via the Internet. However, it is also vulnerable to malicious plagiarism, which can seriously infringe upon the rights of creators and dampen their enthusiasm. To protect creators’ rights and interests, a sophisticated method is necessary to authenticate digital intellectual property rights. Traditional authentication methods rely on centralized, trustworthy organizations that are susceptible to single points of failure. Additionally, these methods are prone to network attacks that can lead to data loss, tampering, or leakage. Moreover, the circulation of copyright information often lacks transparency and traceability in traditional systems, which leads to information asymmetry and prevents creators from controlling the use and protection of their personal information during the authentication process. Blockchain technology, with its decentralized, tamper-proof, and traceable attributes, addresses these issues perfectly. In blockchain technology, each node is a peer, ensuring the symmetry of information. However, the transparent feature of blockchains can lead to the leakage of user privacy data. Therefore, this study designs and implements an Ethereum blockchain-based intellectual property authentication scheme with privacy protection. Firstly, we propose a method that combines elliptic curve cryptography (ECC) encryption with digital signatures to achieve selective encryption of user personal information. Subsequently, an authentication algorithm based on Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) is adopted to complete the authentication of intellectual property ownership while encrypting personal privacy data. Finally, we adopt the InterPlanetary File System (IPFS) to store large files, solving the problem of blockchain storage space limitations.

Shorter ZK-SNARKs from square span programs over ideal lattices

Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are cryptographic protocols that offer efficient and privacy-preserving means of verifying NP language relations and have drawn considerable attention for their appealing applications, e.g., verifiable computation and anonymous payment protocol. Compared with the pre-quantum case, the practicability of this primitive in the post-quantum setting is still unsatisfactory, especially for the space complexity. To tackle this issue, this work seeks to enhance the efficiency and compactness of lattice-based zk-SNARKs, including proof length and common reference string (CRS) length. In this paper, we develop the framework of square span program-based SNARKs and design new zk-SNARKs over cyclotomic rings. Compared with previous works, our construction is without parallel repetition and achieves shorter proof and CRS lengths than previous lattice-based zk-SNARK schemes. Particularly, the proof length of our scheme is around 23.3%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$23.3\\%$$\\end{document} smaller than the recent shortest lattice-based zk-SNARKs by Ishai et al. (in: Proceedings of the 2021 ACM SIGSAC conference on computer and communications security, pp 212–234, 2021), and the CRS length is 3.6×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.6\ imes$$\\end{document} smaller. Our constructions follow the framework of Gennaro et al. (in: Proceedings of the 2018 ACM SIGSAC conference on computer and communications security, pp 556–573, 2018), and adapt it to the ring setting by slightly modifying the knowledge assumptions. We develop concretely small constructions by using module-switching and key-switching procedures in a novel way.

A privacy-preserving key transmission protocol to distribute QRNG keys using zk-SNARKs

High-entropy random numbers are an essential part of cryptography, and Quantum Random Number Generators (QRNG) are an emergent technology that can provide high-quality keys for cryptographic algorithms but unfortunately are currently difficult to access. Existing Entropy-as-a-Service solutions require users to trust the central authority distributing the key material, which is not desirable in a high-privacy environment. In this paper, we present a novel key transmission protocol that allows users to obtain cryptographic material generated by a QRNG in such a way that the server is unable to identify which user is receiving each key. This is achieved with the inclusion of Zero Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARK), a cryptographic primitive that allow users to prove knowledge of some value without needing to reveal it. The security analysis of the protocol proves that it satisfies the properties of Anonymity, Unforgeability and Confidentiality, as defined in this document. We also provide an implementation of the protocol demonstrating its functionality and performance, using NFC as the transmission channel for the QRNG key.

Zero-knowledge proofs in education: a pathway to disability inclusion and equitable learning opportunities

In the evolving landscape of global education, the significance of inclusivity and equity has never been more important. Emphasizing the United Nation Sustainable Development Goal 4, this paper explores the innovative application of blockchain-powered Zero-Knowledge Proofs (ZKPs) technology in education, with a particular focus on disability inclusion. This study introduces a novel disability management system powered by Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK). This advanced system enables educational institutions to verify the status of students with disabilities without compromising their personal information, thereby preserving their privacy and reinforcing their identity. This paper evaluates the potential operational efficiency of this prototype system against the existing costs incurred by higher education institutions in disability schemes. It also examines the system’s potential to enhance self-disclosure among students with disability, which is pivotal for their academic success. By advocating for privacy and inclusivity, this study highlights the transformative potential of ZKP in creating an educational environment where students with disabilities can comfortably disclose their needs. This approach not only protects their confidentiality but also empowers them academically, aligning with the global commitment to accessible and inclusive education.

Obtaining simulation extractable NIZKs in the updatable CRS model generically

Non-interactive zero-knowledge proofs as well as succinct non-interactive argument of knowledge (SNARK) are playing a central role in both theory and application of cryptography. Simulation extractable for SNARKs is considered a necessary security requirement by most applications which prevents the protocol from malleable attacks. However, a trusted party is required to generate the common reference string (CRS) for SNARKs which can be quite problematic in real applications. Recently, the subvertible and updatable CRS model has been proposed to relax the trust in the CRS generation procedure.In this paper, we propose two generic compilers that can achieve simulation extractable in the updatable CRS model. By using an efficient updatable verifiable random function defined in this paper which may be of independent interest, we show that our compiler can lift the updatable knowledge soundness of the underlying SNARKs to achieve updatable simulation extractability. We extend our results by proposing another compiler that can lift a NIZK that has an even weaker security notion called updatable soundness to achieve updatable simulation extractability. We instantiate our compilers and compare them to other related works. This shows that our efficient compilers can be used in various applications.

Simulation extractable versions of Groth’s zk-SNARK revisited

Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are the most efficient proof systems in terms of proof size and verification. Currently, Groth’s scheme from EUROCRYPT 2016, Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}, is the state-of-the-art and is widely deployed in practice. Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} is originally proven to achieve knowledge soundness, which does not guarantee the non-malleability of proofs. There has been considerable progress in presenting new zk-SNARKs or modifying Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} to efficiently achieve strong Simulation extractability, which is shown to be a necessary requirement in some applications. In this paper, we revise the Random oracle based variant of Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} proposed by Bowe and Gabizon, BG18, the most efficient one in terms of prover efficiency and CRS size among the candidates, and present a more efficient variant that saves 2 pairings in the verification and 1 group element in the proof. This supersedes our preliminary construction, presented in CANS 2020 (Baghery et al. in CANS 20, volume 12579 of LNCS, Springer, Heidelberg. pp 453-461, 2020), which saved 1 pairing in the verification, and was proven in the generic group model. Our new construction also improves on BG18 in that our proofs are in the algebraic group model with Random Oracles and reduces security to standard computational assumptions in bilinear groups (as opposed to using the full power of the generic group model (GGM)). We implement our proposed simulation extractable zk-SNARK (SE zk-SNARK) along with BG18 in the Arkworks library, and compare the efficiency of our scheme with some related works. Our empirical experiences confirm that our SE zk-SNARK is more efficient than all previous simulation extractable (SE) schemes in most dimensions and it has very close efficiency to the original Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}.

Zk-SNARKs As A Cryptographic Solution For Data Privacy And Security In The Digital Era

This research brings the concept of zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge) in the context of data security and privacy in the digital world. zk-SNARKs is a cryptographic technology that allows individuals to prove a statement or knowledge without having to reveal the actual details of the information. We illustrate this concept through a simple example of proving age over 18 without revealing the actual date of birth. This research highlights the importance of maintaining data privacy in various technological applications, including the use of zk-SNARKs in blockchain to maintain transaction privacy and personal data protection in increasingly sophisticated applications. However, the implementation of zk-SNARKs requires deep mathematical understanding and strong data security concerns. With great potential to support data privacy and security in the evolving digital era, zk-SNARKs is a highly relevant tool in addressing privacy-related challenges in the digital world. The conclusion of this research is that zk-SNARKs is an important tool in maintaining data privacy and security in the digital age. With its ability to allow individuals to prove knowledge or assertions without revealing actual details of information, this technology has wide applications in various sectors, including finance, data management, and data privacy protection. However, it should be emphasized that the implementation of zk-SNARKs requires extra care in securing the system and ensuring that the technology is used properly to maintain high data privacy and security. With further development and understanding in this technology, zk-SNARKs can be an integral component in building a safer and more private digital world.

CuZK: Accelerating Zero-Knowledge Proof with A Faster Parallel Multi-Scalar Multiplication Algorithm on GPUs

Zero-knowledge proof is a critical cryptographic primitive. Its most practical type, called zero-knowledge Succinct Non-interactive ARgument of Knowledge (zkSNARK), has been deployed in various privacy-preserving applications such as cryptocurrencies and verifiable machine learning. Unfortunately, zkSNARK like Groth16 has a high overhead on its proof generation step, which consists of several time-consuming operations, including large-scale matrix-vector multiplication (MUL), number-theoretic transform (NTT), and multi-scalar multiplication (MSM). Therefore, this paper presents cuZK, an efficient GPU implementation of zkSNARK with the following three techniques to achieve high performance. First, we propose a new parallel MSM algorithm. This MSM algorithm achieves nearly perfect linear speedup over the Pippenger algorithm, a well-known serial MSM algorithm. Second, we parallelize the MUL operation. Along with our self-designed MSM scheme and well-studied NTT scheme, cuZK achieves the parallelization of all operations in the proof generation step. Third, cuZK reduces the latency overhead caused by CPU-GPU data transfer by 1) reducing redundant data transfer and 2) overlapping data transfer and device computation. The evaluation results show that our MSM module provides over 2.08x (up to 2.94x) speedup versus the state-of-the-art GPU implementation. cuZK achieves over 2.65x (up to 4.86x) speedup on standard benchmarks and 2.18× speedup on a GPU-accelerated cryptocurrency application, Filecoin.

BV-ICVs: A privacy-preserving and verifiable federated learning framework for V2X environments using blockchain and zkSNARKs

As part of vehicle to everything (V2X) environments, intelligent connected vehicles (ICVs) generate a large amount of data, which can be exploited securely and effectively through decentralized techniques such as federated learning (FL). Existing FL systems, however, are vulnerable to attacks and barely meet the security requirements for real-world applications. If malicious or compromised ICVs upload inaccurate or low-quality local model updates to the central aggregator, they may reduce the accuracy of the global model, thereby reducing drivers safety and efficiency. This paper aims to alleviate these concerns by presenting BV-ICVs, a blockchain-enabled and privacy-preserving FL framework for ICVs in an edge-envisioned V2X environment. This system uses Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zkSNARKs) verification that is compiled as smart contracts to prevent malicious, compromised or even rational ICVs from uploading unreliable, erroneous or low-quality model updates. The verification process is embedded within the consensus of the underlying permissioned blockchain, which maximizes both the efficiency of the process and the utilization of computer resources. As demonstrated by discussions, security analysis, and numerical results, BV-ICVs reduced data poisoning attacks and increased the privacy protection and accuracy of FL.

Speeding Up Multi-Scalar Multiplication over Fixed Points Towards Efficient zkSNARKs

The arithmetic of computing multiple scalar multiplications in an elliptic curve group then adding them together is called multi-scalar multiplication (MSM). MSM over fixed points dominates the time consumption in the pairing-based trusted setup zero-knowledge succinct non-interactive argument of knowledge (zkSNARK), thus for practical applications we would appreciate fast algorithms to compute it. This paper proposes a bucket set construction that can be utilized in the context of Pippenger’s bucket method to speed up MSM over fixed points with the help of precomputation. If instantiating the proposed construction over BLS12-381 curve, when computing n-scalar multiplications for n = 2e (10 ≤ e ≤ 21), theoretical analysis ndicates that the proposed construction saves more than 21% computational cost compared to Pippenger’s bucket method, and that it saves 2.6% to 9.6% computational cost compared to the most popular variant of Pippenger’s bucket method. Finally, our experimental result demonstrates the feasibility of accelerating the computation of MSM over fixed points using large precomputation tables as well as the effectiveness of our new construction.

A hybrid blockchain-based identity authentication scheme for Mobile Crowd Sensing

With the continuous innovative development and popularization of mobile smart devices, the application of Mobile Crowd Sensing (MCS) continues to be studied extensively. However, existing centralized MCS applications that use servers for task publishing and data collection exhibit common problems, such as single points of failure and security vulnerabilities. Accordingly, we proposed a hybrid blockchain-based identity authentication scheme for MCS called HBIA, which uses blockchain technology to resolve the single-point failure problem. HBIA builds a cluster structure based on factors such as geographical location and balance, and uses it to construct a hybrid blockchain, with the cluster head node and internal cluster node authenticating on the public and private chains, respectively. We also implemented zero-knowledge proof (ZKP) to ensure the privacy of participants’ identities, thus balancing the contradiction between blockchain transparency and security. In addition, HBIA uses the zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) technology to enable off-chain computing and on-chain verification, further reducing the blockchain’s workload. Finally,​ HBIA was evaluated based on the pavement crack detection task and tested on the Ethereum public test network known as Ropsten. The test results indicate that the identity authentication scheme proposed in this paper is superior to existing schemes in terms of authentication time.

PvCNN: Privacy-Preserving and Verifiable Convolutional Neural Network Testing

We propose a new approach for privacy-preserving and verifiable convolutional neural network (CNN) testing in a distrustful multi-stakeholder environment. The approach is aimed to enable that a CNN model <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">developer</i> convinces a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user</i> of the truthful CNN performance over non-public data from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple testers</i> , while respecting model and data privacy. To balance the security and efficiency issues, we appropriately integrate three tools with the CNN testing, including collaborative inference, homomorphic encryption (HE) and zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK). We start with strategically partitioning a CNN model into a private part kept locally by the model developer, and a public part outsourced to an outside server. Then, the private part runs over the HE-protected test data sent by a tester, and transmits its outputs to the public part for accomplishing subsequent computations of the CNN testing. Second, the correctness of the above CNN testing is enforced by generating zk-SNARK based proofs, with an emphasis on optimizing proving overhead for two-dimensional (2-D) convolution operations, since the operations dominate the performance bottleneck during generating proofs. We specifically present a new quadratic matrix program (QMP)-based arithmetic circuit with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a single multiplication gate</i> for expressing 2-D convolution operations between multiple filters and inputs in a batch manner. Third, we aggregate multiple proofs with respect to a same CNN model but different testers’ test data ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., different statements) into one proof, and ensure that the validity of the aggregated proof implies the validity of the original multiple proofs. Lastly, our experimental results demonstrate that our QMP-based zk-SNARK performs nearly 13.9× faster than the existing quadratic arithmetic program (QAP)-based zk-SNARK in proving time, and 17.6× faster in Setup time, for high-dimension matrix multiplication. Besides, the limitation on handling a bounded number of multiplications of QAP-based zk-SNARK is relieved.

Split: A Hash-based Memory Optimization Method for Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK)

Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) is a practical zero-knowledge proof system for Rank-1 Constraint Satisfaction (R1CS), enabling privacy preservation and addressing the previous scalability concerns on zero-knowledge proofs. Existing constructions of zk-SNARKs require huge memory overhead to generate proofs in that the size of the zk-SNARK circuit can be large even for a very simple use case, which limits the applications for regular resource-constrained users. To reduce the memory utilization of zk-SNARKs, this paper presents a hash-based method “Split”. Concretely, Split intends to partition the zk-SNARK circuits so that components can be processed sequentially while ensuring strong security properties leveraging hash circuits. As a zk-SNARK circuit is partitioned, obsolete variables are no longer preserved in the memory. We further propose an enhanced Split as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -Split, which leads to better optimization by properly choosing multiple splits. Our experimental results validate the effectiveness and efficiency of Split in conserving memory usage for resource-constrained provers as long as the circuit can be partitioned to a Good Split, indicating that via Split zk-SNARKs can be brought one step closer to practical applications.

Digital Identity Verification and Management System of Blockchain-Based Verifiable Certificate with the Privacy Protection of Identity and Behavior

Due to the advantages in self-sovereignty identity management and scalability of blockchain, digital identity verification and management systems (DIVMS) of blockchain-based verifiable certificates (VC) are getting more and more attention. However, user privacy in the systems’ traditional architectures cannot be guaranteed. In this paper, the zero-knowledge succinct noninteractive arguments of knowledge (zkSNARKs) referred to as Groth16 are introduced in order to implement privacy protection of the user’s identity and behavior of DIVMS of blockchain-based VC. In the proposed architecture, the malleability attack of Groth16 is considered, and verifications of zero-knowledge proof (ZKP) and the digital signature of an identity provider (IDP) attached to VC and the status management of VC are implemented on the smart contracts of the blockchain to overcome single point failure. Furthermore, a prototype system is designed to verify the proposed architecture’s capability in privacy protection and to evaluate its performances in cost and throughput. Finally, the security of the proposed architecture is discussed, and its comparisons are conducted with those existing blockchain-based DIVMSs, especially those systems using Groth16 of zkSNARKs to improve the privacy of user. All results mentioned above have shown that the proposed system is efficient and safe, and it can improve the privacy of DIVMS of the blockchain based VC while avoiding single point failure.

Efficient multivariate low-degree tests via interactive oracle proofs of proximity for polynomial codes

We consider the proximity testing problem for error-correcting codes which consist in evaluations of multivariate polynomials either of bounded individual degree or bounded total degree. Namely, given an oracle function $$f :L^m \rightarrow {\mathbb {F}}_q$$ , where $$L\subset {\mathbb {F}}_q$$ , a verifier distinguishes whether f is the evaluation of a low-degree polynomial or is far (in relative Hamming distance) from being one, by making only a few queries to f. This topic has been studied in the context of locally testable codes, interactive proofs, probalistically checkable proofs, and interactive oracle proofs. We present the first interactive oracle proofs of proximity (IOPP) for tensor products of Reed–Solomon codes (evaluation of polynomials with bounds on individual degrees) and for Reed–Muller codes (evaluation of polynomials with a bound on the total degree) that simultaneously achieve logarithmic query complexity, logarithmic verification time, linear oracle proof length and linear prover running time. Such low-degree polynomials play a central role in constructions of probabilistic proof systems and succinct non-interactive arguments of knowledge with zero-knowledge. For these applications, highly-efficient multivariate low-degree tests are desired, but prior probabilistic proofs of proximity required super-linear proving time. In contrast, for multivariate codes of length N, our constructions admit a prover running in time linear in N and a verifier which is logarithmic in N. Our constructions are directly inspired by the IOPP for Reed–Solomon codes of [Ben-Sasson et al., ICALP 2018] named “FRI protocol”. Compared to the FRI protocol, our IOPP for tensor products of Reed–Solomon codes achieves the same efficiency parameters. As for Reed–Muller codes, for fixed constant number of variables m, the concrete efficiency of our IOPP for Reed–Muller codes compares well, all things equal.

Enabling zero knowledge proof by accelerating zk-SNARK kernels on GPU

As a recent cryptography protocol, Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) allows one party to prove that it possesses certain information without revealing information to these untrusted proof provers. This mechanism has the ability to provide the function for constructing and verifying information integrity without privacy leaking. However, the computation kernels of zk-SNARK consume too much computing power and produce a significant performance bottleneck with the growing data volume and security requirement. In this paper, we take advantage of Graphic Processing Unit (GPU) to enhance zk-SNARK efficiency by accelerating the most time-consuming computation kernels: modular multiplication and Number-Theoretic Transform (NTT)/Inverse Number-Theoretic Transform (INTT) in Elliptic Curve Cryptography (ECC) pairing with two major improvements: (1) Adopting interval limbs multiply-add quaternary operation to directly accelerate ECC pairing by making full advantage of information entropy within the limited hardware bit width; (2) Data layout and shuffle methods in GPU global memory and shared memory for data space consistency maintenance accelerating NTT/INTT which indirectly works on ECC pairing. To the best of our knowledge, our work would be the first exploration to accelerate these improvements on GPU. The measured results show that our methods are able to accelerate modular multiplication and NTT/INNT by 1.22× and 4.67× times respectively compared with the previous GPU implementation. With these accelerated kernels, we are able to achieve 3.14× speedup for Groth16, which is the most efficient zk-SNARK implementation working on BLS12-381 ECC field. With the bottleneck tackled, our work will expand the deployment scenarios of zk-SNARK in Zero Knowledge Proof (ZKP).