Here are recent papers from 2020 onwards that discuss Zero-Knowledge Proofs (ZK-proofs) and their prototypes addressing real-world problems:
1. Deploying ZKP Frameworks with Real-World Data: Challenges and Proposed Solutions - This study presents Fact Fortress, a framework for deploying zero-knowledge proofs to enhance data privacy and integrity, focusing on blockchain technology for verifying ZK proofs and tracking data access without revealing the data itself. Scalability improvements are needed despite fair performance with large datasets (Mallozzi, 2023).
Abstract: Zero-knowledge proof (ZKP) frameworks have the potential to revolutionize the handling of sensitive data in various domains. However, deploying ZKP frameworks with real-world data presents several challenges, including scalability, usability, and interoperability. This project presents Fact Fortress, an end-to-end framework for designing and deploying zero-knowledge proofs of general statements. Our solution leverages proofs of data provenance and auditable data access policies to ensure the trustworthiness of how sensitive data is handled and provide assurance of the computations that have been performed on it. ZKP is mostly associated with blockchain technology, where it enhances transaction privacy and scalability through rollups, addressing the data inherent to the blockchain. Our approach focuses on safeguarding the privacy of data external to the blockchain, with the blockchain serving as publicly auditable infrastructure to verify the validity of ZK proofs and track how data access has been granted without revealing the data itself. Additionally, our framework provides high-level abstractions that enable developers to express complex computations without worrying about the underlying arithmetic circuits and facilitates the deployment of on-chain verifiers. Although our approach demonstrated fair scalability for large datasets, there is still room for improvement, and further work is needed to enhance its scalability. By enabling on-chain verification of computation and data provenance without revealing any information about the data itself, our solution ensures the integrity of the computations on the data while preserving its privacy (Mallozzi, 2023).
2. Experimenting with Zero-Knowledge Proofs of Training - This research formulates zero-knowledge proof of training (zkPoT) and proposes a novel protocol for logistic regression, offering privacy-preserving proofs of model training with improved practicality and scalability (Garg et al., 2023).
Abstract: How can a model owner prove they trained their model according to the correct specification? More importantly, how can they do so while preserving the privacy of the underlying dataset and the final model? We study this problem and formulate the notion of zero-knowledge proof of training (zkPoT), which formalizes rigorous security guarantees that should be achieved by a privacy-preserving proof of training. While it is theoretically possible to design zkPoT for any model using generic zero-knowledge proof systems, this approach results in extremely unpractical proof generation times. Towards designing a practical solution, we propose the idea of combining techniques from MPC-in-the-head and zkSNARKs literature to strike an appropriate trade-off between proof size and proof computation time. We instantiate this idea and propose a concretely efficient, novel zkPoT protocol for logistic regression. Crucially, our protocol is streaming-friendly and does not require RAM proportional to the size of the training circuit, hence, can be done without special hardware. We expect the techniques developed in this paper to also generally be useful for designing efficient zkPoT protocols for other, more sophisticated, ML models. We implemented and benchmarked prover/verifier running times and proof sizes for training a logistic regression model using mini-batch gradient descent on a 4~GB dataset of 262,144 records with 1024 features. We divide our protocol into three phases: (1) data-independent offline phase (2) data-dependent phase that is independent of the model (3) online phase that depends both on the data and the model. The total proof size (across all three phases) is less than 10% of the data set size (<350 MB). In the online phase, the prover and verifier times are under 10 minutes and half a minute respectively, whereas in the data-dependent phase, they are close to one hour and a few seconds respectively (Garg et al., 2023).
3. PipeZK: Accelerating Zero-Knowledge Proof with a Pipelined Architecture - PipeZK is introduced as a pipelined accelerator for ZKP, achieving significant speedup in proof generation for privacy-preserving applications including blockchain (Zhang et al., 2021).
Abstract: Zero-knowledge proof (ZKP) is a promising cryptographic protocol for both computation integrity and privacy. It can be used in many privacy-preserving applications including verifiable cloud outsourcing and blockchains. The major obstacle of using ZKP in practice is its time-consuming step for proof generation, which consists of large-size polynomial computations and multi-scalar multiplications on elliptic curves. To efficiently and practically support ZKP in real-world applications, we propose PipeZK, a pipelined accelerator with two subsystems to handle the aforementioned two intensive compute tasks, respectively. The first subsystem uses a novel dataflow to decompose large kernels into smaller ones that execute on bandwidth-efficient hardware modules, with optimized off-chip memory accesses and on-chip compute resources. The second subsystem adopts a lightweight dynamic work dispatch mechanism to share the heavy processing units, with minimized resource underutilization and load imbalance. When evaluated in 28 nm, PipeZK can achieve 10x speedup on standard cryptographic benchmarks, and 5x on a widely-used cryptocurrency application, Zcash (Zhang et al., 2021).
4. MIRAGE: Succinct Arguments for Randomized Algorithms with Applications to Universal zk-SNARKs - This paper presents MIRAGE, a new zk-SNARK system for randomized algorithms, offering practical prover times and very succinct proofs for universal zk-SNARK applications (Kosba et al., 2020).
Abstract: The last few years have witnessed increasing interest in the deployment of zero-knowledge proof systems, in particular ones with succinct proofs and efficient verification (zk-SNARKs). One of the main challenges facing the wide deployment of zk-SNARKs is the requirement of a trusted key generation phase per different computation to achieve practical proving performance. Existing zero-knowledge proof systems that do not require trusted setup or have a single trusted preprocessing phase suffer from increased proof size and/or additional verification overhead. On the other other hand, although universal circuit generators for zk-SNARKs (that can eliminate the need for per-computation preprocessing) have been introduced in the literature, the performance of the prover remains far from practical for real-world applications. In this paper, we first present a new zk-SNARK system that is well-suited for randomized algorithms—in particular it does not encode randomness generation within the arithmetic circuit allowing for more practical prover times. Then, we design a universal circuit that takes as input any arithmetic circuit of a bounded number of operations as well as a possible value assignment, and performs randomized checks to verify consistency. Our universal circuit is linear in the number of operations instead of quasi-linear like other universal circuits. By applying our new zk-SNARK system to our universal circuit, we build MIRAGE, a universal zk-SNARK with very succinct proofs—the proof contains just one additional element compared to the per-circuit preprocessing state-of-the-art zk-SNARK by Groth (Eurocrypt 2016). Finally, we implement MIRAGE and experimentally evaluate its performance for different circuits and in the context of privacy-preserving smart contracts. ∗ A major part of this work was done while Ahmed Kosba was a postdoctoral scholar at UC Berkeley. † Part of this work was done while Charalampos Papamanthou was with Oasis Labs (Kosba et al., 2020).
5. Simulation-Extractable zk-SNARK With a Single Verification - The study introduces novel SE-SNARK constructions that minimize proof size and verification time while achieving non-malleability, significantly improving upon existing methods (Kim, Lee, & Oh, 2020).
Abstract: Among the zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARK), the simulation-extractable zk-SNARK (SE-SNARK) introduces a security notion of non-malleability. The existing pairing-based zk-SNARKs designed from linear encoding are known to be vulnerable to algebraic manipulation of the proof. The latest SE-SNARKs check the proof consistency by increasing the proof size and the verification cost. In particular, the number of pairings increases almost doubles due to further verification. In this article, we propose two novel SE-SNARK constructions with a single verification. The consistency check is subsumed in a single verification through employing a hash function. The proof size and verification time of the proposed SE-SNARK schemes are minimal in that it is the same as the state-of-the-art zk-SNARK without non-malleability. The proof in our SE-SNARK constructions comprises only three group elements (type III) in the QAP-based scheme and two group elements (type I) in the SAP-based scheme. The verification time in both requires only 3 pairings. The soundness of the proposed schemes is proven under the hash-algebraic knowledge (HAK) assumption and the (linear) collision-resistant hash assumption (Kim, Lee, & Oh, 2020).
6. GZKP: A GPU Accelerated Zero-Knowledge Proof System - This paper develops GZKP, an efficient GPU-accelerated ZKP system that significantly speeds up proof generation, making ZKP more practical for online applications (Ma et al., 2023).
Abstract: Zero-knowledge proof (ZKP) is a cryptographic protocol that allows one party to prove the correctness of a statement to another party without revealing any information beyond the correctness of the statement itself. It guarantees computation integrity and confidentiality, and is therefore increasingly adopted in industry for a variety of privacy-preserving applications, such as verifiable outsource computing and digital currency. A significant obstacle in using ZKP for online applications is the performance overhead of its proof generation. We develop GZKP, a GPU accelerated zero-knowledge proof system that supports different levels of security requirements and brings significant speedup toward making ZKP truly usable. For polynomial computation over a large finite field, GZKP promotes a cache-friendly memory access pattern while eliminating the costly external shuffle in existing solutions. For multi-scalar multiplication, GZKP adopts a new parallelization strategy, which aggressively combines integer elliptic curve point operations and exploits fine-grained task parallelism with load balancing for sparse integer distribution. GZKP outperforms the state-of-the-art ZKP systems by an order of magnitude, achieving up to 48.1× and 17.6× speedup with standard cryptographic benchmarks and a real-world application workload, respectively (Ma et al., 2023).
7. Zilch: A Framework for Deploying Transparent Zero-Knowledge Proofs - Zilch is introduced to simplify the deployment of verifiable computation and zero-knowledge proofs, using a MIPS-like processor model and a cross-compiler for improved usability and flexibility (Mouris & Tsoutsos, 2021).
Abstract: As cloud computing becomes more popular, research has focused on usable solutions to the problem of verifiable computation (VC), where a computationally weak device (Verifier) outsources a program execution to a powerful server (Prover) and receives guarantees that the execution was performed faithfully. A Prover can further demonstrate knowledge of a secret input that causes the Verifier’s program to satisfy certain assertions, without ever revealing which input was used. State-of-the-art Zero-Knowledge Proofs of Knowledge (ZKPK) methods encode a computation using arithmetic circuits and preserve the privacy of Prover’s inputs while attesting the integrity of program execution. Nevertheless, developing, debugging, and optimizing programs as circuits remains a daunting task, as most users are unfamiliar with this programming paradigm. In this work, we present Zilch, a framework that accelerates and simplifies the deployment of VC and ZKPK for any application transparently, i.e., without the need of trusted setup. Zilch uses traditional instruction sequences rather than static arithmetic circuits that would need to be regenerated for each different computation. Towards that end, we have implemented Z MIPS: a MIPS-like processor model that allows verifying each instruction independently and compose a proof for the execution of the target application. To foster usability, Zilch incorporates a novel cross-compiler from an object-oriented Java-like language tailored to ZKPK and optimized our Z MIPS model, as well as a powerful API that enables integration of ZKPK within existing C/C++ programs. In our experiments, we demonstrate the flexibility of Zilch using two real-life applications, and evaluate Prover and Verifier performance on a variety of benchmarks (Mouris & Tsoutsos, 2021).
8. ZPiE: Zero-knowledge Proofs in Embedded systems - This paper presents ZPiE, a library for creating ZKP applications on embedded systems, demonstrating its portability and effectiveness in resource-limited devices (Salleras & Daza, 2021).
Abstract: Zero-Knowledge Proofs (ZKPs) are cryptographic primitives allowing a party to prove to another party that the former knows some information while keeping it secret. Such a premise can lead to the development of numerous privacy-preserving protocols in different scenarios, like proving knowledge of some credentials to a server without leaking the identity of the user. Even when the applications of ZKPs were endless, they were not exploited in the wild for a couple of decades due to the fact that computing and verifying proofs was too computationally expensive. However, the advent of efficient schemes (in particular, zk-SNARKs) made this primitive to break into the scene in fields like cryptocurrencies, smart-contracts, and more recently, self-sovereign scenarios: private-by-design identity management and authentication. Nevertheless, its adoption in environments like the Internet of Things (IoT) remains unexplored due to the computational limitations of embedded systems. In this paper, we introduce ZPiE, a C library intended to create ZKP applications to be executed in embedded systems. Its main feature is portability: it can be compiled, executed, and used out-of-the-box in a wide variety of devices. Moreover, our proof-of-concept has been proved to work smoothly in different devices with limited resources, which can execute state-of-the-art ZKP authentication protocols (Salleras & Daza, 2021).
These papers illustrate the diverse applications of ZK-proofs, from blockchain privacy and secure model training to accelerating proof systems and enabling ZKP in embedded systems.
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