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arxiv: 2408.00243 · v2 · submitted 2024-08-01 · 💻 cs.CR · cs.CC

A Survey on the Applications of Zero-Knowledge Proofs

Ryan Lavin , Xuekai Liu , Hardhik Mohanty , Logan Norman , Giovanni Zaarour , Bhaskar Krishnamachari This is my paper

Pith reviewed 2026-05-23 22:40 UTC · model grok-4.3

classification 💻 cs.CR cs.CC
keywords zero-knowledge proofszkSNARKsblockchain privacycomputational integritysurveyproof systemsprivacy-preserving computation
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The pith

This survey organizes zero-knowledge proof applications into a taxonomy and compares zkSNARK systems on proof size, setup assumptions, and performance metrics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compiles a technical overview of zero-knowledge proofs with primary attention to zkSNARKs and their growing use in real systems. It supplies a taxonomy that groups applications into blockchain privacy, scaling, storage, interoperability, and non-blockchain areas such as voting, authentication, and machine learning. Evaluation criteria covering proof size, prover and verifier time, memory, and setup assumptions are defined, then applied in comparative tables that highlight tradeoffs among representative systems. The work also reviews supporting infrastructure such as zero-knowledge virtual machines, domain-specific languages, and libraries while contrasting zkSNARKs against zkSTARKs and Bulletproofs on transparency and performance.

Core claim

Zero-knowledge proofs enable computational integrity and privacy with advantages in universality and minimal trust assumptions over alternatives like homomorphic encryption. The survey maps their deployments across blockchain and non-blockchain domains, supplies consistent comparison criteria, and presents tables that summarize key tradeoffs and representative systems, while noting future research directions.

What carries the argument

A taxonomy of application areas paired with evaluation criteria (proof size, prover/verifier time, memory, setup assumptions) and comparative tables that contrast zkSNARKs, zkSTARKs, and Bulletproofs.

If this is right

  • Developers can use the tables to match specific requirements for proof size or setup trust to available zkSNARK implementations.
  • Blockchain projects gain a structured way to evaluate ZKP options for privacy-preserving transactions or layer-2 scaling.
  • Non-blockchain domains such as private machine learning inference obtain explicit criteria for assessing verification overhead.
  • The comparison with zkSTARKs and Bulletproofs clarifies when transparent setups are preferable to trusted setups.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The taxonomy could be extended by adding new application categories as ZKP use expands into areas like secure hardware attestation.
  • Periodic updates to the tables would be needed as new zkSNARK constructions improve prover time or reduce setup assumptions.
  • The evaluation criteria might serve as a template for comparing ZKP libraries against other privacy technologies such as secure multiparty computation.

Load-bearing premise

The chosen applications, systems, and evaluation criteria are representative enough to capture the main practical tradeoffs across the field.

What would settle it

Identification of a deployed ZKP system whose measured proof size, setup requirements, or runtime characteristics fall outside the patterns summarized in the survey tables would indicate incomplete coverage.

Figures

Figures reproduced from arXiv: 2408.00243 by Bhaskar Krishnamachari, Giovanni Zaarour, Hardhik Mohanty, Logan Norman, Ryan Lavin, Xuekai Liu.

Figure 1
Figure 1. Figure 1: Survey Structure languages, and pertinent libraries. Next, Section IV provides an extensive dissection of blockchain applications, which reviews the role of ZKPs across various blockchain layers and functionalities. Section V extends the discussion to non-blockchain application domains, detailing ZKPs’ utility in diverse contexts such as machine learning and digital identity verification. Finally, Section … view at source ↗
Figure 2
Figure 2. Figure 2: An arithmetic circuit representation [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: General zkVM Architecture Depending on the proving system, the setup phase begins after the program has been interpreted and translated to bytecode. This step involves tasks such as concealing private inputs, initializing a polynomial commitment scheme, key generation, and others. A set of constraints is placed on the program and the witness to enforce computational integrity in the computation trace. Buil… view at source ↗
Figure 4
Figure 4. Figure 4: Timeline of zkVM Popular Projects decade such as TinyRAM [25], Hawk [26], Zinc [27] , RISC Zero [28], CarioVM [29], Leo [30], Miden [24], Triton [31], OlaVM [32] , Powdr [33], and Jolt [34]. Some other zkVMs that are on the rise as of writing this paper are SP1 [35], Nexus [36], and Valida [37]. A project in the space is RISC Zero’s [28] zkVM which allows users to demonstrate the accurate execution of arbi… view at source ↗
Figure 5
Figure 5. Figure 5: Arithmetization Schemes [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Timeline of Popular zk-DSLs succinct verification of applications is made accessible to anyone, irrespective of the application’s size. Leo maintains a set of tools, including a testing framework, pack￾age registry, import resolver, remote compiler, formally defined language, and theo￾rem prover, specifically tailored for general-purpose zero-knowledge applications. To summarize, zkDSLs emerge as versatile… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of Layer-1 Data Compression and Privacy Approaches using ZKPs [PITH_FULL_IMAGE:figures/full_fig_p038_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Generalized ZK Rollup Architecture, redrawn based on [68] [PITH_FULL_IMAGE:figures/full_fig_p043_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Aztec’s high-level network architecture, redrawn based on [76] [PITH_FULL_IMAGE:figures/full_fig_p048_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: zkBridge architecture when used for a cross-chain token transfer, redrawn based [PITH_FULL_IMAGE:figures/full_fig_p050_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Supply Chain features fulfilled by Blockchain and Zero-Knowledge Proofs [PITH_FULL_IMAGE:figures/full_fig_p059_12.png] view at source ↗
read the original abstract

Zero-knowledge proofs (ZKPs) enable computational integrity and privacy by allowing one party to prove the truth of a statement without revealing underlying data. Compared with alternatives such as homomorphic encryption and secure multiparty computation, ZKPs offer distinct advantages in universality and minimal trust assumptions, with applications spanning blockchain systems and confidential verification of computational tasks. This survey provides a technical overview of ZKPs with a focus on an increasingly relevant subset called zkSNARKs. Unlike prior surveys emphasizing algorithmic and theoretical aspects, we take a broader view of practical deployments and recent use cases across multiple domains including blockchain privacy, scaling, storage, and interoperability, as well as non-blockchain applications such as voting, authentication, timelocks, and machine learning. To support consistent comparison, we provide (i) a taxonomy of application areas, (ii) evaluation criteria including proof size, prover and verifier time, memory, and setup assumptions, and (iii) comparative tables summarizing key tradeoffs and representative systems. The survey also covers supporting infrastructure, including zero-knowledge virtual machines, domain-specific languages, libraries, and frameworks. While emphasizing zkSNARKs for their prevalence in deployed systems, we compare them with zkSTARKs and Bulletproofs to clarify transparency and performance tradeoffs. We conclude with future research and application directions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a survey on zero-knowledge proofs (ZKPs) with emphasis on zkSNARKs. It supplies a technical overview, a taxonomy of application areas (blockchain privacy/scaling/storage/interoperability and non-blockchain uses such as voting, authentication, timelocks, and ML), evaluation criteria (proof size, prover/verifier time, memory, setup assumptions), comparative tables of representative systems and tradeoffs, coverage of supporting infrastructure (ZKVMs, DSLs, libraries, frameworks), explicit comparisons to zkSTARKs and Bulletproofs on transparency and performance, and concluding remarks on future directions.

Significance. If the selected systems, criteria, and comparisons are representative and accurate, the survey could provide a useful consolidated reference for practitioners and researchers seeking to navigate practical ZKP deployments and tradeoffs. The explicit provision of evaluation criteria and tables for consistent comparison, along with infrastructure coverage, strengthens its potential utility as a practical guide.

minor comments (2)
  1. [Abstract] Abstract: the claim of taking 'a broader view of practical deployments and recent use cases' than prior surveys would be strengthened by an explicit, itemized comparison (in §1 or a dedicated related-work subsection) to the most recent prior ZKP surveys, citing their scopes and limitations.
  2. The manuscript should verify that all cited systems and performance numbers in the comparative tables remain current as of the 2024 submission date, particularly for rapidly evolving zkSNARK implementations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of the manuscript, its potential utility as a practical reference, and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

This is a survey paper whose central contribution is a descriptive compilation: a taxonomy of ZKP applications, evaluation criteria (proof size, times, memory, setup), and comparative tables drawn from prior literature. The abstract and scope contain no new theorems, derivations, equations, fitted parameters, or predictions that could reduce to inputs by construction. No load-bearing steps exist that invoke self-citation chains, ansatzes, or uniqueness claims internal to the work. The reader's assessment of representativeness is a standard survey limitation, not an internal inconsistency. The derivation chain is empty; the paper is self-contained as a literature overview.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a survey paper there are no free parameters, axioms, or invented entities; the contribution is organizational and draws entirely from cited prior literature.

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Forward citations

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Reference graph

Works this paper leans on

117 extracted references · 117 canonical work pages · cited by 3 Pith papers · 2 internal anchors

  1. [1]

    Proofs that yield nothing but their validity and a methodology of cryptographic protocol design,

    O. Goldreich, S. Micali, and A. Wigderson, “Proofs that yield nothing but their validity and a methodology of cryptographic protocol design,” in 27th Annual Symposium on Foundations of Computer Science (sfcs 1986) , 1986, pp. 174–187

    work page 1986

  2. [2]

    Proofs that yield nothing but their validity or all languages in np have zero-knowledge proof systems,

    ——, “Proofs that yield nothing but their validity or all languages in np have zero-knowledge proof systems,” Journal of the ACM (JACM) , vol. 38, no. 3, pp. 690–728, 1991

    work page 1991

  3. [3]

    Everything provable is provable in zero-knowledge,

    M. Ben-Or, O. Goldreich, S. Goldwasser, J. H ˚astad, J. Kilian, S. Micali, and P. Rogaway, “Everything provable is provable in zero-knowledge,” in Advances in Cryptology—CRYPTO’88: Proceedings 8 . Springer, 1990, pp. 37–56

    work page 1990

  4. [4]

    From extractable collision resistance to succinct non- interactive arguments of knowledge, and back again

    N. Bitansky, R. Canetti, A. Chiesa, and E. Tromer, “From extractable collision resistance to succinct non- interactive arguments of knowledge, and back again.” IACR Cryptology ePrint Archive , vol. 2011, p. 443, 01 2011

    work page 2011

  5. [5]

    Short pairing-based non-interactive zero-knowledge arguments,

    J. Groth, “Short pairing-based non-interactive zero-knowledge arguments,” in Advances in Cryptology - ASIACRYPT 2010, M. Abe, Ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 321–340

    work page 2010

  6. [6]

    A note on efficient zero-knowledge proofs and arguments,

    J. Kilian, “A note on efficient zero-knowledge proofs and arguments,” in Proceedings of the twenty-fourth annual ACM symposium on Theory of computing , 1992, pp. 723–732

    work page 1992

  7. [7]

    Security and privacy on blockchain,

    R. Zhang, R. Xue, and L. Liu, “Security and privacy on blockchain,” ACM Computing Surveys (CSUR), vol. 52, no. 3, pp. 1–34, 2019

    work page 2019

  8. [8]

    On data banks and privacy homomorphisms,

    R. L. Rivest, L. Adleman, M. L. Dertouzos et al., “On data banks and privacy homomorphisms,” Foundations of secure computation , vol. 4, no. 11, pp. 169–180, 1978. 75

    work page 1978

  9. [9]

    Protocols for secure computations,

    A. C. Yao, “Protocols for secure computations,” in 23rd annual symposium on foundations of computer science (sfcs 1982). IEEE, 1982, pp. 160–164

    work page 1982

  10. [10]

    Design choices and trade-offs in health care blockchain implementations: systematic review,

    O. O’Donoghue, A. A. Vazirani, D. Brindley, and E. Meinert, “Design choices and trade-offs in health care blockchain implementations: systematic review,”Journal of medical Internet research, vol. 21, no. 5, p. e12426, 2019

    work page 2019

  11. [11]

    Why and How zk-SNARK Works

    M. Petkus, “Why and how zk-snark works,” arXiv preprint arXiv:1906.07221 , 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1906

  12. [12]

    A survey on zero knowledge range proofs and applications,

    E. Morais, T. Koens, C. Van Wijk, and A. Koren, “A survey on zero knowledge range proofs and applications,” SN Applied Sciences , vol. 1, pp. 1–17, 2019

    work page 2019

  13. [13]

    A survey on zero-knowledge proof in blockchain,

    X. Sun, F. R. Yu, P. Zhang, Z. Sun, W. Xie, and X. Peng, “A survey on zero-knowledge proof in blockchain,” IEEE network, vol. 35, no. 4, pp. 198–205, 2021

    work page 2021

  14. [14]

    The knowledge complexity of interactive proof-systems (extended abstract)

    S. Goldwasser, S. Micali, and C. Rackoff, “The knowledge complexity of interactive proof-systems,” in Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing , ser. STOC ’85. New York, NY , USA: Association for Computing Machinery, 1985, p. 291–304. [Online]. Available: https://doi.org/10.1145/22145.22178

    work page doi:10.1145/22145.22178 1985

  15. [15]

    Snarks for c: Verifying program executions succinctly and in zero knowledge,

    E. Ben-Sasson, A. Chiesa, D. Genkin, E. Tromer, and M. Virza, “Snarks for c: Verifying program executions succinctly and in zero knowledge,” in Annual cryptology conference . Springer, 2013, pp. 90–108

    work page 2013

  16. [16]

    Customizable constraint systems for succinct arguments,

    S. Setty, J. Thaler, and R. Wahby, “Customizable constraint systems for succinct arguments,” Cryptology ePrint Archive, Paper 2023/552, 2023, https://eprint.iacr.org/2023/552. [Online]. Available: https://eprint.iacr.org/2023/552

    work page 2023

  17. [17]

    Quadratic span programs and succinct nizks without pcps,

    R. Gennaro, C. Gentry, B. Parno, and M. Raykova, “Quadratic span programs and succinct nizks without pcps,” in Advances in Cryptology–EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings 32 . Springer, 2013, pp. 626–645

    work page 2013

  18. [18]

    Constant-size commitments to polynomials and their applications,

    A. Kate, G. M. Zaverucha, and I. Goldberg, “Constant-size commitments to polynomials and their applications,” in Advances in Cryptology-ASIACRYPT 2010: 16th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 5-9, 2010. Proceedings 16 . Springer, 2010, pp. 177–194

    work page 2010

  19. [19]

    Secure sampling of public parameters for succinct zero knowledge proofs,

    E. Ben-Sasson, A. Chiesa, M. Green, E. Tromer, and M. Virza, “Secure sampling of public parameters for succinct zero knowledge proofs,” in 2015 IEEE Symposium on Security and Privacy , 2015, pp. 287–304

    work page 2015

  20. [20]

    How to prove yourself: Practical solutions to identification and signature problems,

    A. Fiat and A. Shamir, “How to prove yourself: Practical solutions to identification and signature problems,” in Conference on the theory and application of cryptographic techniques . Springer, 1986, pp. 186–194

    work page 1986

  21. [21]

    On the size of pairing-based non-interactive arguments,

    J. Groth, “On the size of pairing-based non-interactive arguments,” in Proceedings, Part II, of the 35th Annual International Conference on Advances in Cryptology — EUROCRYPT 2016 - Volume 9666 . Springer-Verlag, 2016, p. 305–326

    work page 2016

  22. [22]

    Nguyen, T.-A

    B. B ¨unz, J. Bootle, D. Boneh, A. Poelstra, P. Wuille, and G. Maxwell, “Bulletproofs: Short proofs for 76 confidential transactions and more,” in 2018 IEEE Symposium on Security and Privacy, SP 2018, Proceedings, 21-23 May 2018, San Francisco, California, USA . IEEE Computer Society, 2018, pp. 315–334. [Online]. Available: https://doi.org/10.1109/SP.2018.00020

    work page doi:10.1109/sp.2018.00020 2018

  23. [23]

    Circom 2 documentation,

    Circom, “Circom 2 documentation,” https://docs.circom.io/, 2024, [Accessed 12-05-2023]

    work page 2024

  24. [24]

    Polygon miden documentation,

    Polygon, “Polygon miden documentation,” https://0xpolygonmiden.github.io/miden-base/introduction.html? search=setup, 2024, [Accessed 01-05-2024]

    work page 2024

  25. [25]

    SNARKs for c: Verifying program executions succinctly and in zero knowledge,

    E. Ben-Sasson, A. Chiesa, D. Genkin, E. Tromer, and M. Virza, “SNARKs for c: Verifying program executions succinctly and in zero knowledge,” Cryptology ePrint Archive, Paper 2013/507, 2013, https://eprint.iacr.org/2013/507. [Online]. Available: https://eprint.iacr.org/2013/507

    work page 2013

  26. [26]

    Hawk: The blockchain model of cryptography and privacy-preserving smart contracts,

    A. Kosba, A. Miller, E. Shi, Z. Wen, and C. Papamanthou, “Hawk: The blockchain model of cryptography and privacy-preserving smart contracts,” in 2016 IEEE Symposium on Security and Privacy (SP) , 2016, pp. 839–858

    work page 2016

  27. [27]

    Labs, “Zinc,” 2020, accessed: July 22, 2024

    M. Labs, “Zinc,” 2020, accessed: July 22, 2024. [Online]. Available: https://blog.matter-labs.io/ release-of-zinc-v0-1-8d949aa9a2f2

    work page 2020

  28. [28]

    Risc zero whitepaper,

    R. Z. T. Jeremy Bruestle, Paul Gafni, “Risc zero whitepaper,” https://dev.risczero.com/proof-system-in-detail. pdf, 2024, [Accessed 02-22-2024]

    work page 2024

  29. [29]

    Cairo and sierra,

    Starknet, “Cairo and sierra,” 2023. [Online]. Available: https://docs.starknet.io/documentation/architecture and concepts/Smart Contracts/cairo-and-sierra/

    work page 2023

  30. [30]

    Aleo: A new platform for private applications,

    “Aleo: A new platform for private applications,” 2023, accessed: November 24, 2023. [Online]. Available: https://www.aleo.org/

    work page 2023

  31. [31]

    Announcing triton vm,

    Neptune, “Announcing triton vm,” 2022, accessed: July 22, 2024. [Online]. Available: https://neptune.cash/ blog/announcing-tvm/

    work page 2022

  32. [32]

    [Online]

    Sin7Y , “Olavm,” 2022, accessed: July 22, 2024. [Online]. Available: https://olavm.org/

    work page 2022

  33. [33]

    Powdr zkvm,

    Powdr, “Powdr zkvm,” 2023, accessed: July 22, 2024. [Online]. Available: https://www.powdr.org/

    work page 2023

  34. [34]

    Jolt: SNARKs for virtual machines via lookups,

    A. Arun, S. Setty, and J. Thaler, “Jolt: SNARKs for virtual machines via lookups,” Cryptology ePrint Archive, Paper 2023/1217, 2023, https://eprint.iacr.org/2023/1217. [Online]. Available: https://eprint.iacr.org/2023/1217

    work page 2023

  35. [35]

    Sp1 zkvm,

    S. Labs, “Sp1 zkvm,” 2024. [Online]. Available: https://blog.succinct.xyz/introducing-sp1/

    work page 2024

  36. [36]

    Nexus 1.0: Enabling verifiable computation,

    D. Marin, M. Abdalla, P. Govereau, J. Groth, S. Judson, K. Sosnin, and G. Vamsi, “Nexus 1.0: Enabling verifiable computation,” 2024. [Online]. Available: https://nexus.xyz/

    work page 2024

  37. [37]

    Lita zkvm,

    Lita, “Lita zkvm,” 2023. [Online]. Available: https://www.lita.foundation/infrastructure#valida

    work page 2023

  38. [38]

    [Online]

    Mina, “O1js,” 2021, accessed: July 22, 2024. [Online]. Available: https://docs.minaprotocol.com/zkapps/o1js

    work page 2021

  39. [39]

    Introducing noir,

    Noir, “Introducing noir,” 2023. [Online]. Available: https://noir-lang.org/

    work page 2023

  40. [40]

    Juvix zkdsl,

    A. Labs, “Juvix zkdsl,” 2017. [Online]. Available: https://github.com/anoma/juvix

    work page 2017

  41. [41]

    LURK: 77 Lambda, the ultimate recursive knowledge,

    N. Amin, J. Burnham, F. Garillot, R. Gennaro, C. K ¨unzang, D. Rogozin, and C. Wong, “LURK: 77 Lambda, the ultimate recursive knowledge,” Cryptology ePrint Archive, Paper 2023/369, 2023, https://eprint.iacr.org/2023/369. [Online]. Available: https://eprint.iacr.org/2023/369

    work page 2023

  42. [42]

    Tornado cash privacy solution,

    A. Pertsev, R. Semenov, and R. Storm, “Tornado cash privacy solution,” 2019. [Online]. Available: https://berkeley-defi.github.io/assets/material/Tornado%20Cash%20Whitepaper.pdf

    work page 2019

  43. [43]

    Dark forest,

    0xPARC, “Dark forest,” https://zkga.me/, 2020, accessed: February 22, 2024

    work page 2020

  44. [44]

    circomlib,

    iden3, “circomlib,” 2018, accessed: July 22, 2024. [Online]. Available: https://github.com/iden3/circomlib

    work page 2018

  45. [45]

    Leo: A programming language for formally verified, zero-knowledge applications,

    C. Chin, H. Wu, R. Chu, A. Coglio, E. McCarthy, and E. Smith, “Leo: A programming language for formally verified, zero-knowledge applications,” Cryptology ePrint Archive, Paper 2021/651, 2021, https://eprint.iacr.org/2021/651. [Online]. Available: https://eprint.iacr.org/2021/651

    work page 2021

  46. [46]

    ethSTARK documentation,

    StarkWare, “ethSTARK documentation,” Cryptology ePrint Archive, Paper 2021/582, 2021, https: //eprint.iacr.org/2021/582. [Online]. Available: https://eprint.iacr.org/2021/582

    work page 2021

  47. [47]

    Plonky2: Fast recursive arguments with plonk and fri,

    P. Z. Team, “Plonky2: Fast recursive arguments with plonk and fri,” 2022, accessed: July 22, 2024. [Online]. Available: https://github.com/0xPolygonZero/plonky2/blob/main/plonky2/plonky2.pdf

    work page 2022

  48. [48]

    Zk bench,

    C. Moore, “Zk bench,” 2023, accessed: July 22, 2024. [Online]. Available: https://zkbench.dev/

    work page 2023

  49. [49]

    zk-bench: A toolset for comparative evaluation and performance benchmarking of SNARKs,

    J. Ernstberger, S. Chaliasos, G. Kadianakis, S. Steinhorst, P. Jovanovic, A. Gervais, B. Livshits, and M. Orr `u, “zk-bench: A toolset for comparative evaluation and performance benchmarking of SNARKs,” Cryptology ePrint Archive, Paper 2023/1503, 2023. [Online]. Available: https://eprint.iacr.org/2023/1503

    work page 2023

  50. [50]

    arkworks zksnark ecosystem,

    arkworks contributors, “ arkworks zksnark ecosystem,” 2022. [Online]. Available: https://arkworks.rs

    work page 2022

  51. [51]

    Consensys/gnark: v0.9.0,

    G. Botrel, T. Piellard, Y . E. Housni, I. Kubjas, and A. Tabaie, “Consensys/gnark: v0.9.0,” Feb. 2023. [Online]. Available: https://doi.org/10.5281/zenodo.5819104

    work page doi:10.5281/zenodo.5819104 2023

  52. [52]

    CirC: Compiler infrastructure for proof systems, software verification, and more,

    A. Ozdemir, F. Brown, and R. S. Wahby, “CirC: Compiler infrastructure for proof systems, software verification, and more,” Cryptology ePrint Archive, Paper 2020/1586, 2020, https://eprint.iacr.org/2020/1586. [Online]. Available: https://eprint.iacr.org/2020/1586

    work page 2020

  53. [53]

    Zokrates - scalable privacy-preserving off-chain computations,

    J. Eberhardt and S. Tai, “Zokrates - scalable privacy-preserving off-chain computations,” in 2018 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData) , 2018, pp. 1084–1091

    work page 2018

  54. [54]

    Mina protocol: The world’s lightest blockchain,

    “Mina protocol: The world’s lightest blockchain,” 2023, accessed: November 24, 2023. [Online]. Available: https://minaprotocol.com/

    work page 2023

  55. [55]

    Zcash halo2 book,

    E. C. Company, “Zcash halo2 book,” 2020, accessed: July 22, 2024. [Online]. Available: https: //zcash.github.io/halo2/index.html

    work page 2020

  56. [56]

    Nova: Recursive zero-knowledge arguments from folding schemes,

    A. Kothapalli, S. Setty, and I. Tzialla, “Nova: Recursive zero-knowledge arguments from folding schemes,” Cryptology ePrint Archive, Paper 2021/370, 2021, https://eprint.iacr.org/2021/370. [Online]. Available: https://eprint.iacr.org/2021/370

    work page 2021

  57. [57]

    Bellpepper zk-snark library,

    L. Labs, “Bellpepper zk-snark library,” 2023. [Online]. Available: https://github.com/lurk-lab/bellpepper 78

    work page 2023

  58. [58]

    Zkp mooc,

    D. Boneh, S. Goldwasser, D. Song, J. Thaler, and Y . Zhang, “Zkp mooc,” https://zk-learning.org/, 2023

    work page 2023

  59. [59]

    Hardware acceleration for zero knowledge proofs,

    G. Konstantopoulos, “Hardware acceleration for zero knowledge proofs,” 2022. [Online]. Available: https://www.paradigm.xyz/2022/04/zk-hardware

    work page 2022

  60. [60]

    Revisiting paradigm “hardware acceleration for zero knowl- edge proofs

    O. Shlomovits, “Revisiting paradigm “hardware acceleration for zero knowl- edge proofs”,” 2023. [Online]. Available: https://medium.com/@omershlomovits/ revisiting-paradigm-hardware-acceleration-for-zero-knowledge-proofs-16f717a49555

    work page 2023

  61. [61]

    Ingonyama,

    Ingonyama, “Ingonyama,” 2022. [Online]. Available: https://www.ingonyama.com/

    work page 2022

  62. [62]

    [Online]

    Cycisic, “Cysic,” 2022. [Online]. Available: https://cysic.xyz/

    work page 2022

  63. [63]

    [Online]

    Fabric, “Fabric,” 2022. [Online]. Available: https://www.fabriccryptography.com/

    work page 2022

  64. [64]

    Irreducible,

    Irreducible, “Irreducible,” 2022. [Online]. Available: https://www.irreducible.com/

    work page 2022

  65. [65]

    Supranational,

    Supranational, “Supranational,” 2023. [Online]. Available: https://www.supranational.net/

    work page 2023

  66. [66]

    Zcash: Privacy-protecting digital currency,

    “Zcash: Privacy-protecting digital currency,” 2023, accessed: November 24, 2023. [Online]. Available: https://z.cash/

    work page 2023

  67. [67]

    Zero-knowledge rollups,

    E. Foundation, “Zero-knowledge rollups,” 2023. [Online]. Available: https://ethereum.org/en/developers/docs/ scaling/zk-rollups/

    work page 2023

  68. [68]

    Zk rollup architecture,

    E. Systems, “Zk rollup architecture,” 2024, accessed: April 10, 2024. [Online]. Available: https: //docs.espressosys.com/sequencer/integrating-a-rollup/integrating-a-zk-rollup/zk-rollup-architecture

    work page 2024

  69. [69]

    zksync era docs,

    M. Labs, “zksync era docs,” 2023. [Online]. Available: https://era.zksync.io/docs/reference/

    work page 2023

  70. [70]

    zkevm wiki,

    P. Labs, “zkevm wiki,” 2023. [Online]. Available: https://wiki.polygon.technology/docs/zkevm/

    work page 2023

  71. [71]

    Cdk wiki,

    ——, “Cdk wiki,” 2023. [Online]. Available: https://wiki.polygon.technology/docs/cdk/

    work page 2023

  72. [72]

    Ethereum & scroll differences,

    Scroll, “Ethereum & scroll differences,” 2023. [Online]. Available: https://docs.scroll.io/en/developers/ ethereum-and-scroll-differences/#evm-opcodes

    work page 2023

  73. [73]

    [Online]

    Linea, “Linea,” 2023. [Online]. Available: https://docs.linea.build/overview

    work page 2023

  74. [74]

    Native account abstraction: Opening blockchain to new possibilities,

    StarkWare, “Native account abstraction: Opening blockchain to new possibilities,” 2023. [Online]. Available: https://starkware.co/resource/native-account-abstraction-opening-blockchain-to-new-possibilities/

    work page 2023

  75. [75]

    High-level overview,

    ——, “High-level overview,” 2023. [Online]. Available: https://docs.starkware.co/starkex/overview.html

    work page 2023

  76. [76]

    Aztec docs,

    Aztec, “Aztec docs,” 2023. [Online]. Available: https://docs.aztec.network/

    work page 2023

  77. [77]

    Introducing noir: The universal language of zero-knowledge,

    A. Labs, “Introducing noir: The universal language of zero-knowledge,” 2023. [Online]. Available: https://aztec.network/blog/introducing-noir-the-universal-language-of-zero-knowledge/

    work page 2023

  78. [78]

    zkbridge: Trustless cross-chain bridges made practical,

    T. Xie, J. Zhang, Z. Cheng, F. Zhang, Y . Zhang, Y . Jia, D. Boneh, and D. Song, “zkbridge: Trustless cross-chain bridges made practical,” in Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security, 2022, pp. 3003–3017

    work page 2022

  79. [79]

    Polyhedra,

    Polyhedra, “Polyhedra,” 2024, [Accessed 05-08-2024]. [Online]. Available: https://www.polyhedra.network/

    work page 2024

  80. [80]

    Telepathy,

    Telepathy, “Telepathy,” 2024. [Online]. Available: https://docs.telepathy.xyz/

    work page 2024

Showing first 80 references.