Skip to main content
SpringerLink
Log in

Fiat-Shamir Security of FRI and Related SNARKs

  • Conference paper
  • First Online:
Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14439))

  • 364 Accesses

Abstract

We establish new results on the Fiat-Shamir (FS) security of several protocols that are widely used in practice, and we provide general tools for establishing similar results for others. More precisely, we: (1) prove the FS security of the FRI and batched FRI protocols; (2) analyze a general class of protocols, which we call \(\delta \)-correlated, that use low-degree proximity testing as a subroutine (this includes many “Plonk-like” protocols (e.g., Plonky2 and Redshift), ethSTARK, RISC Zero, etc.); and (3) prove FS security of the aforementioned “Plonk-like” protocols, and sketch how to prove the same for the others.

We obtain our first result by analyzing the round-by-round (RBR) soundness and RBR knowledge soundness of FRI. For the second result, we prove that if a \(\delta \)-correlated protocol is RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials, then it is RBR (knowledge) sound in general. Equipped with this tool, we prove our third result by formally showing that “Plonk-like” protocols are RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials. We then outline analogous arguments for the remainder of the aforementioned protocols.

To the best of our knowledge, ours is the first formal analysis of the Fiat-Shamir security of FRI and widely deployed protocols that invoke it.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A protocol is public-coin if all messages sent by the verifier are sampled uniformly at random from a challenge space and are independent of all prior prover and verifier messages.

  2. 2.

    More formally, the BCS transformation is applied to interactive oracle proofs [9].

  3. 3.

    Actually, [9, 25] prove this for state-restoration soundness; however, subsequent works observed that round-by-round soundness is an upper bound on state-restoration soundness [22, 25, 26, 44].

  4. 4.

    Informally, functions have \(\delta \)-correlated agreement if they are all \(\delta \)-close to some pre-specified Reed-Solomon code and all have the same agreement set; see [14] for full details.

  5. 5.

    [4] refers to this as the commit phase. We view the term “folding phase” as more appropriate given the nature of the compression.

  6. 6.

    In practice to save on communication, only a single \(\alpha \) is sent and the linear combination is computed with \(\alpha _i = \alpha ^{i-1}\), at the cost of an increased soundness error; see [14] for details.

  7. 7.

    This is necessary, if a malicious prover is allowed to send dishonest \(f_1^*,\dotsc , f_t^*\) such that all are \(\delta \)-close, then the protocol reduces to the honest prover analysis.

  8. 8.

    This is not entirely accurate; for precise bounds, see Theorem 8.

References

  1. Abdalla, M., An, J.H., Bellare, M., Namprempre, C.: From identification to signatures via the Fiat-Shamir transform: minimizing assumptions for security and forward-security. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 418–433. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_28

    Chapter  Google Scholar 

  2. Attema, T., Fehr, S., Klooß, M.: Fiat-Shamir transformation of multi-round interactive proofs. In: Kiltz, E., Vaikuntanathan, V. (eds.) TCC 2022, Part I. LNCS, vol. 13747, pp. 113–142. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-22318-1_5

    Chapter  Google Scholar 

  3. Barak, B.: How to go beyond the black-box simulation barrier. In: 42nd FOCS, pp. 106–115. IEEE Computer Society Press (2001). https://doi.org/10.1109/SFCS.2001.959885

  4. Ben-Sasson, E., Bentov, I., Horesh, Y., Riabzev, M.: Fast reed-solomon interactive oracle proofs of proximity. In: Chatzigiannakis, I., Kaklamanis, C., Marx, D., Sannella, D. (eds.) ICALP 2018. LIPIcs, vol. 107, pp. 14:1–14:17. Schloss Dagstuhl (2018). https://doi.org/10.4230/LIPIcs.ICALP.2018.14

  5. Ben-Sasson, E., Bentov, I., Horesh, Y., Riabzev, M.: Scalable, transparent, and post-quantum secure computational integrity. Cryptology ePrint Archive, Report 2018/046 (2018). https://eprint.iacr.org/2018/046

  6. Ben-Sasson, E., Carmon, D., Ishai, Y., Kopparty, S., Saraf, S.: Proximity gaps for reed-solomon codes. Cryptology ePrint Archive, Paper 2020/654 (2020). https://eprint.iacr.org/2020/654, full version of the same work published at FOCS 2020. https://doi.org/10.1109/FOCS46700.2020.00088

  7. Ben-Sasson, E., Chiesa, A., Genkin, D., Tromer, E.: Fast reductions from RAMs to delegatable succinct constraint satisfaction problems: extended abstract. In: Kleinberg, R.D. (ed.) ITCS 2013, pp. 401–414. ACM (2013). https://doi.org/10.1145/2422436.2422481

  8. Ben-Sasson, E., Chiesa, A., Riabzev, M., Spooner, N., Virza, M., Ward, N.P.: Aurora: transparent succinct arguments for R1CS. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part I. LNCS, vol. 11476, pp. 103–128. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_4

    Chapter  Google Scholar 

  9. Ben-Sasson, E., Chiesa, A., Spooner, N.: Interactive oracle proofs. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part II. LNCS, vol. 9986, pp. 31–60. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_2

    Chapter  Google Scholar 

  10. Ben-Sasson, E., Goldberg, L., Kopparty, S., Saraf, S.: DEEP-FRI: sampling outside the box improves soundness. In: Vidick, T. (ed.) ITCS 2020, vol. 151, pp. 5:1–5:32. LIPIcs (2020). https://doi.org/10.4230/LIPIcs.ITCS.2020.5

  11. Ben-Sasson, E., Kopparty, S., Saraf, S.: Worst-case to average case reductions for the distance to a code. In: Servedio, R.A. (ed.) 33rd Computational Complexity Conference, CCC 2018, 22–24 June 2018, San Diego, CA, USA. LIPIcs, vol. 102, pp. 24:1–24:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018). https://doi.org/10.4230/LIPIcs.CCC.2018.24

  12. Bernhard, D., Pereira, O., Warinschi, B.: How not to prove yourself: pitfalls of the Fiat-Shamir heuristic and applications to Helios. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 626–643. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_38

    Chapter  Google Scholar 

  13. Bitansky, N., et al.: Why “Fiat-Shamir for proofs’’ lacks a proof. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 182–201. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_11

    Chapter  Google Scholar 

  14. Block, A.R., Garreta, A., Katz, J., Thaler, J., Tiwari, P.R., Zając, M.: Fiat-Shamir security of FRI and related snarks. Cryptology ePrint Archive, Paper 2023/1071 (2023). https://eprint.iacr.org/2023/1071

  15. Blum, M., Evans, W., Gemmell, P., Kannan, S., Naor, M.: Checking the correctness of memories. Algorithmica 12, 225–244 (1994)

    Article  MathSciNet  Google Scholar 

  16. Blumberg, A.J., Thaler, J., Vu, V., Walfish, M.: Verifiable computation using multiple provers. Cryptology ePrint Archive, Report 2014/846 (2014). https://eprint.iacr.org/2014/846

  17. Bonneau, J., Clark, J., Goldfeder, S.: On bitcoin as a public randomness source. IACR Cryptology ePrint Archive, p. 1015 (2015)

    Google Scholar 

  18. Bootle, J., Cerulli, A., Chaidos, P., Groth, J., Petit, C.: Efficient zero-knowledge arguments for arithmetic circuits in the discrete log setting. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 327–357. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_12

    Chapter  Google Scholar 

  19. Bootle, J., Cerulli, A., Groth, J., Jakobsen, S., Maller, M.: Arya: nearly linear-time zero-knowledge proofs for correct program execution. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11272, pp. 595–626. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03326-2_20

    Chapter  Google Scholar 

  20. Bünz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell, G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy, pp. 315–334. IEEE Computer Society Press (2018). https://doi.org/10.1109/SP.2018.00020

  21. Bünz, B., Fisch, B., Szepieniec, A.: Transparent SNARKs from DARK compilers. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 677–706. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_24

    Chapter  Google Scholar 

  22. Canetti, R., et al.: Fiat-Shamir: from practice to theory. In: Charikar, M., Cohen, E. (eds.) 51st ACM STOC, pp. 1082–1090. ACM Press (2019). https://doi.org/10.1145/3313276.3316380

  23. Canetti, R., Chen, Y., Reyzin, L., Rothblum, R.D.: Fiat-Shamir and correlation intractability from strong KDM-secure Encryption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part I. LNCS, vol. 10820, pp. 91–122. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_4

    Chapter  Google Scholar 

  24. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004). https://doi.org/10.1145/1008731.1008734

    Article  MathSciNet  Google Scholar 

  25. Chiesa, A., Manohar, P., Spooner, N.: Succinct arguments in the quantum random oracle model. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019, Part II. LNCS, vol. 11892, pp. 1–29. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36033-7_1

    Chapter  Google Scholar 

  26. Chiesa, A., Ojha, D., Spooner, N.: Fractal: post-quantum and transparent recursive proofs from holography. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 769–793. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_27

    Chapter  Google Scholar 

  27. Cormode, G., Mitzenmacher, M., Thaler, J.: Practical verified computation with streaming interactive proofs. In: Goldwasser, S. (ed.) ITCS 2012, pp. 90–112. ACM (2012). https://doi.org/10.1145/2090236.2090245

  28. Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_19

    Chapter  Google Scholar 

  29. Dao, Q., Miller, J., Wright, O., Grubbs, P.: Weak fiat-shamir attacks on modern proof systems. Cryptology ePrint Archive, Paper 2023/691 (2023). https://eprint.iacr.org/2023/691

  30. Dusk Network: Plonkup. https://github.com/dusk-network/plonkup. Accessed 24 May 2023

  31. Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12

    Chapter  Google Scholar 

  32. Gabizon, A., Williamson, Z.J.: The turbo-plonk program syntax for specifying snark programs. https://docs.zkproof.org/pages/standards/accepted-workshop3/proposal-turbo_plonk.pdf. Accessed 23 May 2023

  33. Gabizon, A., Williamson, Z.J.: plookup: a simplified polynomial protocol for lookup tables. Cryptology ePrint Archive, Paper 2020/315 (2020). https://eprint.iacr.org/2020/315

  34. Gabizon, A., Williamson, Z.J., Ciobotaru, O.: PLONK: permutations over lagrange-bases for oecumenical noninteractive arguments of knowledge. Cryptology ePrint Archive, Report 2019/953 (2019). https://eprint.iacr.org/2019/953

  35. Ghoshal, A., Tessaro, S.: Tight state-restoration soundness in the algebraic group model. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part III. LNCS, vol. 12827, pp. 64–93. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84252-9_3

    Chapter  Google Scholar 

  36. Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: 44th FOCS, pp. 102–115. IEEE Computer Society Press (2003). https://doi.org/10.1109/SFCS.2003.1238185

  37. Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: Delegating computation: interactive proofs for muggles. In: Ladner, R.E., Dwork, C. (eds.) 40th ACM STOC, pp. 113–122. ACM Press (2008). https://doi.org/10.1145/1374376.1374396

  38. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989). https://doi.org/10.1137/0218012

    Article  MathSciNet  Google Scholar 

  39. Haböck, U.: A summary on the FRI low degree test. Cryptology ePrint Archive, Report 2022/1216 (2022). https://eprint.iacr.org/2022/1216

  40. Holmgren, J., Lombardi, A.: Cryptographic hashing from strong one-way functions (or: one-way product functions and their applications). In: Thorup, M. (ed.) 59th FOCS, pp. 850–858. IEEE Computer Society Press (2018). https://doi.org/10.1109/FOCS.2018.00085

  41. Holmgren, J., Lombardi, A., Rothblum, R.D.: Fiat-Shamir via list-recoverable codes (or: parallel repetition of GMW is not zero-knowledge). In: Khuller, S., Williams, V.V. (eds.) 53rd ACM STOC, pp. 750–760. ACM Press (2021). https://doi.org/10.1145/3406325.3451116

  42. Kalai, Y.T., Rothblum, G.N., Rothblum, R.D.: From obfuscation to the security of Fiat-Shamir for proofs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part II. LNCS, vol. 10402, pp. 224–251. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_8

    Chapter  Google Scholar 

  43. Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_11

    Chapter  Google Scholar 

  44. Kattis, A.A., Panarin, K., Vlasov, A.: RedShift: transparent SNARKs from list polynomial commitments. In: Yin, H., Stavrou, A., Cremers, C., Shi, E. (eds.) ACM CCS 2022, pp. 1725–1737. ACM Press (2022). https://doi.org/10.1145/3548606.3560657

  45. Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: 24th ACM STOC, pp. 723–732. ACM Press (1992). https://doi.org/10.1145/129712.129782

  46. L2BEAT: L2BEAT total value locked. https://l2beat.com/scaling/tvl. Accessed 22 May 2023

  47. Lipton, R.J.: Fingerprinting sets. Princeton University, Department of Computer Science (1989)

    Google Scholar 

  48. Lipton, R.J.: Efficient checking of computations. In: Choffrut, C., Lengauer, T. (eds.) STACS 1990. LNCS, vol. 415, pp. 207–215. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52282-4_44

    Chapter  Google Scholar 

  49. Lund, C., Fortnow, L., Karloff, H.J., Nisan, N.: Algebraic methods for interactive proof systems. J. ACM 39(4), 859–868 (1992). https://doi.org/10.1145/146585.146605

    Article  MathSciNet  Google Scholar 

  50. Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: Zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 2111–2128. ACM Press (2019). https://doi.org/10.1145/3319535.3339817

  51. Matter Labs: zksync 2.0: Hello ethereum! https://blog.matter-labs.io/zksync-2-0-hello-ethereum-ca48588de179. Accessed 24 May 2023

  52. Merkle, R.: Secrecy, authentication, and public key systems (1979)

    Google Scholar 

  53. Micali, S.: CS proofs (extended abstracts). In: 35th FOCS, pp. 436–453. IEEE Computer Society Press (1994). https://doi.org/10.1109/SFCS.1994.365746

  54. Micali, S.: Computationally sound proofs. SIAM J. Comput. 30(4), 1253–1298 (2000). https://doi.org/10.1137/S0097539795284959

    Article  MathSciNet  Google Scholar 

  55. Mina: Mina book: Background on plonk. https://o1-labs.github.io/proof-systems/plonk/overview.html. Accessed 24 May 2023

  56. =nil; Foundation: Circuit definition library for =nil; foundation’s cryptography suite. https://github.com/NilFoundation/zkllvm-blueprint. Accessed 24 May 2023

  57. Pierrot, C., Wesolowski, B.: Malleability of the blockchain’s entropy. Cryptogr. Commun. 10(1), 211–233 (2018)

    Article  MathSciNet  Google Scholar 

  58. Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_33

    Chapter  Google Scholar 

  59. Polygon Labs: FRI verification procedures. https://wiki.polygon.technology/docs/miden/user_docs/stdlib/crypto/fri/. Accessed 23 May 2023

  60. Polygon Zero Team: Plonky2: Fast recursive arguments with plonk and FRI. https://github.com/mir-protocol/plonky2/tree/main/plonky2

  61. Rabin, M.O.: Transaction protection by beacons. J. Comput. Syst. Sci. 27(2), 256–267 (1983). https://doi.org/10.1016/0022-0000(83)90042-9

    Article  MathSciNet  Google Scholar 

  62. Reed, I.S., Solomon, G.: Polynomial codes over certain finite fields. J. Soc. Ind. Appl. Math. 8(2), 300–304 (1960). https://doi.org/10.1137/0108018

    Article  MathSciNet  Google Scholar 

  63. Ron-Zewi, N., Rothblum, R.D.: Local proofs approaching the witness length [extended abstract]. In: 61st FOCS, pp. 846–857. IEEE Computer Society Press (2020). https://doi.org/10.1109/FOCS46700.2020.00083

  64. Setty, S.: Spartan: efficient and general-purpose zkSNARKs without trusted setup. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part III. LNCS, vol. 12172, pp. 704–737. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56877-1_25

    Chapter  Google Scholar 

  65. StarkWare: ethstark documentation. Cryptology ePrint Archive, Paper 2021/582 (2021). https://eprint.iacr.org/2021/582

  66. StarkWare Industries: Starkex documentation: Customers and their deployment contract addresses. https://docs.starkware.co/starkex/deployments-addresses.html. Accessed 22 May 2023

  67. Succinct Labs: gnark-plonky2-verifier. https://github.com/succinctlabs/gnark-plonky2-verifier. Accessed 24 May 2023

  68. Team, R.Z.: RISC zero’s proof system for a zkVM (2023). https://github.com/risc0/risc0. github repository

  69. Thaler, J.: Time-optimal interactive proofs for circuit evaluation. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 71–89. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_5

    Chapter  Google Scholar 

  70. Thaler, J.: Proofs, arguments, and zero-knowledge (2022). https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.html

  71. Wahby, R.S., Tzialla, I., shelat, a., Thaler, J., Walfish, M.: Doubly-efficient zkSNARKs without trusted setup. In: 2018 IEEE Symposium on Security and Privacy, pp. 926–943. IEEE Computer Society Press (2018). https://doi.org/10.1109/SP.2018.00060

  72. Wikström, D.: Special soundness in the random oracle model. Cryptology ePrint Archive, Report 2021/1265 (2021). https://eprint.iacr.org/2021/1265

  73. Zhang, Y., Genkin, D., Katz, J., Papadopoulos, D., Papamanthou, C.: vRAM: faster verifiable ram with program-independent preprocessing. In: 2018 IEEE Symposium on Security and Privacy (SP), pp. 908–925. IEEE (2018)

    Google Scholar 

Download references

Acknowledgements

Alexander R. Block was supported by DARPA under Contract Nos. HR00112020022 and HR00112020025. Albert Garreta and Michał Zając were supported by Ethereum Foundation grant FY23-0885. Work of Jonathan Katz was supported by NSF award CNS-2154705 and by DARPA under Contract No. HR00112020025. Work of Justin Thaler was supported by NSF CAREER award CCF-1845125 and by DARPA under Contract No. HR00112020022. Pratyush Ranjan Tiwari was supported by NSF award CNS-1814919 and a Google Security and Privacy research award to Matthew Green. The views, opinions, findings, conclusions, and/or recommendations expressed in this material are those of the authors and should not be interpreted as reflecting the position or policy of DARPA or the United States Government, and no official endorsement should be inferred.

Author information

Authors and Affiliations

  1. Georgetown University, Washington, D.C., USA

    Alexander R. Block & Justin Thaler

  2. University of Maryland, College Park, USA

    Alexander R. Block & Jonathan Katz

  3. Nethermind, London, UK

    Albert Garreta & Michał Zając

  4. Johns Hopkins University, Baltimore, USA

    Pratyush Ranjan Tiwari

  5. A16z Crypto Research, Menlo Park, USA

    Justin Thaler

Authors
  1. Alexander R. Block
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Albert Garreta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jonathan Katz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Justin Thaler
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pratyush Ranjan Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Michał Zając
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander R. Block .

Editor information

Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

Rights and permissions

Reprints and permissions

Copyright information

© 2023 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Block, A.R., Garreta, A., Katz, J., Thaler, J., Tiwari, P.R., Zając, M. (2023). Fiat-Shamir Security of FRI and Related SNARKs. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14439. Springer, Singapore. https://doi.org/10.1007/978-981-99-8724-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-99-8724-5_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-8723-8

  • Online ISBN: 978-981-99-8724-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation