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Updatable Trapdoor SPHFs: Modular Construction of Updatable Zero-Knowledge Arguments and More

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Information Security and Privacy (ACISP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13083))

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Abstract

Recently, motivated by its increased use in real-world applications, there has been a growing interest on the reduction of trust in the generation of the common reference string (CRS) for zero-knowledge (ZK) proofs. This line of research was initiated by the introduction of subversion non-interactive ZK (NIZK) proofs by Bellare et al. (ASIACRYPT’16). Here, the zero-knowledge property needs to hold even in case of a malicious generation of the CRS. Groth et al. (CRYPTO’18) then introduced the notion of updatable zk-SNARKS, later adopted by Lipmaa (SCN’20) to updatable quasi-adaptive NIZK (QA-NIZK) proofs. In contrast to the subversion setting, in the updatable setting one can achieve stronger soundness guarantees at the cost of reintroducing some trust, resulting in a model in between the fully trusted CRS generation and the subversion setting. It is a promising concept, but all previous updatable constructions are ad-hoc and tailored to particular instances of proof systems. Consequently, it is an interesting question whether it is possible to construct updatable ZK primitives in a more modular way from simpler building blocks.

In this work we revisit the notion of trapdoor smooth projective hash functions (TSPHFs) in the light of an updatable CRS. TSPHFs have been introduced by Benhamouda et al. (CRYPTO’13) and can be seen as a special type of a 2-round ZK proof system. In doing so, we first present a framework called lighter TSPHFs (L-TSPHFs). Building upon it, we introduce updatable L-TSPHFs as well as instantiations in bilinear groups. We then show how one can generically construct updatable quasi-adaptive zero-knowledge arguments from updatable L-TSPHFs. Our instantiations are generic and more efficient than existing ones. Finally, we discuss applications of (updatable) L-TSPHFs to efficient (updatable) 2-round ZK arguments as well as updatable password-authenticated key-exchange (uPAKE).

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Notes

  1. 1.

    HAK is essentially a concrete Algebraic Group Model (AGM) [24] version of the generic group model with hashing that models the ability of an adversary to create elliptic-curve group elements by using elliptic-curve hashing without knowing their discrete logarithm.

  2. 2.

    We note that all ZK arguments we consider in this paper are in the quasi-adaptive setting and we might sometimes omit to make this explicit.

  3. 3.

    We note that in the SPHF/TSPHF and their applications in zero-knowledge proofs, one wants to simulate a proof without knowing the trapdoor \(\mathbf {\Gamma }\) of the base elements of the statement to be proven.

References

  1. Abdalla, M., Benhamouda, F., Pointcheval, D.: Disjunctions for hash proof systems: new constructions and applications. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 69–100. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_3

    Chapter  Google Scholar 

  2. Abdalla, M., Chevalier, C., Pointcheval, D.: Smooth projective hashing for conditionally extractable commitments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 671–689. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_39

    Chapter  Google Scholar 

  3. Abdolmaleki, B., Baghery, K., Lipmaa, H., Siim, J., Zajac, M.: UC-secure CRS generation for SNARKs. In: Buchmann, J., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2019. LNCS, vol. 11627, pp. 99–117. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-23696-0_6

  4. Abdolmaleki, B., Baghery, K., Lipmaa, H., Zajac, M.: A subversion-resistant SNARK. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 3–33. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_1

  5. Abdolmaleki, B., Khoshakhlagh, H., Lipmaa, H.: Smooth zero-knowledge hash functions. Cryptology ePrint Archive, Report 2021/653. https://eprint.iacr.org/2021/653

  6. Abdolmaleki, B., Lipmaa, H., Siim, J., Zajac, M.: On QA-NIZK in the BPK model. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part I. LNCS, vol. 12110, pp. 590–620. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_20

  7. Abdolmaleki, B., Ramacher, S., Slamanig, D.: Lift-and-shift: obtaining simulation extractable subversion and updatable SNARKs generically. In: ACM CCS (2020)

    Google Scholar 

  8. Abe, M., Jutla, C.S., Ohkubo, M., Roy, A.: Improved (almost) tightly-secure simulation-sound QA-NIZK with applications. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part I. LNCS, vol. 11272, pp. 627–656. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03326-2_21

    Chapter  Google Scholar 

  9. Bellare, M., Fuchsbauer, G., Scafuro, A.: NIZKs with an untrusted CRS: security in the face of parameter subversion. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 777–804. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_26

    Chapter  MATH  Google Scholar 

  10. Ben Hamouda-Guichoux, F.: Diverse modules and zero-knowledge. Ph.D. thesis, École Normale Supérieure, Paris, France

    Google Scholar 

  11. Ben-Sasson, E., Chiesa, A., Green, M., Tromer, E., Virza, M.: Secure sampling of public parameters for succinct zero knowledge proofs. In: 2015 IEEE Symposium on Security and Privacy. IEEE (2015)

    Google Scholar 

  12. Benhamouda, F., Blazy, O., Chevalier, C., Pointcheval, D., Vergnaud, D.: New Techniques for SPHFs and Efficient One-Round PAKE Protocols. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8042, pp. 449–475. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_25

    Chapter  Google Scholar 

  13. Benhamouda, F., Blazy, O., Chevalier, C., Pointcheval, D., Vergnaud, D.: New techniques for SPHFs and efficient one-round PAKE protocols. Cryptology ePrint Archive, Report 2015/188. http://eprint.iacr.org/2015/188

  14. Benhamouda, F., Pointcheval, D.: Trapdoor smooth projective hash functions. Cryptology ePrint Archive, Report 2013/341. http://eprint.iacr.org/2013/341

  15. Bowe, S., Gabizon, A., Green, M.D.: A multi-party protocol for constructing the public parameters of the pinocchio zk-snark. Cryptology ePrint Archive, Report 2017/602. https://eprint.iacr.org/2017/602

  16. Campanelli, M., Fiore, D., Querol, A.: LegoSNARK: modular design and composition of succinct zero-knowledge proofs. In: ACM CCS (2019)

    Google Scholar 

  17. Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.: Marlin: preprocessing zkSNARKs with universal and updatable SRS. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 738–768. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_26

    Chapter  Google Scholar 

  18. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  19. Damgård, I.: Towards practical public key systems secure against chosen ciphertext attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445–456. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_36

    Chapter  Google Scholar 

  20. Danezis, G., Fournet, C., Groth, J., Kohlweiss, M.: Square Span Programs with Applications to Succinct NIZK Arguments. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part I. LNCS, vol. 8873, pp. 532–550. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_28

    Chapter  Google Scholar 

  21. Daza, V., Ràfols, C., Zacharakis, A.: Updateable inner product argument with logarithmic verifier and applications. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part I. LNCS, vol. 12110, pp. 527–557. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_18

    Chapter  Google Scholar 

  22. Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for diffie-hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_8

    Chapter  Google Scholar 

  23. Fuchsbauer, G.: Subversion-zero-knowledge SNARKs. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part I. LNCS, vol. 10769, pp. 315–347. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_11

    Chapter  Google Scholar 

  24. Fuchsbauer, G., Kiltz, E., Loss, J.: The Algebraic Group Model and its Applications. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part II. LNCS, vol. 10992, pp. 33–62. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_2

    Chapter  Google Scholar 

  25. Gennaro, R., Gentry, C., Parno, B., Raykova, M.: Quadratic span programs and succinct NIZKs without PCPs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 626–645. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_37

    Chapter  Google Scholar 

  26. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18, 186–208 (1989)

    Article  MathSciNet  Google Scholar 

  27. Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_19

    Chapter  Google Scholar 

  28. Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_11

    Chapter  Google Scholar 

  29. Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to zk-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 698–728. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_24

    Chapter  Google Scholar 

  30. Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_21

    Chapter  Google Scholar 

  31. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24

    Chapter  Google Scholar 

  32. Jutla, C.S., Roy, A.: Shorter quasi-adaptive NIZK proofs for linear subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 1–20. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42033-7_1

    Chapter  Google Scholar 

  33. Jutla, C.S., Roy, A.: Switching lemma for bilinear tests and constant-size NIZK proofs for linear subspaces. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 295–312. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_17

    Chapter  Google Scholar 

  34. Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: 24th ACM STOC (1992)

    Google Scholar 

  35. Kiltz, E., Wee, H.: Quasi-adaptive NIZK for linear subspaces revisited. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 101–128. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_4

    Chapter  Google Scholar 

  36. Libert, B., Peters, T., Joye, M., Yung, M.: Non-malleability from malleability: simulation-sound quasi-adaptive NIZK proofs and CCA2-secure encryption from homomorphic signatures. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 514–532. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_29

    Chapter  Google Scholar 

  37. Libert, B., Peters, T., Joye, M., Yung, M.: Compactly hiding linear spans. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015, Part I. LNCS, vol. 9452, pp. 681–707. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_28

    Chapter  Google Scholar 

  38. Lipmaa, H.: Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments. In: TCC (2012)

    Google Scholar 

  39. Lipmaa, H.: Simulation-extractable snarks revisited. Cryptology ePrint Archive, Report 2019/612. https://eprint.iacr.org/2019/612

  40. Lipmaa, H.: Key-and-argument-updatable QA-NIZKs. In: SCN (2020)

    Google Scholar 

  41. Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: Zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: ACM CCS (2019)

    Google Scholar 

  42. Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7

    Chapter  Google Scholar 

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Acknowledgements

This work received funding from European Union’s Horizon 2020 ECSEL Joint Undertaking project under grant agreement  783119 (Secredas), from the European Union’s Horizon 2020 research and innovation programme under grant agreement 871473 (Kraken) and by the Austrian Science Fund (FWF) and netidee SCIENCE under grant agreement P31621-N38 (Profet).

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Authors and Affiliations

  1. Max Planck Institute for Security and Privacy, Bochum, Germany

    Behzad Abdolmaleki

  2. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

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Correspondence to Behzad Abdolmaleki .

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  1. University of Wollongong, Wollongong, NSW, Australia

    Joonsang Baek

  2. Data61, CSIRO, Marsfield, NSW, Australia

    Sushmita Ruj

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Abdolmaleki, B., Slamanig, D. (2021). Updatable Trapdoor SPHFs: Modular Construction of Updatable Zero-Knowledge Arguments and More. In: Baek, J., Ruj, S. (eds) Information Security and Privacy. ACISP 2021. Lecture Notes in Computer Science(), vol 13083. Springer, Cham. https://doi.org/10.1007/978-3-030-90567-5_3

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