Skip to main content
Springer Nature Link
Log in

Set (Non-)Membership NIZKs from Determinantal Accumulators

  • Conference paper
  • First Online:
Progress in Cryptology – LATINCRYPT 2023 (LATINCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14168))

Abstract

We construct a falsifiable set (non-)membership NIZK \(\mathbf {\Pi ^*}\) that is considerably more efficient than known falsifiable set (non-)membership NIZKs. It also has a universal CRS. \(\mathbf {\Pi ^*}\) is based on the novel concept of determinantal accumulators. Determinantal primitives have a similar relation to recent pairing-based (non-succinct) NIZKs of Couteau and Hartmann (Crypto 2020) and Couteau et al. (CLPØ, Asiacrypt 2021) that structure-preserving primitives have to the Groth-Sahai NIZK. We also extend CLPØ by proposing efficient (non-succinct) set non-membership arguments for a large class of languages.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    We follow the literature by using “universal” both in universal accumulators (have a non-membership argument) and universal CRS (does not depend on the language).

  2. 2.

    We use the standard additive bracket notation for pairing-based setting. For example, \([\chi ]_{1} = \chi [1]_{1}\), where \([1]_{1}\) is a generator of \(\mathbb {G}_{1}\).

  3. 3.

    In our new primitives, the set consists of only one polyomial. However, the framework is valid in the more general case.

  4. 4.

    In the collision-resistance proof of \(\textsf{ACC}_{\textsf{Nguyen}}\), \(\chi \) and \(\textsf{r}\) are given as integers and thus do not depend on \(\sigma \). Such a problem did also not exist in [13, 14] since there the CRS only contained a single element \([\textsf{e}]_{2}\) and thus did not depend on \(\sigma \).

References

  1. Abdolmaleki, B., Lipmaa, H., Siim, J., Zając, 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

    Chapter  Google Scholar 

  2. Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. J. Cryptol. 29(2), 363–421 (2015). https://doi.org/10.1007/s00145-014-9196-7

    Article  MathSciNet  Google Scholar 

  3. Acar, T., Nguyen, L.: Revocation for delegatable anonymous credentials. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 423–440. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_26

    Chapter  Google Scholar 

  4. Au, M.H., Tsang, P.P., Susilo, W., Mu, Y.: Dynamic universal accumulators for DDH groups and their application to attribute-based anonymous credential systems. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 295–308. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00862-7_20

    Chapter  Google Scholar 

  5. Barić, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_33

    Chapter  Google Scholar 

  6. Belenkiy, M., Chase, M., Kohlweiss, M., Lysyanskaya, A.: P-signatures and noninteractive anonymous credentials. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 356–374. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_20

    Chapter  Google Scholar 

  7. Benaloh, J., de Mare, M.: One-way accumulators: a decentralized alternative to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_24

    Chapter  Google Scholar 

  8. Blazy, O., Bultel, X., Lafourcade, P., Kempner, O.P.: Generic plaintext equality and inequality proofs. In: Borisov, N., Diaz, C. (eds.) FC 2021. LNCS, vol. 12674, pp. 415–435. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64322-8_20

    Chapter  Google Scholar 

  9. Blazy, O., Chevalier, C., Vergnaud, D.: Non-interactive zero-knowledge proofs of non-membership. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 145–164. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16715-2_8

    Chapter  Google Scholar 

  10. Blazy, O., Derler, D., Slamanig, D., Spreitzer, R.: Non-interactive plaintext (in-)equality proofs and group signatures with verifiable controllable linkability. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 127–143. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29485-8_8

    Chapter  Google Scholar 

  11. Buldas, A., Laud, P., Lipmaa, H.: Accountable certificate management using undeniable attestations. In: Gritzalis, D., Jajodia, S., Samarati, P. (eds.) ACM CCS 2000, pp. 9–17. ACM Press (2000). https://doi.org/10.1145/352600.352604

  12. Buldas, A., Laud, P., Lipmaa, H.: Eliminating counterevidence with applications to accountable certificate management. J. Comput. Secur. 10(3), 273–296 (2002)

    Article  Google Scholar 

  13. Couteau, G., Hartmann, D.: Shorter non-interactive zero-knowledge arguments and ZAPs for algebraic languages. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part III. LNCS, vol. 12172, pp. 768–798. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56877-1_27

    Chapter  Google Scholar 

  14. Couteau, G., Lipmaa, H., Parisella, R., Ødegaard, A.T.: Efficient NIZKs for algebraic sets. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021, Part III. LNCS, vol. 13092, pp. 128–158. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92078-4_5

    Chapter  Google Scholar 

  15. Damgård, I., Triandopoulos, N.: Supporting non-membership proofs with bilinear-map accumulators. Cryptology ePrint Archive, Report 2008/538 (2008). https://eprint.iacr.org/2008/538

  16. Daza, V., González, A., Pindado, Z., Ràfols, C., Silva, J.: Shorter quadratic QA-NIZK proofs. In: Lin, D., Sako, K. (eds.) PKC 2019, Part I. LNCS, vol. 11442, pp. 314–343. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17253-4_11

    Chapter  Google Scholar 

  17. 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 

  18. Li, J., Li, N., Xue, R.: Universal accumulators with efficient nonmembership proofs. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 253–269. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72738-5_17

    Chapter  Google Scholar 

  19. Lipmaa, H.: Secure accumulators from euclidean rings without trusted setup. In: Bao, F., Samarati, P., Zhou, J. (eds.) ACNS 2012. LNCS, vol. 7341, pp. 224–240. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31284-7_14

    Chapter  Google Scholar 

  20. Lipmaa, H., Parisella, R.: Set (non-)membership NIZKs from determinantal accumulators. Cryptology ePrint Archive, Report 2022/1570 (2022). https://eprint.iacr.org/2022/1570

  21. Nguyen, L.: Accumulators from bilinear pairings and applications. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 275–292. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30574-3_19

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Simula UiB, Bergen, Norway

    Helger Lipmaa & Roberto Parisella

Authors
  1. Helger Lipmaa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Parisella
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberto Parisella .

Editor information

Editors and Affiliations

  1. Technology Innovation Institute, Abu Dhabi, United Arab Emirates

    Abdelrahaman Aly

  2. NTT Social Informatics Laboratories, Tokyo, Japan

    Mehdi Tibouchi

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lipmaa, H., Parisella, R. (2023). Set (Non-)Membership NIZKs from Determinantal Accumulators. In: Aly, A., Tibouchi, M. (eds) Progress in Cryptology – LATINCRYPT 2023. LATINCRYPT 2023. Lecture Notes in Computer Science, vol 14168. Springer, Cham. https://doi.org/10.1007/978-3-031-44469-2_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-44469-2_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-44468-5

  • Online ISBN: 978-3-031-44469-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics