Skip to main content
Springer Nature Link
Log in

Universal Vector Commitments

  • Conference paper
  • First Online:
Security and Cryptography for Networks (SCN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14973))

Included in the following conference series:

  • 210 Accesses

Abstract

We propose a new notion of vector commitment schemes with proofs of (non-)membership that we call universal vector commitments. We show how to build them directly from (i) Merkle commitments, and (ii) a universal accumulator and a plain vector commitment scheme. We also present a generic construction for universal accumulators over large domains from any vector commitment scheme, using cuckoo hashing. Leveraging the aforementioned generic constructions, we show that universal vector commitment schemes are implied by plain vector commitments and cuckoo hashing.

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.

    For soundness, we must also show that the leaves are stored in sorted order.

  2. 2.

    This induces a binary search tree over the interior nodes.

  3. 3.

    This checks that if the middle path is to the right of \({\textsf{node}} _{\cdot , \kappa }\), then the first path is comprised of nodes going rightward, the second path is comprised of nodes going leftward and the third path ends in a node to the immediate right of the middle node. This is similarly extended to the case when the middle path is to the left of \({\textsf{node}} _{\cdot , \kappa }\).

  4. 4.

    This checks whether the first path is comprised of nodes going rightward, and the second path is comprised of nodes going leftward.

References

  1. Agrawal, S., Raghuraman, S.: KVaC: key-value commitments for blockchains and beyond. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020, Part III. LNCS, vol. 12493, pp. 839–869. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_28

    Chapter  Google Scholar 

  2. Boneh, D., Bünz, B., Fisch, B.: Batching techniques for accumulators with applications to IOPs and stateless blockchains. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part I. LNCS, vol. 11692, pp. 561–586. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_20

    Chapter  Google Scholar 

  3. Baldimtsi, F., et al.: Accumulators with applications to anonymity-preserving revocation. In: 2017 IEEE European Symposium on Security and Privacy (EuroS &P), pp. 301–315 (2017)

    Google Scholar 

  4. 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 

  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. Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55–72. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_5

    Chapter  Google Scholar 

  7. Camenisch, J., Lysyanskaya, A.: Dynamic accumulators and application to efficient revocation of anonymous credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_5

    Chapter  Google Scholar 

  8. de Castro, L., Peikert, C.: Functional commitments for all functions, with transparent setup and from sis. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023, Part III. LNCS, vol. 14006, pp. 287–320. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-30620-4_10

    Chapter  Google Scholar 

  9. Dahlberg, R., Pulls, T., Peeters, R.: Efficient sparse Merkle trees. In: Brumley, B.B., Röning, J. (eds.) NordSec 2016. LNCS, vol. 10014, pp. 199–215. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47560-8_13

    Chapter  Google Scholar 

  10. Fisch, B.: Tight proofs of space and replication. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 324–348. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17656-3_12

    Chapter  Google Scholar 

  11. Fiore, D., Kolonelos, D., Perthuis, P.D.: Cuckoo commitments: registration-based encryption and key-value map commitments for large spaces. In: Guo, J., Steinfeld, R. (eds.) ASIACRYPT 2023. LNCS, vol. 14442, pp. 166–200. Springer, Singapore (2023). https://doi.org/10.1007/978-981-99-8733-7_6

    Chapter  Google Scholar 

  12. Goyal, R., Vusirikala, S.: Verifiable registration-based encryption. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part I. LNCS, vol. 12170, pp. 621–651. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56784-2_21

    Chapter  Google Scholar 

  13. Juels, A., Kaliski Jr., B.S.: Pors: proofs of retrievability for large files. In: Ning, P., De Capitani di Vimercati, S., Syverson, P.F. (eds.) ACM CCS 2007, Alexandria, Virginia, USA, pp. 584–597. ACM Press (2007)

    Google Scholar 

  14. Konstantopoulos, G.: Plasma cash: towards more efficient plasma constructions (2019)

    Google Scholar 

  15. Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based accumulators: logarithmic-size ring signatures and group signatures without trapdoors. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 1–31. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_1

    Chapter  Google Scholar 

  16. 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 

  17. Ling, S., Nguyen, K., Wang, H., Xu, Y.: Lattice-based group signatures: achieving full dynamicity with ease. In: Gollmann, D., Miyaji, A., Kikuchi, H. (eds.) ACNS 2017. LNCS, vol. 10355, pp. 293–312. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61204-1_15

    Chapter  Google Scholar 

  18. Rodler, F.F., Pagh, R.: Cuckoo hashing. J. Algorithms 51, 122–144 (2004)

    Article  MathSciNet  Google Scholar 

  19. Reyzin, L., Yakoubov, S.: Efficient asynchronous accumulators for distributed PKI. In: Zikas, V., De Prisco, R. (eds.) SCN 2016. LNCS, vol. 9841, pp. 292–309. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44618-9_16

    Chapter  Google Scholar 

  20. Schumm, D., Mukta, R., Paik, H.: Efficient credential revocation using cryptographic accumulators. In: 2023 IEEE International Conference on Decentralized Applications and Infrastructures (DAPPS), pp. 127–134 (2023)

    Google Scholar 

  21. Tomescu, A., Bhupatiraju, V., Papadopoulos, D., Papamanthou, C., Triandopoulos, N., Devadas, S.: Transparency logs via append-only authenticated dictionaries. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS 2019, London, UK, 11–15 November 2019, pp. 1299–1316. ACM (2019)

    Google Scholar 

  22. Yu, Z., Au, M.H., Yang, R., Lai, J., Xu, Q.: Lattice-based universal accumulator with nonmembership arguments. In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 502–519. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93638-3_29

    Chapter  Google Scholar 

  23. Yeo, K.: Cuckoo hashing in cryptography: optimal parameters, robustness and applications. In: Handschuh, H., Lysyanskaya, A. (eds.) CRYPTO 2023. LNCS, vol. 14084, pp. 197–230. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-38551-3_7

    Chapter  Google Scholar 

  24. Zhang, Y., Katz, J., Papamanthou, C.: An expressive (zero-knowledge) set accumulator. In: 2017 IEEE European Symposium on Security and Privacy, EuroS &P 2017, Paris, France, 26–28 April 2017, pp. 158–173. IEEE (2017)

    Google Scholar 

Download references

Acknowledgements

Foteini Baldimtsi and Aayush Yadav were supported by NSF #2143287 and #2247304. Aayush Yadav, Ojaswi Acharya and Dov Gordon were supported by NSF #1942575. Daniel McVicker and Dov Gordon were supported by NSF #1955264.

Author information

Authors and Affiliations

  1. University of Massachusetts Amherst, Amherst, USA

    Ojaswi Acharya

  2. George Mason University, Fairfax, USA

    Foteini Baldimtsi, Samuel Dov Gordon, Daniel McVicker & Aayush Yadav

Authors
  1. Ojaswi Acharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Foteini Baldimtsi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Samuel Dov Gordon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daniel McVicker
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Aayush Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aayush Yadav .

Editor information

Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. Télécom Paris, Paris, France

    Duong Hieu Phan

Rights and permissions

Reprints and permissions

Copyright information

© 2024 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

Acharya, O., Baldimtsi, F., Gordon, S.D., McVicker, D., Yadav, A. (2024). Universal Vector Commitments. In: Galdi, C., Phan, D.H. (eds) Security and Cryptography for Networks. SCN 2024. Lecture Notes in Computer Science, vol 14973. Springer, Cham. https://doi.org/10.1007/978-3-031-71070-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-71070-4_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-71069-8

  • Online ISBN: 978-3-031-71070-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics