Skip to main content

Zero-Knowledge Elementary Databases with More Expressive Queries

  • Conference paper
  • First Online:
Public-Key Cryptography – PKC 2019 (PKC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11442))

Included in the following conference series:

Abstract

Zero-knowledge elementary databases (ZK-EDBs) are cryptographic schemes that allow a prover to commit to a set \(\mathsf {D}\) of key-value pairs so as to be able to prove statements such as “x belongs to the support of \(\mathsf {D}\) and \(\mathsf {D}(x)=y\)” or “x is not in the support of \(\mathsf {D}\)”. Importantly, proofs should leak no information beyond the proven statement and even the size of \(\mathsf {D}\) should remain private. Chase et al. (Eurocrypt’05) showed that ZK-EDBs are implied by a special flavor of non-interactive commitment, called mercurial commitment, which enables efficient instantiations based on standard number theoretic assumptions. On the other hand, the resulting ZK-EDBs are only known to support proofs for simple statements like (non-)membership and value assignments. In this paper, we show that mercurial commitments actually enable significantly richer queries. We show that, modulo an additional security property met by all known efficient constructions, they actually enable range queries over keys and values – even for ranges of super-polynomial size – as well as membership/non-membership queries over the space of values. Beyond that, we exploit the range queries to realize richer queries such as \(k\)-nearest neighbors and revealing the \(k\) smallest or largest records within a given range. In addition, we provide a new realization of trapdoor mercurial commitment from standard lattice assumptions, thus obtaining the most expressive quantum-safe ZK-EDB construction so far.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

Similar content being viewed by others

References

  1. Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: STOC, pp. 103–112. ACM (1988)

    Google Scholar 

  2. Catalano, D., Dodis, Y., Visconti, I.: Mercurial commitments: minimal assumptions and efficient constructions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 120–144. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_7

    Chapter  Google Scholar 

  3. 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 

  4. Catalano, D., Fiore, D., Messina, M.: Zero-knowledge sets with short proofs. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 433–450. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_25

    Chapter  Google Scholar 

  5. Chase, M., Healy, A., Lysyanskaya, A., Malkin, T., Reyzin, L.: Mercurial commitments with applications to zero-knowledge sets. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 422–439. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_25

    Chapter  Google Scholar 

  6. Chase, M., Healy, A., Lysyanskaya, A., Malkin, T., Reyzin, L.: Mercurial commitments with applications to zero-knowledge sets. J. Cryptology 26(2), 251–279 (2013)

    Article  MathSciNet  Google Scholar 

  7. Chase, M., Visconti, I.: Secure database commitments and universal arguments of quasi knowledge. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 236–254. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_15

    Chapter  Google Scholar 

  8. Ducas, L., Micciancio, D.: Improved short lattice signatures in the standard model. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 335–352. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_19

    Chapter  MATH  Google Scholar 

  9. Gennaro, R., Micali, S.: Independent zero-knowledge sets. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 34–45. Springer, Heidelberg (2006). https://doi.org/10.1007/11787006_4

    Chapter  Google Scholar 

  10. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008 (2008)

    Google Scholar 

  11. Ghosh, E., Ohrimenko, O., Tamassia, R.: Verifiable order queries and order statistics on a list in zero-knowledge. In: ACNS (2015)

    Google Scholar 

  12. Ghosh, E., Ohrimenko, O., Tamassia, R.: Efficient verifiable range and closest point queries in zero-knowledge. PoPETs 2016(4), 373–388 (2016)

    Google Scholar 

  13. Goyal, V., Ostrovsky, R., Scafuro, A., Visconti, I.: Black-box non-black-box zero knowledge. In: STOC (2014)

    Google Scholar 

  14. Ishai, Y., Kushilevitz, E., Ostrovksy, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: STOC (2007)

    Google Scholar 

  15. 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 

  16. Kawachi, A., Tanaka, K., Xagawa, K.: Concurrently secure identification schemes based on the worst-case hardness of lattice problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 372–389. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_23

    Chapter  Google Scholar 

  17. Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 499–517. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_30

    Chapter  Google Scholar 

  18. Liskov, M.: Updatable zero-knowledge databases. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 174–198. Springer, Heidelberg (2005). https://doi.org/10.1007/11593447_10

    Chapter  Google Scholar 

  19. Lyubashevsky, V.: Fiat-shamir with aborts: applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598–616. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_35

    Chapter  Google Scholar 

  20. Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_21

    Chapter  Google Scholar 

  21. Micali, S., Rabin, M.O., Kilian, J.: Zero-knowledge sets. In: 44th FOCS (2003)

    Google Scholar 

  22. Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41

    Chapter  Google Scholar 

  23. Micciancio, D., Peikert, C.: Hardness of SIS and LWE with small parameters. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 21–39. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_2

    Chapter  Google Scholar 

  24. Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)

    Article  MathSciNet  Google Scholar 

  25. Naor, D., Naor, M., Lotspiech, J.: Revocation and tracing schemes for stateless receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_3

    Chapter  Google Scholar 

  26. Naor, M., Nissim, K.: Certificate revocation and certificate update. In: 7th USENIX Security Symposium (1998)

    Google Scholar 

  27. Naor, M., Ziv, A.: Primary-secondary-resolver membership proof systems. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 199–228. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_8

    Chapter  Google Scholar 

  28. Ostrovsky, R., Rackoff, C., Smith, A.: Efficient consistency proofs for generalized queries on a committed database. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1041–1053. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27836-8_87

    Chapter  Google Scholar 

  29. Papadopoulos, D., Papadopoulos, S., Triandopoulos, N.: Taking authenticated range queries to arbitrary dimensions. In: ACM-CCS (2014)

    Google Scholar 

  30. Papamanthou, C., Tamassia, R., Triandopoulos, N.: Optimal verification of operations on dynamic sets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 91–110. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_6

    Chapter  Google Scholar 

  31. Prabhakaran, M., Xue, R.: Statistically hiding sets. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 100–116. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00862-7_7

    Chapter  Google Scholar 

  32. Tamassia, R.: Authenticated data structures. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 2–5. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39658-1_2

    Chapter  Google Scholar 

Download references

Acknowledgements

Part of this research was funded by Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S). Another part was funded by BPI-France in the context of the national project RISQ (P141580). This work was also supported in part by the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701). Khoa Nguyen was also supported by the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2018. Huaxiong Wang was also supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Strategic Capability Research Centres Funding Initiative.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Benjamin Hong Meng Tan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Libert, B., Nguyen, K., Tan, B.H.M., Wang, H. (2019). Zero-Knowledge Elementary Databases with More Expressive Queries. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11442. Springer, Cham. https://doi.org/10.1007/978-3-030-17253-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-17253-4_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17252-7

  • Online ISBN: 978-3-030-17253-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics