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Verifiable Zero-Knowledge Order Queries and Updates for Fully Dynamic Lists and Trees

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Security and Cryptography for Networks (SCN 2016)

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Abstract

We propose a three-party model for maintaining a dynamic data structure that supports verifiable and privacy-preserving (zero-knowledge) queries. We give efficient constructions supporting this model for order queries on data organized in lists, trees, and partially-ordered sets of bounded dimension.

Research supported in part by the U.S. National Science Foundation and by the Kanellakis Fellowship at Brown University.

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Notes

  1. 1.

    This is not a limiting constraint, as we can easily force this behavior by checking if a query/update is valid in the \(\mathsf {Real}\) game.

References

  1. Ahn, J.H., Boneh, D., Camenisch, J., Hohenberger, S., Waters, B.: Computing on authenticated data. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 1–20. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: new privacy definitions and constructions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 367–385. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, M., Zito, J.: Two simplified algorithms for maintaining order in a list. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 152–164. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, Eli (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Brzuska, C., et al.: Redactable signatures for tree-structured data: definitions and constructions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 87–104. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Catalano, D., Fiore, D.: Vector commitments and their applications. In: PKC (2013)

    Google Scholar 

  8. Catalano, D., Fiore, D., Messina, M.: Zero-knowledge sets with short proofs. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 433–450. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Chang, E.-C., Lim, C.L., Xu, J.: Short redactable signatures using random trees. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 133–147. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Devanbu, P.T., Gertz, M., Martel, C.U., Stubblebine, S.G.: Authentic third-party data publication. In: DBSec (2000)

    Google Scholar 

  12. Ghosh, E., Goodrich, M.T., Ohrimenko, O., Tamassia, R.: Fully-dynamic verifiable zero-knowledge order queries for network data. ePrint 2015/283 (2015)

    Google Scholar 

  13. Ghosh, E., Ohrimenko, O., Papadopoulos, D., Tamassia, R., Triandopoulos, N.: Zero-knowledge accumulators and set operations. ePrint 2015/404 (2015)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  16. Goldberg, S., Naor, M., Papadopoulos, D., Reyzin, L., Vasant, S., Ziv, A.: NSEC5: provably preventing DNSSEC zone enumeration. In: NDSS (2015)

    Google Scholar 

  17. Goldreich, O.: The Foundations of Cryptography - Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  18. Goodrich, M.T., Nguyen, D., Ohrimenko, O., Papamanthou, C., Tamassia, R., Triandopoulos, N., Lopes, C.V.: Efficient verification of web-content searching through authenticated web crawlers. PVLDB 5(10), 920–931 (2012)

    Google Scholar 

  19. Itai, A., Konheim, A.G., Rodeh, M.: A sparse table implementation of priority queues. In: Even, S., Kariv, O. (eds.) Automata, Languages and Programming. LNCS, vol. 115, pp. 417–431. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

  20. Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Kundu, A., Atallah, M.J., Bertino, E.: Leakage-free redactable signatures. In: CODASPY (2012)

    Google Scholar 

  22. Kundu, A., Bertino, E.: Structural signatures for tree data structures. In: PVLDB (2008)

    Google Scholar 

  23. Kundu, A., Bertino, E.: Privacy-preserving authentication of trees and graphs. Int. J. Inf. Secur. 12, 467–494 (2013)

    Article  Google Scholar 

  24. 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)

    Chapter  Google Scholar 

  25. Liskov, M.: Updatable zero-knowledge databases. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 174–198. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)

    Google Scholar 

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

    Google Scholar 

  28. Naor, M., Teague, V.: Anti-presistence: history independent data structures. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, 6–8 July 2001 (2001)

    Google Scholar 

  29. Naor, M., Ziv, A.: Primary-secondary-resolver membership proof systems. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 199–228. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  30. 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)

    Chapter  Google Scholar 

  31. Papadopoulos, D., Papamanthou, C., Tamassia, R., Triandopoulos, N.: Practical authenticated pattern matching with optimal proof size. PVLDB 8(7), 750–761 (2015)

    Google Scholar 

  32. Poehls, H.C., Samelin, K., Posegga, J., De Meer, H.: Length-hiding redactable signatures from one-way accumulators in \(O(n)\). Technical report MIP-1201, FIM. University of Passau (2012)

    Google Scholar 

  33. Pöhls, H.C., Samelin, K.: On updatable redactable signatures. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 457–475. Springer, Heidelberg (2014)

    Google Scholar 

  34. Prabhakaran, M., Xue, R.: Statistically hiding sets. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 100–116. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  35. Samelin, K., Pöhls, H.C., Bilzhause, A., Posegga, J., de Meer, H.: Redactable signatures for independent removal of structure and content. In: Ryan, M.D., Smyth, B., Wang, G. (eds.) ISPEC 2012. LNCS, vol. 7232, pp. 17–33. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  36. Steinfeld, R., Bull, L., Zheng, Y.: Content extraction signatures. In: Kim, K. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 285–304. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  37. Tamassia, R.: Authenticated data structures. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 2–5. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  38. Wang, Z.: Improvement on Ahn et al.’s RSA P-homomorphic signature scheme. In: Keromytis, A.D., Di Pietro, R. (eds.) SecureComm 2012. LNICST, vol. 106, pp. 19–28. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  39. Willard, D.E.: A density control algorithm for doing insertions and deletions in a sequentially ordered file in good worst-case time. Inf. Comput. 97, 150–204 (1992)

    Article  MATH  Google Scholar 

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Ghosh, E., Goodrich, M.T., Ohrimenko, O., Tamassia, R. (2016). Verifiable Zero-Knowledge Order Queries and Updates for Fully Dynamic Lists and Trees. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_12

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