Advertisement

Secure Database Commitments and Universal Arguments of Quasi Knowledge

  • Melissa ChaseEmail author
  • Ivan Visconti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)

Abstract

In this work we focus on a simple database commitment functionality where besides the standard security properties, one would like to hide the size of the input of the sender. Hiding the size of the input of a player is a critical requirement in some applications, and relatively few works have considered it. Notable exceptions are the work on zero-knowledge sets introduced in [14], and recent work on size-hiding private set intersection [1]. However, neither of these achieves a secure computation (i.e., a reduction of a real-world attack of a malicious adversary into an ideal-world attack) of the proposed functionality.

The first result of this submission consists in defining “secure” database commitment and in observing that previous constructions do not satisfy this definition. This leaves open the question of whether there is any way this functionality can be achieved.

We then provide an affirmative answer to this question by using new techniques that combined together achieve “secure” database commitment. Our construction is in particular optimized to require only a constant number of rounds, to provide non-interactive proofs on the content of the database, and to rely on the existence of a family of CRHFs. This is the first result where input-size hiding secure computation is achieved for an interesting functionality and moreover we obtain this result with standard security (i.e., simulation in expected polynomial time against fully malicious adversaries, without random oracles, without non-black-box extraction assumptions, without hardness assumptions against super-polynomial time adversaries).

A key building block in our construction is a universal argument enjoying an improved proof of knowledge property, that we call quasi-knowledge. This property is significantly closer to the standard proof of knowledge property than the weak proof of knowledge property satisfied by previous constructions.

Keywords

ZK sets universal arguments input-size hiding security 

References

  1. 1.
    Ateniese, G., De Cristofaro, E., Tsudik, G.: (If) Size Matters: Size-Hiding Private Set Intersection. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 156–173. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Barak, B.: How to Go Beyond the Black-Box Simulation Barrier. In: FOCS 2001, pp. 106–115. IEEE Computer Society Press (2001)Google Scholar
  3. 3.
    Barak, B.: Non-Black-Box Techniques in Cryptography, Ph.D. Thesis. Weizmann Institute of Science (2004)Google Scholar
  4. 4.
    Barak, B., Goldreich, O.: Universal Arguments and Their Applications. In: CCC 2002. IEEE Computer Society Press (2002)Google Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Goldreich, O.: Foundations of Cryptography - Volume II - Basic Applications. Cambridge Press (2004)Google Scholar
  10. 10.
    Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game - A Completeness Theorem for Protocols with Honest Majority. In: STOC 1987, pp. 218–229 (1987)Google Scholar
  11. 11.
    Hada, S., Tanaka, T.: On the Existence of 3-Round Zero-Knowledge Protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Ishai, Y., Paskin, A.: Evaluating Branching Programs on Encrypted Data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Micali, S., Rabin, M., Kilian, J.: Zero-knowledge sets. In: FOCS 2003, pp. 80–91 (2003)Google Scholar
  15. 15.
    Prabhakaran, M., Xue, R.: Statistically Hiding Sets. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 100–116. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Dipartimento di InformaticaUniversity of SalernoFiscianoItaly

Personalised recommendations