Journal of Cryptology

, Volume 26, Issue 2, pp 251–279 | Cite as

Mercurial Commitments with Applications to Zero-Knowledge Sets

  • Melissa Chase
  • Alexander Healy
  • Anna Lysyanskaya
  • Tal Malkin
  • Leonid Reyzin
Article

Abstract

We introduce a new flavor of commitment schemes, which we call mercurial commitments. Informally, mercurial commitments are standard commitments that have been extended to allow for soft decommitment. Soft decommitments, on the one hand, are not binding but, on the other hand, cannot be in conflict with true decommitments.

We then demonstrate that a particular instantiation of mercurial commitments has been implicitly used by Micali, Rabin and Kilian to construct zero-knowledge sets. (A zero-knowledge set scheme allows a Prover to (1) commit to a set S in a way that reveals nothing about S and (2) prove to a Verifier, in zero-knowledge, statements of the form xS and xS.) The rather complicated construction of Micali et al. becomes easy to understand when viewed as a more general construction with mercurial commitments as an underlying building block.

By providing mercurial commitments based on various assumptions, we obtain several different new zero-knowledge set constructions.

Key words

Commitments Zero-knowledge sets Database privacy Verifiable queries Outsourced databases 

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References

  1. [1]
    M. Bellare, M. Yung, Certifying permutations: non-interactive zero-knowledge based on any trapdoor permutation. J. Cryptol. 9(3), 149–166 (1996) MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    M. Blum, A. De Santis, S. Micali, G. Persiano, Non-interactive zero-knowledge. SIAM J. Comput. 20(6), 1084–1118 (1991) MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    G. Brassard, D. Chaum, C. Crépeau, Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988) MATHCrossRefGoogle Scholar
  4. [4]
    D. Catalano, Y. Dodis, I. Visconti, Mercurial commitments: minimal assumptions and efficient constructions, in Third Theory of Cryptography Conference, TCC 2006, ed. by S. Halevi, T. Rabin. Lecture Notes in Computer Science, vol. 3876 (Springer, Berlin, 2006), pp. 120–144 Google Scholar
  5. [5]
    D. Catalano, D. Fiore, M. Messina, Zero-knowledge sets with short proofs, in Advances in Cryptology—EUROCRYPT 2008, ed. by N.P. Smart. Lecture Notes in Computer Science, vol. 4965 (Springer, Berlin, 2008), pp. 433–450 CrossRefGoogle Scholar
  6. [6]
    M. Chase, A. Healy, A. Lysyanskaya, T. Malkin, L. Reyzin, Mercurial commitments with applications to zero-knowledge sets, in Advances in Cryptology—EUROCRYPT 2005, ed. by R. Cramer. Lecture Notes in Computer Science, vol. 3494 (Springer, Berlin, 2005), pp. 422–439 CrossRefGoogle Scholar
  7. [7]
    U. Feige, D. Lapidot, A. Shamir, Multiple noninteractive zero knowledge proofs under general assumptions. SIAM J. Comput. 29(1), 1–28 (1999) MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    M. Fischlin, Trapdoor commitment schemes and their applications. PhD thesis, University of Frankfurt am Main, December 2001 Google Scholar
  9. [9]
    M. Fischlin, R. Fischlin, The representation problem based on factoring, in RSA Security 2002 Cryptographer’s Track. Lecture Notes in Computer Science, vol. 2271 (Springer, Berlin, 2002) Google Scholar
  10. [10]
    R. Gennaro, S. Micali, Independent zero-knowledge sets, in 33rd International Colloquium on Automata, Languages and Programming (ICALP) (2006) Google Scholar
  11. [11]
    S. Goldwasser, R. Ostrovsky, Invariant signatures and non-interactive zero-knowledge proofs are equivalent, in Advances in Cryptology—CRYPTO’92, ed. by E.F. Brickell. Lecture Notes in Computer Science, vol. 740 (Springer, Berlin, 1992), pp. 228–244 Google Scholar
  12. [12]
    S. Goldwasser, S. Micali, R. Rivest, A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988) MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    J. Håstad, R. Impagliazzo, L.A. Levin, M. Luby, A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999) MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    C.H. Lim, P.J. Lee, More flexible exponentiation with precomputation, in Advances in Cryptology—CRYPTO’94, 21–25 August, ed. by Y.G. Desmedt. Lecture Notes in Computer Science, vol. 839 (Springer, Berlin, 1994), pp. 95–107 Google Scholar
  15. [15]
    M. Liskov, Updatable zero-knowledge databases, in Advances in Cryptology—ASIACRYPT 2005. Lecture Notes in Computer Science, vol. 3788 (Springer, Berlin, 2005), pp. 174–198 CrossRefGoogle Scholar
  16. [16]
    A. Lysyanskaya, Unique signatures and verifiable random functions from the DH-DDH separation, in Advances in Cryptology—CRYPTO 2002, ed. by M. Yung. Lecture Notes in Computer Science (Springer, Berlin, 2002), pp. 597–612 CrossRefGoogle Scholar
  17. [17]
    A. Lysyanskaya, Signature schemes and applications to cryptographic protocol design. PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, September 2002 Google Scholar
  18. [18]
    S. Micali, 6.875: Introduction to Cryptography. MIT course taught in Fall 1997 Google Scholar
  19. [19]
    S. Micali, M. Rabin, S. Vadhan, Verifiable random functions, in Proc. 40th IEEE Symposium on Foundations of Computer Science (FOCS) (IEEE Computer Society Press, Los Alamitos, 1999), pp. 120–130 Google Scholar
  20. [20]
    S. Micali, M. Rabin, J. Kilian, Zero-knowledge sets, in Proc. 44th IEEE Symposium on Foundations of Computer Science (FOCS) (IEEE Computer Society Press, Los Alamitos, 2003), pp. 80–91 Google Scholar
  21. [21]
    M. Naor, Bit commitment using pseudorandomness. J. Cryptol. 4(2), 51–158 (1991) CrossRefGoogle Scholar
  22. [22]
    R. Ostrovsky, C. Rackoff, A. Smith, Efficient consistency proof on a committed database, in Automata, Languages and Programming: 31st International Colloquium, ICALP 2004, Turku, Finland, July 12–16, 2004. Lecture Notes in Computer Science, vol. 3142 (Springer, Berlin, 2004), pp. 1041–1053 CrossRefGoogle Scholar
  23. [23]
    T.P. Pedersen, Non-interactive and information-theoretic secure verifiable secret sharing, in Advances in Cryptology—CRYPTO’91, ed. by J. Feigenbaum. Lecture Notes in Computer Science, vol. 576 (Springer, Berlin, 1992), pp. 129–140 Google Scholar
  24. [24]
    M. Prabhakaran, R. Xue, Statistically hiding sets. Cryptology ePrint Archive, Report 2007/349, 2007. http://eprint.iacr.org/

Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Melissa Chase
    • 1
  • Alexander Healy
    • 2
  • Anna Lysyanskaya
    • 3
  • Tal Malkin
    • 4
  • Leonid Reyzin
    • 5
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Division of Engineering and Applied SciencesHarvard UniversityCambridgeUSA
  3. 3.Department of Computer ScienceBrown UniversityProvidenceUSA
  4. 4.Department of Computer ScienceColumbia UniversityNew YorkUSA
  5. 5.Department of Computer ScienceBoston UniversityBostonUSA

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