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Mercurial Commitments with Applications to Zero-Knowledge Sets

Journal of Cryptology volume 26, pages 251–279 (2013)Cite this 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 x∈S and x∉S.) 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.

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Author information

Authors and Affiliations

  1. Microsoft Research, Redmond, WA, 98052, USA

    Melissa Chase

  2. Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Alexander Healy

  3. Department of Computer Science, Brown University, Providence, RI, 02912, USA

    Anna Lysyanskaya

  4. Department of Computer Science, Columbia University, New York, NY, 10027, USA

    Tal Malkin

  5. Department of Computer Science, Boston University, Boston, MA, 02215, USA

    Leonid Reyzin

Authors
  1. Melissa Chase
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  2. Alexander Healy
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  3. Anna Lysyanskaya
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  4. Tal Malkin
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  5. Leonid Reyzin
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Corresponding author

Correspondence to Leonid Reyzin.

Additional information

A preliminary version of this work appeared in Eurocrypt 2005 [6].

Most of the M. Chase work done while at Brown University.

Communicated by Moti Yung

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Chase, M., Healy, A., Lysyanskaya, A. et al. Mercurial Commitments with Applications to Zero-Knowledge Sets. J Cryptol 26, 251–279 (2013). https://doi.org/10.1007/s00145-012-9122-9

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  • DOI: https://doi.org/10.1007/s00145-012-9122-9

Key words

  • Commitments
  • Zero-knowledge sets
  • Database privacy
  • Verifiable queries
  • Outsourced databases