, Volume 26, Issue 2, pp 251279
First online:
Mercurial Commitments with Applications to ZeroKnowledge Sets
 Melissa ChaseAffiliated withMicrosoft Research
 , Alexander HealyAffiliated withDivision of Engineering and Applied Sciences, Harvard University
 , Anna LysyanskayaAffiliated withDepartment of Computer Science, Brown University
 , Tal MalkinAffiliated withDepartment of Computer Science, Columbia University
 , Leonid ReyzinAffiliated withDepartment of Computer Science, Boston University Email author
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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 zeroknowledge sets. (A zeroknowledge 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 zeroknowledge, 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 zeroknowledge set constructions.
Key words
Commitments Zeroknowledge sets Database privacy Verifiable queries Outsourced databases Title
 Mercurial Commitments with Applications to ZeroKnowledge Sets
 Journal

Journal of Cryptology
Volume 26, Issue 2 , pp 251279
 Cover Date
 201304
 DOI
 10.1007/s0014501291229
 Print ISSN
 09332790
 Online ISSN
 14321378
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Commitments
 Zeroknowledge sets
 Database privacy
 Verifiable queries
 Outsourced databases
 Industry Sectors
 Authors

 Melissa Chase ^{(1)}
 Alexander Healy ^{(2)}
 Anna Lysyanskaya ^{(3)}
 Tal Malkin ^{(4)}
 Leonid Reyzin ^{(5)}
 Author Affiliations

 1. Microsoft Research, Redmond, WA, 98052, USA
 2. Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
 3. Department of Computer Science, Brown University, Providence, RI, 02912, USA
 4. Department of Computer Science, Columbia University, New York, NY, 10027, USA
 5. Department of Computer Science, Boston University, Boston, MA, 02215, USA