Chapter

Advances in Cryptology – EUROCRYPT 2005

Volume 3494 of the series Lecture Notes in Computer Science pp 422-439

Mercurial Commitments with Applications to Zero-Knowledge Sets

Extended Abstract
  • Melissa ChaseAffiliated withBrown University
  • , Alexander HealyAffiliated withHarvard University
  • , Anna LysyanskayaAffiliated withBrown University
  • , Tal MalkinAffiliated withColumbia University
  • , Leonid ReyzinAffiliated withBoston University

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.