Welcome to the resource topic for 2005/438
Title:
Minimal Assumptions for Efficient Mercurial Commitments
Authors: Yevgeniy Dodis
Abstract:Mercurial commitments were introduced by Chase et al. (Eurocrypt 2005)
and form a key building block for constructing zero-knowledge sets
(introduced by Micali, Rabin and Kilian (FOCS’03)}). Unlike regular
commitments, which are strictly binding, mercurial commitments allow
for certain amount of (limited) freedom. The notion of Chase et al.
also required that mercurial commitments should be equivocable given a
certain trapdoor, although the notion is interesting even without this
condition. While trivially implying regular (trapdoor) commitments, it
was not clear from the prior work if the converse was true: Chase et
al. gave several constructions of mercurial commitments from various
incompatible assumptions, leaving open if they can be built from any
(trapdoor) commitment scheme, and, in particular, from any one-way
function. We give an affirmative answer to this question, by giving
two simple constructions of mercurial commitments from any trapdoor
bit commitment scheme. By plugging in various (trapdoor) bit
commitment schemes, we get all the efficient constructions from
Chase et al. and Micali et al., as well as several immediate new
constructions.
Our results imply that (a) ** mercurial commitments can be viewed as
surprisingly simple variations of regular (trapdoor) commitments **
(and, thus, can be built from one-way functions and, more efficiently,
from a variety of other assumptions); and (b) ** the existence of
zero-knowledge sets is equivalent to the existence of
collision-resistant hash functions ** (moreover, the former can be
efficiently built from the latter and trapdoor commitments). Of
independent interest, we also give a stronger and yet much simpler
definition of mercurial commitments than that of Chase et al. (which
is also met by our constructions). Overall, we believe that our
results eludicate the notion of mercurial commitments, and better
explain the rational following the previous constructions of
mercurial commitments.
ePrint: https://eprint.iacr.org/2005/438
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