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Non-interactive and Reusable Non-malleable Commitment Schemes
Authors: Ivan Damgård, Jens GrothAbstract:
We consider non-malleable (NM) and universally composable (UC)
commitmentschemes in the common reference string (CRS) model.
We show how to construct non-interac-tive NM commitments that
remain non-malleable even if the adversary has access to an
arbitrary number of commitments from honest players - rather than
one, as in several previous schemes. We show this is a strictly
stronger security notion. Our construction is the first
non-interactive scheme achieving this that can be based
on the minimal assumption of existence of one-way
functions. But it can also be instantiated in a very efficient
version based on the strong RSA assumption. For UC commitments,
we show that existence of a UC commitment scheme in the CRS model
(interactive or not) implies key exchange and - for a uniform
reference string - even implies oblivious transfer. This indicates
that UC commitment is a strictly stronger primitive than NM. Finally,
we show that our strong RSA based construction can be used to improve
the most efficient known UC commitment scheme so it can work with
a CRS of size independent of the number of players, without loss of
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