  We reconsider the concept of multi-prover commitments, as introduced in the
late eighties in the seminal work by Ben-Or et al. As was recently shown by
Cr\'{e}peau et al., the security of known two-prover commitment schemes not
only relies on the explicit assumption that the provers cannot communicate, but
also depends on their information processing capabilities. For instance, there
exist schemes that are secure against classical provers but insecure if the
provers have quantum information processing capabilities, and there are schemes
that resist such quantum attacks but become insecure when considering general
so-called non-signaling provers, which are restricted solely by the requirement
that no communication takes place.
  This poses the natural question whether there exists a two-prover commitment
scheme that is secure under the sole assumption that no communication takes
place; no such scheme is known.
  In this work, we give strong evidence for a negative answer: we show that any
single-round two-prover commitment scheme can be broken by a non-signaling
attack. Our negative result is as bad as it can get: for any candidate scheme
that is (almost) perfectly hiding, there exists a strategy that allows the
dishonest provers to open a commitment to an arbitrary bit (almost) as
successfully as the honest provers can open an honestly prepared commitment,
i.e., with probability (almost) 1 in case of a perfectly sound scheme. In the
case of multi-round schemes, our impossibility result is restricted to
perfectly hiding schemes.
  On the positive side, we show that the impossibility result can be
circumvented by considering three provers instead: there exists a three-prover
commitment scheme that is secure against arbitrary non-signaling attacks.
