  We introduce a new setting for two-party cryptography with temporarily
trusted third parties. In addition to Alice and Bob in this setting, there are
additional third parties, which Alice and Bob both trust to be honest during
the protocol. However, once the protocol concludes, there is no guarantee over
the behaviour of these third parties. It is possible that they collaborate and
act adversarially. Our goal is to use these third parties to facilitate
protocols which are impossible in two-party cryptography. We implement a
variant of bit commitment in this setting, which we call erasable bit
commitment. In this primitive, Alice has the choice of either opening or
erasing her commitment after the commit phase. The ability to ask for an
erasure allows Alice to ask the trusted parties to erase her commitment in case
the trust period is about to expire. This erasure prevents a future coalition
of the third parties and Bob from extracting any information about the
commitment. However, this ability also makes erasable bit commitment weaker
than the standard version of bit commitment. In addition to satisfying the
security requirements of bit commitment, our protocol also does not reveal any
information about the commitment to the third parties. Lastly, our protocol for
this primitive requires a constant number of trusted third parties and can
tolerate a small number of corrupt trusted parties as well as implementation
errors.
