  Commitment is an important cryptographic primitive. It is well known that
noisy channels are a promising resource to realize commitment in an
information-theoretically secure manner. However, oftentimes, channel behaviour
may be poorly characterized thereby limiting the commitment throughput and/or
degrading the security guarantees; particularly problematic is when a dishonest
party, unbeknown to the honest one, can maliciously alter the channel
characteristics. Reverse elastic channels (RECs) are an interesting class of
such unreliable channels, where only a dishonest committer, say, Alice can
maliciously alter the channel. RECs have attracted recent interest in the study
of several cryptographic primitives.
  Our principal contribution is the REC commitment capacity characterization;
this proves a recent related conjecture. A key result is our tight converse
which analyses a specific cheating strategy by Alice. RECs are closely related
to the classic unfair noisy channels (UNCs); elastic channels (ECs), where only
a dishonest receiver Bob can alter the channel, are similarly related. In stark
contrast to UNCs, both RECs and ECs always exhibit positive commitment
throughput for all non-trivial parameters. Interestingly, our results show that
channels with exclusive one-sided elasticity for dishonest parties, exhibit a
fundamental asymmetry where a committer with one-sided elasticity has a more
debilitating effect on the commitment throughput than a receiver.
