  Bit commitment is a fundamental cryptographic primitive in which Bob wishes
to commit a secret bit to Alice. Perfectly secure bit commitment has been
proven impossible through asynchronous exchange of classical and quantum
information. Perfect security is however possible by restraining the exchange
of classical and quantum information to suitably chosen relativistic
constraints. This requires Alice (and Bob) to split into two remote agents
performing space-like separated classical communication, and in one agent
exchanging quantum bits with the other party. The duration of the commitment is
given by the distance between the two remote agents. The original protocol
requires the quantum communication to happen at a precise location and time
with respect to the classical communication. We show how the protocol can be
modified to relax this constraint such that the quantum part of the protocol
can be performed at any time before the actual commitment, making it much more
practical. Finally, we present an experimental demonstration of this protocol
realized with a commercial quantum key distribution system and with
synchronized classical agents located in Geneva and Singapore, yielding a
commitment time of 15 ms. Our work includes a complete security analysis,
accounting for experimental imperfections (multi-photon emission, transmission
loss, detector inefficiency and dark counts) and finite statistics.
