  The design of quantum protocols for secure key generation poses many
challenges: On the one hand, they need to be practical concerning experimental
realisations. On the other hand, their theoretical description must be simple
enough to allow for a security proof against all possible attacks. Often, these
two requirements are in conflict with each other, and the differential phase
shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be
implementable with current optical telecommunication technology, which, for
this protocol, comes at the cost that many standard security proof techniques
do not apply to it. After about 20 years since its invention, this work
presents the first full security proof of DPS QKD against general attacks,
including finite-size effects. The proof combines techniques from quantum
information theory, quantum optics, and relativity. We first give a security
proof of a QKD protocol whose security stems from relativistic constraints. We
then show that security of DPS QKD can be reduced to security of the
relativistic protocol. In addition, we show that coherent attacks on the DPS
protocol are, in fact, stronger than collective attacks. Our results have broad
implications for the development of secure and reliable quantum communication
technologies, as they shed light on the range of applicability of
state-of-the-art security proof techniques.
