Upper Bounds for the Security of two Distributed-Phase Reference Protocols of Quantum Cryptography (Coherent-One-Way and Differential-Phase-Shift)

The Differential-Phase-Shift (DPS) and the Coherent-One-Way (COW) are among the most practical protocols for quantum cryptography, and are therefore the object of fast-paced experimental developments. The assessment of their security is also a challenge for theorists: the existing tools, that allow to prove security against the most general attacks, do not apply to these two protocols in any straightforward way. We present new upper bounds for their security in the limit of large distances ($d \gtrsim 50$km with typical values in optical fibers) by considering a large class of collective attacks, namely those in which the adversary attaches ancillary quantum systems to each pulse or to each pair of pulses. We introduce also two modified versions of the COW protocol, which may prove more robust than the original one.