  In this Letter, we prove the unconditional security of single-photon
differential phase shift quantum key distribution (DPS-QKD) protocol, based on
the conversion to an equivalent entanglement-based protocol. We estimate the
upper bound of the phase error rate from the bit error rate, and show that
DPS-QKD can generate unconditionally secure key when the bit error rate is not
greater than 4.12%. This proof is the first step to the unconditional security
proof of coherent state DPS-QKD.
