  To guarantee the security of quantum key distribution (QKD), several
assumptions on light sources must be satisfied. For example, each random bit
information is precisely encoded on an optical pulse and the photon-number
probability distribution of the pulse is exactly known. Unfortunately, however,
it is hard to check if all the assumptions are really met in practice, and it
is preferable that we have minimal number of device assumptions. In this paper,
we adopt the differential-phase-shift (DPS) QKD protocol and drastically
mitigate the requirements on light sources. Specifically, we only assume the
independence among emitted pulses, the independence of the vacuum emission
probability from a chosen bit, and upper bounds on the tail distribution
function of the total photon number in a single block of pulses for single, two
and three photons. Remarkably, no other detailed characterizations, such as the
amount of phase modulation, are required. Our security proof significantly
relaxes demands for light sources, which paves a route to guarantee
implementation security with simple verification of the devices.
