  We present a quantum fingerprinting protocol relying on two-photon
interference which does not require a shared phase reference between the
parties preparing optical signals carrying data fingerprints. We show that the
scaling of the protocol, in terms of transmittable classical information, is
analogous to the recently proposed and demonstrated scheme based on coherent
pulses and first-order interference, offering comparable advantage over
classical fingerprinting protocols without access to shared prior randomness.
We analyze the protocol taking into account non-Poissonian photon statistics of
optical signals and a variety of imperfections, such as transmission losses,
dark counts, and residual distinguishability. The impact of these effects on
the protocol performance is quantified with the help of Chernoff information.
