  The security of a standard bi-directional "plug & play" quantum key
distribution (QKD) system has been an open question for a long time. This is
mainly because its source is equivalently controlled by an eavesdropper, which
means the source is unknown and untrusted. Qualitative discussion on this
subject has been made previously. In this paper, we present the first
quantitative security analysis on a general class of QKD protocols whose
sources are unknown and untrusted. The securities of standard BB84 protocol,
weak+vacuum decoy state protocol, and one-decoy decoy state protocol, with
unknown and untrusted sources are rigorously proved. We derive rigorous lower
bounds to the secure key generation rates of the above three protocols. Our
numerical simulation results show that QKD with an untrusted source gives a key
generation rate that is close to that with a trusted source.
