  In comparison to conventional discrete-variable (DV) quantum key distribution
(QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has
distinct advantages of lower-cost implementation and affinity to wavelength
division multiplexing. On the other hand, its continuous nature makes it harder
to accommodate to practical signal processing, which is always discretized,
leading to lack of complete security proofs so far. Here we propose a tight and
robust method of estimating fidelity of an optical pulse to a coherent state
via heterodyne measurements. We then construct a binary phase modulated CV QKD
protocol and prove its security in the finite-key-size regime against general
coherent attacks, based on proof techniques of DV QKD. Such a complete security
proof achieves a significant milestone in exploiting the benefits of CV QKD.
