  We develop a method to connect the infinite-dimensional description of
optical continuous-variable quantum key distribution (QKD) protocols to a
finite-dimensional formulation. The secure key rates of the optical QKD
protocols can then be evaluated using recently-developed reliable numerical
methods for key rate calculations. We apply this method to obtain asymptotic
key rates for discrete-modulated continuous-variable QKD protocols, which are
of practical significance due to their experimental simplicity and potential
for large-scale deployment in quantum-secured networks. Importantly, our
security proof does not require the photon-number cutoff assumption relied upon
in previous works. We also demonstrate that our method can provide practical
advantages over the flag-state squasher when applied to discrete-variable
protocols.
