  We propose the continuous-variable quantum key distribution protocol based on
the Gaussian modulation of a single quadrature of the coherent states of light,
which is aimed to provide simplified implementation compared to the
symmetrically modulated Gaussian coherent-state protocols. The protocol waives
the necessity in phase quadrature modulation and the corresponding channel
transmittance estimation. The security of the protocol against collective
attacks in a generally phase-sensitive Gaussian channels is analyzed and is
shown achievable upon certain conditions. Robustness of the protocol to channel
imperfections is compared to that of the symmetrical coherent-state protocol.
The simplified unidimensional protocol is shown possible at a reasonable
quantitative cost in terms of key rate and of tolerable channel excess noise.
