  A numerical security proof technique is used to analyse the security of
continuous-variable quantum key distribution (CV-QKD) protocols with
phase-shift keying modulation against collective attacks in the asymptotic
limit. We argue why it is sufficient to consider protocols with a maximum
number of eight signal states and analyse different postselection strategies
for protocols with four (QPSK) and eight (8PSK) signal states for untrusted
ideal and trusted nonideal detectors. We introduce a \emph{cross-shaped}
postselection strategy, and show that both cross-shaped and radial and angular
postselection clearly outperform a radial postselection scheme (and no
postselection) for QPSK protocols. For all strategies studied, we provide
analytical results for the operators defining the respective regions in phase
space. We outline several use-cases of postselection, which can easily be
introduced in the data processing of both new and existing CV-QKD systems:
Motivated by the high computational effort for error-correction, we studied the
case when a large fraction of the raw key is eliminated by postselection and
observed that this can be achieved while increasing the secure key rate.
Postselection can also be used to partially compensate the disadvantage of QPSK
protocols over 8PSK protocols for high transmission distances, while being
experimentally less demanding. Finally, we highlight that postselection can be
used to reduce the key rate gap between scenarios with trusted and untrusted
detectors while relying on less assumptions on Eve's power.
