  We study electrical and thermal conductivities of degenerate electrons
emitting and absorbing phonons in a strongly magnetized crystalline neutron
star crust. We take into account modification of the phonon spectrum of a
Coulomb solid of ions caused by a strong magnetic field. Boltzmann transport
equation is solved using a generalized variational method. The ensuing
three-dimensional integrals over the transferred momenta are evaluated by two
different numerical techniques, the Monte-Carlo method and a regular
integration over the first Brillouin zone. The results of the two numerical
approaches are shown to be in a good agreement. An appreciable growth of
electrical and thermal resistivities is reported at quantum and intermediate
temperatures $T \lesssim 0.1 T_{\rm p}$ ($T_{\rm p}$ is the ion plasma
temperature) in a wide range of chemical compositions and mass densities of
matter even for moderately magnetized crystals $\omega_{\rm B} \sim \omega_{\rm
p}$ ($\omega_{\rm B}$ and $\omega_{\rm p}$ are the ion cyclotron and plasma
frequencies). This effect is due to an appearance of a soft ($\omega \propto
k^2$) phonon mode in the magnetized ion Coulomb crystal, which turns out to be
easier to excite than acoustic phonons characteristic of the field-free case.
These results are important for modelling magneto-thermal evolution of neutron
stars.
