  In this paper we analyze in detail the production of strangeness in
proton-proton collisions in the kinematics of large transverse momenta $p_{T}$
of produced hadrons. Using the color dipole framework, we estimated the
production cross-sections for kaons, and demonstrated that the shapes of the
$p_{T}$-dependence are in agreement with available experimental data. We also
analyzed the self-normalized yields of strange hadrons as a function of
multiplicity of co-produced hadrons, and found that the predictions are in
agreement with the faster-than-linear growth seen in experimental data. Our
description is largely parameter-free and complements our previous studies
dedicated to the explanation of multiplicity enhancement of quarkonia, as well
as $D$- and $B$-mesons.
