  Particle correlations at small relative momenta can be used to measure the
space$-$time characteristics of particle production on the femtoscopic
(fm=10$^{-15}$ m) level in high-energy collisions. Such correlations arise due
to quantum statistics and final state interactions. We report correlations of
two charged identical kaons measured in p$-$Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV by the ALICE experiment at the LHC. The femtoscopic invariant
radii and correlation strengths are extracted from the one-dimensional kaon
correlation functions and are compared to those obtained in pp and Pb$-$Pb
collisions at $\sqrt{s}=7$ TeV and $\sqrt{s_{\rm NN}}=2.76$ TeV, respectively.
Kaon femtoscopy in p$-$Pb collisions is an important supplement to that in pp
and Pb$-$Pb collisions because it allows one to understand the particle
production mechanisms in different collision systems. It also complements the
existing pion correlation results. The obtained radii increase with increasing
multiplicity and decrease with increasing pair transverse momentum. At
comparable multiplicity, the radii measured in p$-$Pb collisions are close to
those observed in pp collisions, whereas it is difficult to compare them with
the results from Pb$-$Pb collisions because of a big multiplicity gap.
