Cross section measurements of $e^{+}e^{-} to K^{+}K^{-}K^{+}K^{-} $ and $ phi K^{+}K^{-}$ at center-of-mass energies from 2.10 to 3.08 GeV

We measure the Born cross sections of the process $e^{+}e^{-} to K^{+}K^{-}K^{+}K^{-}$ at center-of-mass (c.m.) energies, $sqrt{s}$, between 2.100 and 3.080 GeV. The data were collected using the BESIII detector at the BEPCII collider. An enhancement at $sqrt{s}= 2.232$ GeV is observed, very close to the $e^{+}e^{-} to Lambda overline{Lambda}$ production threshold. A similar enhancement at the same c.m. energy is observed in the $e^{+}e^{-} to phi K^{+}K^{-}$ cross section. The energy dependence of the $K^{+}K^{-}K^{+}K^{-}$ and $phi K^{+}K^{-}$ cross sections differs significantly from that of $e^{+}e^{-} to phi pi^{+}pi^{-}$.