  The increase of the measured hadronic total cross sections at the highest
energies is empirically described by squared log of center-of-mass energy sqrt
s as sigma(tot)= B (log s)2, consistent with the energy dependence of the
Froissart unitarity bound. The coefficient B is argued to have a universal
value, but this is not proved directly from QCD. In the previous tests of this
universality, the p(pbar)p, pi p, and K p forward scatterings were analyzed
independently and found to be consistent with B(pp) = B(pip) = B(Kp), although
the determined value of B(Kp) had large uncertainty. In the present work, we
have further analyzed forward Kp scattering to obtain a more exact value of
B(Kp). Making use of continuous moment sum rules(CMSR) we have fully exploited
the information of low-energy scattering data to predict the high-energy
behavior of the amplitude hrough duality. The estimation of B(Kp) is improved
remarkably, and our result strongly supports the universality of B.
