Total and differential cross sections are presented for the reaction Kip + Kip from 1.3 to 8 0 0 GeV/c as measured in an exposure of the SLAC 40-inch hydrogen bubble chamber to a neu-tral beam. The forward points of $$(KLp-+ Kgp) together with K+n and K-n total cross sections are used to determine the inter-cept of the effective Regge trajectory, a(O) =0.47&O. 09, and the regeneration phase, $f =-43 ’ f 8’. /(A shorter version of this paper has been submitted to Phys. Rev. Letters.