The dissociation of water under pressure is investigated with a series of ab initio molecular dynamics simulations at thermodynamic conditions close to those obtained in shock wave experiments. We find that molecular dissociation occurs via a bimolecular process similar to ambient conditions, leading to the formation of short-lived hydronium ions. Up to twofold compression and 2000 K, the oxygen diffusion coefficient is characteristic of a fluid. Our findings do not support models used to estimate the liquid electrical conductivity and interpret Raman spectra that assume the presence of free protons.