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The effects on the structural and transport properties of a proton in water confined in carbon nanotubes of radii ranging from 5.42 to 10.85 Å were studied by employing a recently devised reactive molecular dynamics (RMD) scheme. The formation of distinct layers was observed in the computed radial density profile of water. Affinity of hydronium ions towards the tube-water interface and its preferential orientation with the oxygen atom protruding towards the wall was observed. The axial water diffusivity was observed to decrease with increasing confinement of water. Analysis of the axial charge diffusivity and its two components (structural and vehicular) was also performed. Confinement was found to have a more significant effect on structural diffusion than on vehicular diffusion. The axial vehicular component of the charge diffusivity in the nanotube of radius 10.85 Å was found to be equal to the value computed in bulk water while structural component was 12% of the value observed in bulk water, which resulted in a total charge diffusivity of 42% of the diffusion in bulk water. The confined geometry affects the system energetically and perturbs the solvation structure around the proton from that found in bulk water. The RMD algorithm, which defines the occurrence of a proton transfer reaction based on the satisfaction of a set of triggers, identified the energetic factor to be greatly responsible for the decreased structural diffusion of a proton. [ABSTRACT FROM AUTHOR]