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Two-input binary exclusive-or logic operations were presented by the assistance of multiwall carbon nanotubes in a double-stage optical Kerr gate scheme with two control beams. The samples were prepared by the aerosol pyrolysis method and decorated by platinum nanoparticles using a chemical vapor deposition technique. The nanostructures were suspended in ethanol to obtain carbon/metal nanoinks with different concentrations and then randomly distributed networks integrated in thin film form were fabricated. Polarization-selectable functions were obtained in the double-stage scheme by using nanosecond third-order nonlinear optical effects at 532 nm wavelength exhibited by the samples. Potential applications for ultrafast identification and encryption of nonlinear optical signals were discussed.