We investigate the robustness to noise of the double-phase encryption method and compare it with the exclusive-OR (XOR) encryption. We consider both additive and multiplicative noise and determine the theoretical mean square error of the decrypted image for the two methods. The theoretical results are verified by computer simulations. Theoretical and computer simulations indicate that the double-phase encryption method produces a lower mean square error than the XOR encryption method. © 1999 Society of Photo-Optical Instrumentation Engineers.