We investigate the robustness to noise of the double-phase encryption metho
d and compare it with the exclusive-OR (XOR) encryption. We consider both a
dditive and multiplicative noise and determine the theoretical mean square
error of the decrypted image for the two methods. The theoretical results a
re verified by computer simulations. Theoretical and computer simulations i
ndicate that the double-phase encryption method produces a lower mean squar
e error than the XOR encryption method. (C) 1999 Society of Photo-Optical I
nstrumentation Engineers. [S0091-3286(99)01001-6].