By combining the iterative phase retrieval algorithm in the Fresnel domain with the shift rotation permutation operations of row vectors and column vectors, a new kind of asymmetric multiple-image authentication based on complex amplitude information multiplexing and RSA algorithm is proposed, where multiple complex amplitude information in the input plane is retrieved and generated by the phase retrieval algorithm in the Fresnel domain. In original binary amplitude mask, the row vector and column vectors random numbers are randomly generated in advance, such that each sampling mask for each authenticator is obtained by the shift rotation permutation operations of corresponding row vector and column vectors random numbers for original binary amplitude mask. Thus, one synthesized complex amplitude is generated by the operations of sampling, overlap and multiplexing, and then sent to the certification center for authentication use. At the same time, the row vector and column vectors random numbers are encoded to ciphers by the public keys of RSA algorithm, and then delivered to the corresponding authenticators. During the authentication process, the row vector and column vectors random numbers are first decoded by the private keys possessed by the authenticator; second, the authenticator’s sampling mask is reconstructed by the shift rotation permutation operations of the above decoded random numbers for original binary amplitude mask. Finally, the authenticator with other additional authentication keys is prompted to place the synthesized complex amplitude information and its sampling mask at the corresponding positions, when the system is illuminated by a plane wave with the correct wavelength. A recovered image is then recorded in the output plane, by calculating and displaying the nonlinear correlation coefficient between the recovered image and the certification image, if there exists a remarkable peak in its nonlinear correlation coefficient distributions, indicating that the authentication is successful. On the contrary, if there is no remarkable peak but uniformly distributed white noise in the map, the authentication process is a failure attempt. Any intruder with randomly generated forged authentication keys will end up with a failure which enhances the security of the system to some extent.