基于复振幅场信息复用和RSA算法的非对称多幅图像认证方法∗

摘要

结合相位恢复和像素行、列循环移动置乱技术，本文提出了一种基于复振幅场信息复用和RSA算法的非对称多幅图像认证方法，通过菲涅耳域的相位恢复算法，依次恢复并生成多幅图像各自所对应的输入平面的复振幅信息，通过各自的行、列向量随机数对原始二值振幅模板进行行、列循环移动置乱操作来获得每幅图像的采样模板，认证系统将多个复振幅场信息采样、叠加并空间复用，同时，行向量随机数和列向量随机数被RSA算法公钥编码成密文。系统认证时，认证方利用自己持有的私钥将密文解码成行向量随机数和列向量随机数，通过行、列循环移动置乱变换后获得各自的采样模板，合成的复振幅信息和采样模板等认证信息均放置在各自正确位置，当认证系统被正确波长的平面波照射时，在输出平面能获得输出图像，通过计算、显示输出图像和对应认证图像的非线性相关系数峰值来判断认证是否成功。%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.