为了阐明相位编码光学加密算法的扩散及混淆特性, 基于傅里叶变换位移定理,从分组密码设计准则出发,以双随机相位光学加密算法为研究对象,分析了采用单个随机相位模板的2-f系统的扩散和混淆特性。将单随机相位加密过程分解为2个相互关联的过程,结果表明, 傅里叶变换在加密算法中引入了混淆操作,而傅里叶变换结合随机相位模板实现了扩散操作。通过数值模拟对上述理论分析进行了验证,引入信息熵来评价加密图像的统计分布特性, 进一步分析了菲涅尔域及分数阶傅里叶变换域随机相位加密算法的扩散混淆特性。研究表明,单随机相位加密和双随机相位加密图像的信息熵分布为7.038和7.157, 而随机振幅加密图像信息熵为4.521。因而, 随机相位加密算法比随机振幅加密算法能实现对信息更好地扩散。

To clarify the diffusion and confusion characteristic of phase encoding optical encryption algorithm, based on the spatial shift theorem of Fourier transform together with the block cipher design criterion, the diffusion and confusion characteristic of 2-f system utilizing single random phase mask is analyzed. Process of single random phase encryption is divided into two individual procedures. The analysis results indicate that the confusion operation is introduced mainly by the Fourier transform and the diffusion operation is achieved by combining the Fourier transform and random phase mask. Numerical simulation is performed to verify the theoretical analysis. The entropy is introduced to evaluate the statistical property of ciphertext. The diffusion and confusion characteristics of optical phase encoding algorithm in the Fresnel domain and fractional Fourier domain are further investigated. The research results indicate the entropy for single random phase encryption and double random phase encryption are 7.038 and 7.157, respectively,while entropy for random amplitude encryption is 4.521. Hence, random phase encoding algorithm can achieve better diffusion on plaintext than random amplitude encoding algorithm.