Diffusion and confusion analysis of optical encryption algorithm based on phase encoding

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.