Avalanche and bit independence characteristics of double random phase encoding in the Fourier and Fresnel domains

In this work, we evaluate the avalanche effect and bit independence properties of the double random phase encoding (DRPE) algorithm in the Fourier and Fresnel domains. Experimental results show that DRPE has excellent bit independence characteristics in both the Fourier and Fresnel domains. However, DRPE achieves better avalanche effect results in the Fresnel domain than in the Fourier domain. DRPE gives especially poor avalanche effect results in the Fourier domain when only one bit is changed in the plaintext or in the encryption key. Despite this, DRPE shows satisfactory avalanche effect results in the Fresnel domain when any other number of bits changes in the plaintext or in the encryption key. To the best of our knowledge, this is the first report on the avalanche effect and bit independence behaviors of optical encryption approaches for bit units.