Interference-based multiple-image encryption using binary phase masks

We propose a new scheme to encrypt multiple images simultaneously using two-dimensional binary phase masks. Each of the original greyscale images is first decomposed into two pure phase-only images, which corresponds to the reverse process of an optical interference. Two phase-only images have random distributions of phases in the range from 0 to 2π, and will serve as a secret image and a private key. Next, each pixel of the secret image is subdivided into four equal segments. Then, the four pixel-quadrants are separately phase encoded in accordance with the four elements of a row of a 4-order Hadamard matrix. By applying this procedure to other secret images, we obtain four phase-encoded images, which are then superimposed to yield the final encrypted image. We can successfully restore the four original images separately when the correct Hadamard matrix and the correct private key are used. We also show that the correlation coefficient (CC) is as low as 0.05 when the decryption is done by wrong Hadamard matrices and/or private keys.