Image encryption is critical for securing visual data during transmission and storage. Traditional methods often rely on spatial or frequency domain operations, which can be vulnerable to attacks. To enhance security, phase encoding techniques have gained attention in recent research.

Dual random phase encoding within a 4f optical system involves two sequential phase encodings. A 4f system consists of two lenses separated by four times the focal length. In this setup, a image undergoes initial phase encoding at the input plane using a random phase mask. The encoded image is then transformed to the Fourier plane via the optical system. A second random phase mask applies additional encoding in the Fourier domain. The double-encoded image is transformed back to the input plane for recording.

Decryption reverses this process: the encrypted image is input into the 4f system, and the same phase masks are applied in reverse order to recover the original image.

Security advantages of this method include:

• Large key space: Random phase masks provide extensive key combinations, making brute-force attacks impractical.
• Noise resistance: Phase encoding maintains robustness against noise contamination.
• Resistance to cropping attacks: Partial image loss can still allow partial recovery of the original data.
• Resistance to chosen-plaintext attacks: Different plaintext images produce distinct phase distributions after encryption.

Applications span:

• Secure image transmission over networks.
• Encrypted storage to prevent unauthorized access.
• Copyright protection for digital images.
• Securing biometric feature images in identification systems.

MATLAB code for generating a random phase mask:

% Generate random phase mask for dual phase encoding
clear; clc;
originalImage = imread('test_image.png');
[rows, cols] = size(originalImage);
subplot(1,2,1);
imshow(originalImage); title('Original Image');
% Create first random phase mask
phaseMask1 = exp(2i * pi * rand(rows, cols));