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Image encryption and the fractional Fourier transform

Bryan M. Hennelly, John T. Sheridan

Published Jan 1, 2003• 165 citations
Publisher
DOI
10.1078/0030-4026-00257

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In the digital era, the security of image data has become increasingly important. This study aims to develop an image encryption scheme based on Quantum Key Distribution (QKD) and Fractional Fourier Transform (FRFT) to enhance the security of image data transmission and storage. The proposed scheme first utilizes QKD to generate and distribute secure encryption keys, ensuring the unconditional security of the key distribution process. Subsequently, FRFT is employed to perform complex transformations on the image data, using fractional order parameters to achieve multi-scale representation of the image in both time and frequency domains, thereby increasing the complexity and security of the encryption process. Experimental results demonstrate that this scheme exhibits significant advantages in terms of the quality of encrypted images and their resistance to attacks. Specifically, the encrypted images possess high Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), effectively resisting various attacks. Comparative analysis further verifies the superiority of this scheme in terms of security and efficiency. In summary, the proposed combination of QKD and FRFT for image encryption holds great potential and research value in the protection of image data.
An advanced iterative phase retrieval algorithm is applied to perform a ciphertext-only attack on the fractional Fourier transform-based double random phase encryption system. With the given complex amplitude of ciphertext and definite support of the object image, the original object image can be recovered by estimating the energy of support area in the recovered image. The encryption system can be attacked by analyzing the sensibility of fractional Fourier transform order keys and evaluating the energy of the object image support area. The proposed algorithm can obtain encrypted fractional order and retrieve two random phase keys. Numerical results demonstrate the efficacy of the proposed attacking method.