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<p>Vortex arrays (VA) have gained significant attention in optical image encryption because of their unique features, such as orbital angular momentum (OAM) and a helical phase structure. Additionally, the distinctive diffraction properties, aperiodicity, and self-similar structure of the Thue-Morse zone plate (TMZP) contribute to further enhancing security. In the proposed double random phase encoding (DRPE) scheme, VA and TMZP are used along with random phase masks (RPMs) as the encryption key. TMZP and VA provide additional degrees of freedom for encoding information. In this cryptosystem, singular value decomposition (SVD) and QZ decomposition are employed to generate private keys for decryption. The input image is first decomposed and then encoded using the fractional Fourier transform (FrFT) with two parameters. The resultant image is than modulated using the encryption key. Finally, the encrypted image is obtained by applying the inverse FrFT to the modulated image. We demonstrated how the combination of decomposition techniques, VA, and TMZP enhances the noise resilience and security of the cryptosystem by evaluating various metrics, including FrFT orders, mean square error (MSE), peak signal-to-noise ratio (PSNR), Structural similarity index measure (SSIM), and correlation coefficient (CC). The robustness was further assessed against basic attacks such as KPA, CPA, and differential attacks. The simulation work was performed using MATLAB (R2024a).</p>

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Vortex array-based cryptosystem using Thue-Morse zone plate, SVD and QZ decomposition in the fractional Fourier transform domain

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Hemant Kumar,
  • Hukum Singh,
  • Vipin Yadav

摘要

Vortex arrays (VA) have gained significant attention in optical image encryption because of their unique features, such as orbital angular momentum (OAM) and a helical phase structure. Additionally, the distinctive diffraction properties, aperiodicity, and self-similar structure of the Thue-Morse zone plate (TMZP) contribute to further enhancing security. In the proposed double random phase encoding (DRPE) scheme, VA and TMZP are used along with random phase masks (RPMs) as the encryption key. TMZP and VA provide additional degrees of freedom for encoding information. In this cryptosystem, singular value decomposition (SVD) and QZ decomposition are employed to generate private keys for decryption. The input image is first decomposed and then encoded using the fractional Fourier transform (FrFT) with two parameters. The resultant image is than modulated using the encryption key. Finally, the encrypted image is obtained by applying the inverse FrFT to the modulated image. We demonstrated how the combination of decomposition techniques, VA, and TMZP enhances the noise resilience and security of the cryptosystem by evaluating various metrics, including FrFT orders, mean square error (MSE), peak signal-to-noise ratio (PSNR), Structural similarity index measure (SSIM), and correlation coefficient (CC). The robustness was further assessed against basic attacks such as KPA, CPA, and differential attacks. The simulation work was performed using MATLAB (R2024a).