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Iterative phase retrieval algorithms. I: optimization.

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    Two novel iterative phase retrieval algorithms, spatial phase perturbation GS (SPP GS) and GS/hybrid input-output (GS/HIOA), significantly improve solutions by avoiding stagnation. These methods enhance performance in optical encryption attacks.

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    Area of Science:

    • Computational optics
    • Image processing
    • Cryptography

    Background:

    • Iterative phase retrieval algorithms like Gerchberg-Saxton (GS) and Hybrid Input-Output (HIO) can suffer from stagnation, limiting solution quality.
    • Existing methods for optical encryption systems are vulnerable to various cryptanalytic attacks.

    Purpose of the Study:

    • To introduce and evaluate two modified iterative phase retrieval algorithms: spatial phase perturbation GS (SPP GS) and a combined GS/hybrid input-output algorithm (GS/HIOA).
    • To demonstrate the improved performance of these algorithms in avoiding stagnation and finding superior solutions.
    • To apply these algorithms for cryptanalysis of double random phase encryption (DRPE) systems.

    Main Methods:

    • Development of the spatial phase perturbation GS algorithm (SPP GSA).
    • Development of a combined GS hybrid input-output algorithm (GS/HIOA).
    • Integration of the error reduction (ER) algorithm with HIO (ER/HIOA) for phase retrieval with partial information.
    • Application of developed algorithms for known plaintext and ciphertext attacks on amplitude encoding (AE) and phase encoding DRPE systems.

    Main Results:

    • SPP GS and GS/HIO algorithms show superior performance in avoiding stagnation compared to standard GS and HIO algorithms.
    • The developed algorithms successfully locate superior solutions in phase retrieval tasks.
    • ER/HIOA is capable of performing ciphertext-only attacks on AE DRPE systems.

    Conclusions:

    • The proposed SPP GS and GS/HIO algorithms offer significant advancements in iterative phase retrieval by mitigating stagnation.
    • These enhanced algorithms provide more robust solutions for phase retrieval problems.
    • The successful application of these algorithms in cryptanalysis highlights vulnerabilities in DRPE systems and demonstrates the power of advanced phase retrieval techniques.