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    Area of Science:

    • Cryptography
    • Image Processing
    • Computer Science

    Background:

    • Homomorphic encryption (HE) applications in image processing are computationally intensive, limiting practical use.
    • Existing encrypted domain transforms like DCT have limitations in efficiency and data handling.

    Purpose of the Study:

    • To develop efficient methods for image processing in the encrypted domain using the Walsh-Hadamard Transform (WHT).
    • To enhance the computational efficiency of encrypted domain WHT through parallel algorithms.
    • To evaluate the performance of encrypted domain WHT against other transforms for HE image applications.

    Main Methods:

    • Implementation of real and complex WHT in the encrypted domain.
    • Development of a parallel algorithm for encrypted domain WHT.
    • Theoretical analysis and experimental comparison with Discrete Cosine Transform (DCT), integer DCT, and Haar transform.
    • Proposal of two encrypted image applications utilizing encrypted domain WHT.
    • Application of two parallelization strategies to accelerate execution.

    Main Results:

    • Encrypted domain WHT demonstrates lower computational complexity and shorter running times compared to DCT, integer DCT, and Haar transform.
    • Encrypted WHT supports larger plaintext data values.
    • Experimental results show a speedup exceeding 12 for homomorphic encrypted image applications.

    Conclusions:

    • The encrypted domain WHT, combined with parallel algorithms, offers a practical and efficient solution for homomorphic encrypted image processing.
    • This approach significantly overcomes the time-consuming limitations of current HE image applications.
    • The proposed methods pave the way for wider adoption of secure image analysis techniques.