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    A novel brute-force attack exploits weaknesses in double random-phase encoding (DRPE) by analyzing smooth error curves. Modular arithmetic pre-coding effectively counters this attack by creating nonlinear, oscillatory curves, enhancing DRPE security.

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    Area of Science:

    • Cryptography
    • Information Security
    • Optical Engineering

    Background:

    • Double Random-Phase Encoding (DRPE) is a cryptosystem susceptible to brute-force attacks.
    • Key-sensitivity analysis often reveals vulnerabilities in cryptosystems.
    • The smoothness of Mean Squared Error (MSE) and Correlation Coefficient (CC) curves was an unreported vulnerability in DRPE.

    Purpose of the Study:

    • To present a smart brute-force attack targeting DRPE.
    • To identify and analyze an unreported vulnerability in DRPE's key-sensitivity analysis.
    • To propose a defense mechanism against this novel attack.

    Main Methods:

    • A brute-force attack exploiting the smoothness of MSE and CC curves was developed.
    • Key-sensitivity analysis was used to visualize the vulnerability.
    • Modular arithmetic pre-coding was implemented as a countermeasure.

    Main Results:

    • The study demonstrated a new vulnerability in DRPE based on smooth MSE and CC curves.
    • Modular arithmetic pre-coding significantly increased robustness against the presented attack.
    • Pre-coding resulted in highly nonlinear and oscillatory MSE and CC curves in the key space.

    Conclusions:

    • The identified vulnerability in DRPE can be exploited by a smart brute-force attack.
    • Modular arithmetic pre-coding is an effective defense, enhancing DRPE security.
    • Understanding this vulnerability improves the design and robustness analysis of DRPE systems.