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Cascade Chaotic System With Applications.

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    This study introduces a cascade chaotic system (CCS) to generate novel chaotic maps with enhanced unpredictability and performance. Applications include a high-quality pseudo-random number generator and a secure data encryption system.

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    Area of Science:

    • Chaos theory
    • Complex systems
    • Applied mathematics

    Background:

    • Chaotic maps are essential tools in various scientific and engineering fields.
    • Existing chaotic maps may have limitations in unpredictability and parameter complexity.
    • Inspiration from electronic circuit cascade structures motivates a new framework.

    Purpose of the Study:

    • To introduce a general framework, the cascade chaotic system (CCS), for generating novel chaotic maps.
    • To enhance the unpredictability, performance, and complexity of chaotic maps.
    • To demonstrate practical applications of CCS-generated maps in pseudo-random number generation and data encryption.

    Main Methods:

    • Developing the cascade chaotic system (CCS) framework.
    • Utilizing two 1-D chaotic maps as seed maps within the CCS.
    • Generating and evaluating new chaotic maps derived from the CCS.
    • Designing and simulating a pseudo-random number generator (PRNG) and a data encryption system based on CCS maps.

    Main Results:

    • The CCS framework successfully generates a large number of new chaotic maps.
    • Generated maps exhibit superior unpredictability and chaotic performance compared to seed maps.
    • The proposed PRNG demonstrates high-quality randomness.
    • The data encryption system offers a high level of security for diverse data types.

    Conclusions:

    • The cascade chaotic system (CCS) is a robust and effective framework for creating advanced chaotic maps.
    • CCS-generated chaotic maps offer improved properties for complex applications.
    • The developed PRNG and data encryption system showcase the practical utility and security benefits of CCS.