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<p>This study proposes a novel two-dimensional Logistic–Chebyshev–Sine hybrid chaotic map (LCSHCM). Effectiveness of the map is evaluated using measures such as the Lyapunov exponent, bifurcation diagrams, information entropy, and approximate entropy, ensuring randomness and unpredictability. Parameter of the proposed map can take any value in the range from 0 to infinity, with positive Lyapunov exponents for each parametric value. The bifurcation diagram exhibits no blank regions, indicating continuous chaotic behavior. Furthermore, an application of the map in color image encryption is presented. The encryption process begins with the application of SHA-256 hashing to the input image to generate parameters and initial values for the proposed chaotic map. LCSHCM is then used in both the confusion and diffusion phases to achieve robust encryption. Bitwise XOR operation is employed for diffusion process. The encryption scheme is tested and its performance is evaluated using performance metrics. The scheme is shown to resist statistical, differential, and noise attacks due to its very large key space of size <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2^{655}\)</EquationSource> </InlineEquation> and high sensitivity, up to a precision level of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10^{-15}\)</EquationSource> </InlineEquation>. The proposed scheme demonstrates superior performance compared to the existing methods.</p>

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A novel two-dimensional Logistic–Chebyshev–Sine hybrid chaotic map for secure color image encryption

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Keshav,
  • A. K. Yadav

摘要

This study proposes a novel two-dimensional Logistic–Chebyshev–Sine hybrid chaotic map (LCSHCM). Effectiveness of the map is evaluated using measures such as the Lyapunov exponent, bifurcation diagrams, information entropy, and approximate entropy, ensuring randomness and unpredictability. Parameter of the proposed map can take any value in the range from 0 to infinity, with positive Lyapunov exponents for each parametric value. The bifurcation diagram exhibits no blank regions, indicating continuous chaotic behavior. Furthermore, an application of the map in color image encryption is presented. The encryption process begins with the application of SHA-256 hashing to the input image to generate parameters and initial values for the proposed chaotic map. LCSHCM is then used in both the confusion and diffusion phases to achieve robust encryption. Bitwise XOR operation is employed for diffusion process. The encryption scheme is tested and its performance is evaluated using performance metrics. The scheme is shown to resist statistical, differential, and noise attacks due to its very large key space of size \(2^{655}\) and high sensitivity, up to a precision level of \(10^{-15}\) . The proposed scheme demonstrates superior performance compared to the existing methods.