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Novel image encryption scheme based on Chebyshev polynomial and Duffing map.

Borislav Stoyanov1, Krasimir Kordov1

  • 1Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, 9712 Shumen, Bulgaria.

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This study introduces a new image encryption algorithm using Chebyshev polynomial and Duffing map. The novel method offers a large key space and strong security, making it suitable for secure image transmission.

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Area of Science:

  • Cryptography
  • Computer Science
  • Information Security

Background:

  • Digital image security is crucial in modern communication.
  • Existing encryption methods may have limitations in terms of security or efficiency.
  • Novel approaches are needed to protect sensitive image data.

Purpose of the Study:

  • To propose a novel image encryption algorithm.
  • To enhance the security and efficiency of image data protection.
  • To utilize Chebyshev polynomial and Duffing map for robust encryption.

Main Methods:

  • Developed a hybrid encryption scheme combining Chebyshev polynomial (permutation and substitution) and Duffing map (substitution).
  • Conducted comprehensive security analyses including key space, histogram, entropy, correlation, differential, and sensitivity tests.
  • Evaluated the algorithm's performance through speed tests.

Main Results:

  • The proposed algorithm achieved a key space exceeding 10^113.
  • Statistical analyses demonstrated desirable security levels with good histogram distribution and high information entropy.
  • Correlation coefficient analysis showed minimal correlation between adjacent pixels, indicating diffusion and confusion.

Conclusions:

  • The novel image encryption algorithm offers a significantly large key space, enhancing resistance to brute-force attacks.
  • The algorithm exhibits strong security properties and good statistical performance, suitable for practical applications.
  • The combination of Chebyshev polynomial and Duffing map provides a robust framework for secure image encryption.