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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme.

Musheer Ahmad1, Eesa Al-Solami2

  • 1Department of Computer Engineering, Jamia Millia Islamia, New Delhi 110025, India.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces key-dependent dynamic substitution-boxes (S-boxes) to enhance cryptosystem security. Evolving S-boxes using a fractional-order Hopfield neural network significantly improves nonlinearity and resistance to cryptanalysis.

Keywords:
block cryptosystemdynamic S-boxfractional Hopfield neural networksecurity

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Area of Science:

  • Cryptography
  • Applied Mathematics
  • Computer Science

Background:

  • Static substitution-boxes (S-boxes) in block ciphers present cryptanalysis vulnerabilities.
  • Key-dependent dynamic S-boxes offer enhanced security and robustness for cryptosystems.

Purpose of the Study:

  • To propose a novel construction for key-dependent dynamic S-boxes with high nonlinearity.
  • To improve the security and robustness of cryptosystems through dynamic S-box evolution.

Main Methods:

  • Construction of key-dependent dynamic S-boxes.
  • Evolution of S-boxes using a fractional-order time-delayed Hopfield neural network.
  • Assessment of cryptographic performance using standard security parameters.

Main Results:

  • The proposed scheme evolves S-boxes with high nonlinearity (mean 111.25).
  • Achieved excellent Strict Avalanche Criterion (SAC) value of 0.5007.
  • Demonstrated low differential uniformity of 10, indicating strong resistance to differential attacks.

Conclusions:

  • The developed key-dependent dynamic S-boxes exhibit excellent cryptographic properties.
  • The proposed scheme offers superior security features compared to existing chaos-based and other S-boxes.
  • The evolved S-boxes are capable of providing high nonlinearity in cryptosystems.