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Fast Fourier Transform01:10

Fast Fourier Transform

451
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Double-Color-Image Compression-Encryption Algorithm Based on Quaternion Multiple Parameter DFrAT and Feature Fusion

Meihua Xiao1, Ruixiao Tan1, Huosheng Ye2

  • 1School of Software, East China Jiaotong University, Nanchang 330013, China.

Entropy (Basel, Switzerland)
|July 27, 2022
PubMed
Summary

A new double-color image encryption algorithm uses quaternion multiple parameter discrete fractional angular transform (QMPDFrAT) and a novel permutation-diffusion mechanism. This method enhances security and improves image reconstruction quality for encrypted color images.

Keywords:
double-color-image encryptionnon-adjacent coupled map latticesquaternionrandom pixel insertion

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Area of Science:

  • Computer Science
  • Cryptography
  • Image Processing

Background:

  • Secure encryption of color images is crucial for data protection.
  • Existing methods often face challenges in balancing security and reconstruction quality.
  • The need for robust algorithms for multiple color image encryption is growing.

Purpose of the Study:

  • To design a secure and efficient double-color image encryption algorithm.
  • To enhance the security and reconstruction quality of encrypted color images.
  • To introduce a novel approach using quaternion transforms and permutation-diffusion.

Main Methods:

  • Definition and application of quaternion multiple parameter discrete fractional angular transform (QMPDFrAT).
  • Utilizing two-dimensional discrete wavelet transform for sub-band decomposition.
  • Implementing a nonlinear spherical transform and a plaintext-related joint permutation-diffusion mechanism.

Main Results:

  • The proposed algorithm successfully encrypts double-color images.
  • Achieved higher quality of image reconstruction compared to similar schemes.
  • Numerical simulations confirmed the algorithm's feasibility and high security.

Conclusions:

  • The developed QMPDFrAT-based algorithm provides a secure method for double-color image encryption.
  • The combination of QMPDFrAT, nonlinear operations, and permutation-diffusion offers enhanced protection.
  • The algorithm demonstrates superior performance in both security and image reconstruction quality.