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Cryptanalysis of an Image Encryption Algorithm Based on a 2D Hyperchaotic Map.

Chengrui Zhang1, Junxin Chen2, Dongming Chen1

  • 1Software College, Northeastern University, Shenyang 110169, China.

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|November 11, 2022
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Summary
This summary is machine-generated.

This study breaks a 2D hyperchaotic map image encryption scheme by simplifying its complex diffusion. The proposed attacks (chosen-plaintext and chosen-ciphertext) efficiently reveal the equivalent key, demonstrating practical vulnerabilities.

Keywords:
chosen-ciphertext attackchosen-plaintext attackdiffusionimage encryptionpermutation

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Area of Science:

  • Cryptography and Information Security
  • Applied Mathematics and Chaos Theory

Background:

  • A novel image encryption scheme utilizing a 2D hyperchaotic map with a permutation-diffusion architecture was recently introduced.
  • This scheme employs a three-step process: permutation, forward diffusion, and backward diffusion for data scrambling.

Purpose of the Study:

  • To critically analyze and break the proposed 2D hyperchaotic map-based image encryption scheme.
  • To demonstrate the effectiveness of chosen-plaintext attack (CPA) and chosen-ciphertext attack (CCA) against this cipher.

Main Methods:

  • Analysis of the permutation-diffusion architecture, specifically simplifying the complex forward and backward diffusion processes.
  • Development and application of CPA and CCA to exploit the simplified diffusion mechanism.
  • Theoretical derivation and experimental validation of the attack's feasibility and efficiency.

Main Results:

  • The complex diffusion steps were successfully simplified into two basic diffusions and a modular addition.
  • The equivalent secret key was recovered using both CPA and CCA, confirming the attack's success.
  • Attack execution time was under 2 hours for a 256x256 image on standard hardware, indicating practical efficiency.

Conclusions:

  • The analyzed image encryption scheme based on a 2D hyperchaotic map is vulnerable to both CPA and CCA.
  • The simplification of diffusion processes is key to efficiently obtaining the equivalent secret key.
  • Suggestions for improving the scheme's security against such attacks are provided, with source code available.