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Norton's Theorem01:14

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Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one depicted...
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Updated: Nov 27, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Novel Image Encryption Scheme Based on Collatz Conjecture.

Dora M Ballesteros1, Jimmy Peña1, Diego Renza1

  • 1Telecommunications Engineering, Universidad Militar Nueva Granada, Carrera 11 No. 101-80, Bogotá 110111, Colombia.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a novel image encryption method using Collatz conjecture-based variable length codes to convert images into audio. The technique offers robust security with high randomness and key sensitivity for effective image privacy protection.

Keywords:
Collatz conjectureciphered audiodiffusionimage encryptionscrambling

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Area of Science:

  • Cryptography
  • Information Security
  • Computer Science

Background:

  • Traditional image encryption methods like scrambling and diffusion are vulnerable to cryptanalysis.
  • Existing techniques often lack robustness and can be compromised.
  • There is a need for novel, secure image encryption schemes.

Purpose of the Study:

  • To propose a new image encryption method that simultaneously performs scrambling and diffusion.
  • To enhance image privacy protection using a non-linear, key-dependent approach.
  • To leverage the Collatz conjecture for secure image data transformation.

Main Methods:

  • Image data is transformed into non-intelligible audio using variable length codes based on the Collatz conjecture.
  • Scrambling and diffusion are integrated into a single, non-linear process.
  • A large key space (8.57 x 10^506) ensures unique ciphered outputs for each key.

Main Results:

  • Ciphered audio signals exhibit maximum randomness, indicated by high entropy and disorder.
  • Fractal behavior is observed in scatter plots of adjacent samples, altering natural image characteristics.
  • The encryption method demonstrates high key sensitivity, rendering images unrecoverable with minor key modifications.

Conclusions:

  • The proposed method offers a highly secure and effective approach to image privacy protection.
  • The simultaneous scrambling and diffusion, combined with non-linearity, enhances cryptographic strength.
  • The method's reliance on the Collatz conjecture provides a unique and robust encryption mechanism.