A Christian Liberal Arts University, Est. 1846

Signal Encryption Using a Chaotic Circuit

  • Project Type: Class
  • Directed Project Contributors: Jordan Melendez

Purpose / Abstract

This project explored the application of chaotic circuits to signal encryption.

Introduction / Background

Chaos theory is a relatively new science that has gained popularity among people ranging from scientists to the common person.  In everyday usage, "chaos" translates roughly to "a state of disarray" or "madness," but in chaos theory the word has a more precise de finition.  Although not everyone agrees on one de finition, chaotic systems are characterized by certain qualities:

  1. Sensitivity to initial conditions
  2. Nonlinear behavior
  3. The error in arbitrarily similar initial conditions grows exponentially with time

One incredible application of coupled chaotic circuits is to the fi eld of cryptography.  Chaotic circuits evolve in seemingly random patterns but coupled chaotic circuits can tell the diff erence between two "diff erent kinds" of randomness.  In one mode, the circuits can synchronize.  In the other they cannot.  Switching between these two modes can be a sort of message.  Because the circuit is behaving eff ectively randomly, one would not be able to tell the di fference in the two modes, in principle.  Only with a particular coupled circuit could one determine the synchronous and asynchronous modes and thus, the encrypted message.

Methods

In this project, a simple electrical circuit that can exhibit chaos was built.  The circuit was modeled by a third-order nonlinear di fferential equation.  Two "identical" chaotic circuits were coupled in an attempt to hide binary signals amongst the chaos.  The speed and accuracy of the decryption mechanism was analyzed.

Results

From di fferent grounds and power supplies, our circuit accurately sent and reconstructed a message with under a 1% error despite an off set voltage of 3V.  Because of the chaotic "noise," coupled chaotic circuits have the potential to be a powerful encryption method.

Conclusions

We designed and build chaotic circuits that can send and receive messages even when the transmitter and
receiver are connected to di fferent power supplies.  The transmitting and receiving circuits can synchronize and desynchronize their chaotic modes to send a binary code.  

Chaotic circuits can provide a cheap and accurate glimpse of chaotic systems at an undergraduate level.

Resources / Links

[1] N. I. Hall (Ed.) (1994), Exploring Chaos: A Guide to the New Science of Disorder (p. 7). W. W. Norton & Company, Inc.
[2] L.M. Pecora & T.L. Carroll, Physical Review Letters 64, 821 (1990)
[3] S. Barnett, "The Encryption and Decryption of Digital Signals with Chaotic Circuits." Dated: 07/16/12
[4] T. Knighton, "Chaos and Analog Signal Encryption." Dated: 1/21/2012
[5] K. Kiers, D. Schmidt, & J.C. Sprott (2004), American Journal of Physics 72, 1

View the research paper (PDF)

Bifurcation Plot

Bifurcation Plot

Decrypted Signal

Decrypted Signal