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07:56
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Public channel cryptography: chaos synchronization and Hilbert's tenth problem.
Ido Kanter1, Evi Kopelowitz, Wolfgang Kinzel
1Department of Physics, Bar-Ilan University, Ramat-Gan, 52900 Israel.
Physical Review Letters
|September 4, 2008
Summary
This study demonstrates secure synchronization of chaotic maps using private filters. The security is linked to NP-complete problems, offering new possibilities for secure communication protocols.
Area of Science:
- Nonlinear Dynamics
- Information Security
- Computational Complexity
Background:
- Deterministic chaotic maps exhibit complex behavior.
- Synchronization of coupled chaotic systems is a key area in nonlinear dynamics.
- Secure communication protocols are essential for data protection.
Purpose of the Study:
- To demonstrate the synchronization of two mutually delayed coupled deterministic chaotic maps.
- To show that synchronization is preserved when signals are concealed using private filters.
- To establish a connection between chaotic system security and computational complexity theory.
Main Methods:
- Analytical and numerical demonstrations of chaotic map synchronization.
- Application of commutative private filters (convolution or powers of delayed signals) for signal concealment.
- Mapping the passive attacker's task to Hilbert's tenth problem, involving nonlinear Diophantine equations.
Main Results:
- Synchronization of chaotic maps is achieved and maintained even with concealed signals.
- The security analysis reveals a link to NP-complete problems, specifically Hilbert's tenth problem.
- The complexity of breaking the security is shown to be NP-complete.
Conclusions:
- The proposed method provides a robust way to synchronize chaotic maps securely.
- The established connection to NP-complete problems offers a theoretical foundation for advanced cryptographic protocols.
- This research opens new avenues for developing secure public-channel communication systems based on chaotic dynamics.
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