Cryptology Transmitted Message Protection - From Deterministic Chaos up to Optical Vortices

Acknowledgments

Contents

About the Authors

Abbreviations

Introduction

1 Deterministic Chaos Phenomenon from the Standpoint of Information Protection Tasks

1.1 Principles and Concepts of the Classical Cryptology as the Traditional Strategy of Information Protection

1.2 The Optical Vortex as a Product of the Beam Perturbation and the Data Carrier in the Communication System

1.3 Examples of Dynamic Systems in Radiophysics and Optics with Complicated Behavior

1.3.1 Examples of Radio Physical Systems with Complicated Behavior

1.3.2 Designs of Nonlinear Elements

1.3.3 The Nonlinear Ring Interferometer as an Example of the Optical System with Complex Behavior

1.4 Principles of Information Protection by the Deterministic Chaos

1.4.1 General Schemes and Functioning Principles of the Confidential Communication Systems in the Mode of the Dynamic Chaos

1.4.2 Examples of Radio Physical Systems for Information Protection

1.4.3 Examples of the Application of Deterministic Chaos in Optical System of the Confidential Communication

1.4.4 Influence of Disturbing Factors on the Characteristics of the Data Transmission System

1.4.5 Classification of Communication Systems Using the Dynamic Chaos

1.5 Conclusions

2 Radiophysical and Optical Chaotic Oscillators Applicable for Information Protection

2.1 The Radio-Electronic Oscillator of the Deterministic Chaos with Nonlinearity in the Form of Parabola Compositions

2.1.1 The Structure and the Mathematical Model of the Oscillator

2.1.2 The Nonlinear Element: A Structure, a Mathematical Description

2.1.3 Analysis of Equilibrium State Stability in the Model of the Deterministic Chaos Oscillator

2.2 Simulation of Static and Dynamic Modes of the Deterministic Chaos Oscillator

2.2.1 Stability of Equilibrium States

2.2.2 Operating Modes in the Deterministic Chaos Oscillator

2.3 Modes and Scenarios of Transitions to Chaotic Oscillations in the Radio-Frequency Oscillator of Deterministic Chaos

2.3.1 The Breadboard of Deterministic Chaos Oscillator

2.3.2 Transition to the Chaos Through the Period Doubling Bifurcation

2.3.3 Transition to the Chaos Through Intermittency

2.3.4 Transition to the Chaos Through a Collapse of Two-Frequency Oscillating Mode

2.3.5 Transition to the Chaos Through a “Semi-Torus” Collapse

2.3.6 Bifurcation Diagrams

2.4 The Ring Interferometer with the Kerr Nonlinear Medium and Its Modifications as the Deterministic Chaos Oscillators

2.4.1 Mathematical Models of Processes in the Nonlinear Ring Interferometer

2.4.2 Double-Circuit Nonlinear Ring Interferometer and Models of Processes in It

2.4.3 Dynamics in the Ring Interferometer Models

2.4.4 The Nonlinear Fiber-Optical Interferometer

2.4.5 The Double-Circuit NRI and Structurally Connected NRIs: Prospects for Chaos Generating and Data Processing

2.5 Conclusions

References

3 Radio Electronic System for Data Transmission on the Base of the Chaotic Oscillator with Nonlinearity in the form of Parabola Composition: Modeling and Experiment

3.1 Description of the Data Transmission System

3.1.1 The Structure of the Data Transmission System on the Base of the Chaotic Oscillator, Its Mathematical Model, and a Quality Criteria

3.1.2 Temperature Dependence of the Transfer Characteristics of the Nonlinear Element

3.1.3 Temperature Compensation in the Voltage Limiter on the Shottky Diodes and a Choice of the Nonlinear Element Parameters

3.2 Numerical Modeling of the Data Transmission System Operation

3.2.1 Lack of the Coincidence Influence of the Transmitter and Receiver Parameters on the Data Transmission Quality

3.2.2 Temperature Mismatching Influence of the Transmitter and the Receiver on Data Transmission Quality

3.2.3 The Role of Noises, Filtering, Level-Discretization in the Communication Channel

3.2.4 From Bias Voltage Manipulation in the Oscillator of the Deterministic Chaos to Transmission and Reception of Digital Signals

3.3 Description and Characteristics of the Chaotic Communication System Breadboard, Experimental Reception-Transmission of Analog, Digital and Video Signals

3.3.1 The Breadboard of the Data Transmission System

3.3.2 SNR Measurement in the Laboratory Experiment at Mismatching of the Transmitter and the Receiver Parameters

3.4 Experimental Operation Studying of the Communication System with the Complete Chaotic Synchronization

3.4.1 Transmission and Reception of Analog, Digital and Video Signals

3.4.2 Influence of Data Transmission System Parameters on SNR

3.5 Conclusions

References

4 Single- and Double-Circuit Nonlinear Ring Interferometer as a Cipherer in Optical Systems of Synchronous Chaotic Communications

4.1 Confident Communication System Based on NRI

4.1.1 Substantiation of the Recovering Possibility for the Signal Made Chaotic by Means of the NRI

4.1.2 “Route-Operator Formalism” and Synthesis of the Cryptosystem Structural Scheme

4.1.3 Simulation of Secret Transmission of Images: Modes of Deterministic Spatial-Temporal and Spatial Chaos

4.1.4 Deciphering Error ?(r, t) as a Wave Process and Its Normalizing Amplitude A? as a Function of Setting Errors of the Decipherer. Evaluation of A?

4.1.5 Statistical Characteristics of the Relative Deciphering Error Amplitude ??(r, t): Simulation Data and Theoretical Estimations

4.1.6 Imitation of “Cracking” of the Delay Time in NRI

4.2 Imitation of the DNRI Parameters Cracking Based on the Correlation Analysis: Discussion of Advantages

4.2.1 The Case of Field Transformation in FBL (Time Delay Estimation)

4.2.2 Cases with the Field Rotation in the One Feedback Loop with the Same and Various Field Rotations in FBL

4.3 Conclusions

References

5 Optical Vortices in Ring and Non-ring Interferometers and a Model of the Digital Communication System

5.1 The Idea of the Singular-Optical Communication System

5.2 Nonlinear Ring Interferometer as an Option Detector for the Screw Dislocation Order

5.3 Rozhdestvenskiy’s Interferometer as a Vortex Detector

5.3.1 A Principle and Description of Vortex Detection with the Help of Rozhdestvenskiy’s Interferometer at Noise Presence

5.3.2 Simulation of Rozhdestvenskiy’s Interferometer Operation as a Vortex Detector and Its Characteristics Analysis at Presence of the White (Phase and Amplitude) Noise

5.3.3 Influence of the Optical Axes Displacement of the Source and Receiver Beam upon the Relative Intensity Value. Possibility of Optical Vortex Position Finding

5.3.4 Determination of the Screw Dislocation Order in the Presence of Beam Distortions Caused by Turbulence

5.4 The Data Transmission System on the Basis of the Optical Vortex Detector: The Operation Principle, a Model, Simulation of Turbulence or Noise Influence

5.4.1 Coding of the Information Bit by the Relative Intensity Value {\rm I}_{{ r}} or Its Change. Theoretical Backgrounds for Calculations of the Probability of Error in Data Transfer

5.4.2 Analysis of the Influence of the Turbulent Screen and Communication System Parameters on the Error in Data Transfer

5.5 The Visual Analysis of Phase and Amplitude Distributions of the Input Signal of Vortex Topologic Charge Detector at Presence of the Turbulence

5.6 Conclusions

References

6 Variety of Nonlinear Type in the Chaotic Oscillator and Structure Organization of the Chaotic Communication System as a Way to Increase the Confidence Degree

6.1 A Variety of Structural Organization of Nonlinear-Dynamic Systems of Confidential Communication and Its Classification

6.2 Elements with Nonlinear Transfer Characteristic: Universality of Its “Constructions” and a Concept of Self-controlled Nonlinearity

6.3 Conclusions

References

7 Nonlinear-Dynamic Cryptology Versus Steganography and Cryptografics

References

Index