Chaos-based Cryptography: Theory, Algorithms and Applications (Studies in Computational Intelligence, 354)

✍ Scribed by Ljupco Kocarev (editor), Shiguo Lian (editor)

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 400
• Category: Library

✦ Synopsis

Chaos-based cryptography, attracting many researchers in the past decade, is a research field across two fields, i.e., chaos (nonlinear dynamic system) and cryptography (computer and data security). It Chaos' properties, such as randomness and ergodicity, have been proved to be suitable for designing the means for data protection.

 

The book gives a thorough description of chaos-based cryptography, which consists of chaos basic theory, chaos properties suitable for cryptography, chaos-based cryptographic techniques, and various secure applications based on chaos. Additionally, it covers both the latest research results and some open issues or hot topics.

 

The book creates a collection of high-quality chapters contributed by leading experts in the related fields. It embraces a wide variety of aspects of the related subject areas and provide a scientifically and scholarly sound treatment of state-of-the-art techniques to students, researchers, academics, personnel of law enforcement and IT practitioners who are interested or involved in the study, research, use, design and development of techniques related to chaos-based cryptography.

 

✦ Table of Contents

Title page
Preface
Contents
Introduction to Chaos
Introduction
Dynamical Systems
Basic Concepts
Complex Behaviour in One-Dimensional Maps
Example: The Logistic and the H´enon maps
Issue of Invertibility
Fixed Points and Attracting Sets
Stability of Fixed Points
Stability of Periodic Orbits
Invariant Sets and Manifolds
Chaotic Behavior
Main Features of Chaotic Dynamics
Sensitive Dependence on Initial Conditions
Bifurcations
Transcritical bifurcation
Period Doubling Bifurcation
Local vs. Global Analysis
Stretching and Folding
Strange Attractors
Symbolic Dynamics
Invariant Densities and Measures
References
Chaos-Based Public-Key Cryptography
Introduction
Public-Key Encryption
Chaotic Maps
Chebyshev Maps
Torus Automorphisms
Floating Point Implementation of Cryptosystem Based on
Chebyshev Polynomials
Cryptosystem
Correctness of the Cryptosystem
Implementation
Security Analysis of Cryptosystem
Floating Point Implementation of Cryptosystem Based on Jacobian Elliptic Chebyshev Rational Maps
Jacobian Elliptic Chebyshev Rational Maps
Cryptosystem
Correctness of the Cryptosystem
Jacobian Elliptic Functions and Jacobian Elliptic Chebyshev Rational Maps
Efficient Computation of $cn(ω, k), sn(ω, k)$ and $cn^−1(v, k)$
Security Analysis of Cryptosystem
Key Agreement by Using Rational Maps
Entity Authentication Based on Chebyshev Polynomials
Integer Implementation of Cryptosystem Based on Chebyshev Polynomials
Floating-Point Arithmetic versus Integer Arithmetic
Modified Chebyshev Polynomials
Software Implementation
ElGamal Public-Key Encryption with Chebyshev Polynomials
RSA Public-Key Encryption with Chebyshev Polynomials
Conclusion
References
Digitized Chaos for Pseudo-random Number Generation in Cryptography
Introduction
Linear vs. Nonlinear Congruential Generators
Statistically Stable Mixing Systems
Statistical Stability and Correlation Decay
True Random Number Generation with R´enyi Maps
Pseudo-chaotic Systems
Almost-Uniform Measure-Preserving Chaotic Transformations
Random Perturbations
Nonlinear Recurrences Derived from the R´enyi Map
Properties of the Digitized R´enyi Maps
Pseudo-random Perturbation of Digitized Chaotic Systems: Setting the Period Length
On the Hardware/Software Implementation of the Digitized R´enyi Map
PRNGs Derived from the R´enyi Map: Design and Testing
Domain Partitioning in Digitized Chaotic Systems
Conclusions
References
Formation of High-Dimensional Chaotic Maps and Their Uses in Cryptography
Introduction
Formulation of High-Dimensional Chaotic Maps
Multidimensional Generalization
Spatial Extension
Properties of the High-Dimensional Chaotic Maps
Recurrence Plot
Complexity Analysis
Mixing Nature
Cryptographic Applications
32-Bit Chaos-Based Random Number Generator
8-Bit Chaos-Based Random Number Generator Design
Chaos-Based Image Encryption
Conclusions
References
Chaos Based Hash Function
Hash Function
Simple Chaotic Map-Based Hash Function
Typical Algorithm One
Typical Algorithm Two and Its Variant
Typical Algorithm Three
Typical Algorithm Four
Typical Algorithm Five
Complex Map-Based Hash Function
Typical Algorithm One (Using Hyper-Chaotic Map)
Typical Algorithm Two (By Influencing the Parameter of Spatiotemporal Chaos)
Typical Algorithm Three (By Adjusting the State of Spatiotemporal Chaos)
Composite Map-Based Hash Function
Algorithm Description
The Performance Analysis
Chaotic Neural Network-Based Hash Function
Typical Algorithm One
Typical Algorithm Two
Parallel Keyed Hash Function Construction Based on Chaotic Maps
Algorithm Structure
Algorithm Description and Its Characteristics
Performance Analysis
Combined Chaotic Cryptographic and Hashing Scheme
Wong’s Algorithm and Its Security Analysis
Modified Scheme and Its Performance Analysis
Other Ideas for Improvement
Some Instructions on Chaos-Based Hash Function Construction
References
Chaos-Based Video Encryption Algorithms
Introduction
Some Requirements of Video Encryption
Some Video File Formats
MPEG-x
H.26x
Chaos-Based Video Encryption Algorithms
Encrypting the Raw Video Data
Encrypting the Video Data in Compression Process
Encrypting the Compressed Video Data
Performance Evaluation
Security Analysis
Encryption Speed Test
Compression Ratio Test
Error-Robustness Test
Performance Comparison
Discussions
Conclusions
References
Cryptanalysis of Chaotic Ciphers
Introduction
Chaotic $Linear$ Ciphers
Algebraic Attacks
Reconstructing Small Permutations
Algebraic Attack on a Cryptosystem Based on Discretized Two-Dimensional Chaotic Maps
Algebraic Cryptanalysis of a Chaotic Cipher Based on Chaotic Map Lattices
Cryptanalysis of Fridrich’s Image Cipher
Conclusion
References
Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers
Introduction
Main Problems in Chaos-Based Cryptography
Problems with the Selection of the Chaotic System
Problems with the Encryption Architecture
Implementation Problems
Design Rules for Chaos-Based Cryptography
Chaos-Based Cryptography: A Conclusion But Not the End of the Road
Chaos-Based Cryptography on Integer Numbers and Finite Fields
References
Hardware Implementation of Chaos Based Cipher: Design of Embedded Systems for Security Applications
Introduction
Related Works
Chaotic Generators Based Encryption
Tri-dimensional Chaotic Systems: Chaos Behavioral Modeling and Software Simulation
Analog Hardware Implementation
Application to COLPITTS System
Synchronization Problems
Digital Hardware Implementation
Digital Implementation Based on Numerical Resolution of 3D Chaotic Systems
Architecture Exploration
Digital Programmable Hardware Implementation Using $FPGAs$
FPGA Technology
Case Study: Lorenz’s System
RTL Architecture
Logic Hardware Modeling and Simulation
Evaluation on the Effect of the Digital Error Types
Logic Synthesis Results
Physical Implementation: Floorplanning, Placement and Routing
Real Time Measurements
Feed-Back Chaotic Synchronization
Application Image Encryption Scheme
Summary
References
Hardware Implementation of Chaos-Secured Optical Communication Systems
Security in Optical Communications at the Physical Layer
Quantum Cryptography
Optical Chaos Encryption
Optical Chaos Generators in Optical Communications
Non-linear Dynamics in Semiconductor Lasers
Non-linear Dynamics in Photonic Integrated Circuits
Chaos Synchronization in Transmitter/Receiver Configurations
Chaos Synchronization of Semiconductor Lasers with Optical Feedback
Types of Synchronization
Measuring Synchronization
Chaos-Secured Optical Communication Systems
Data Encoding Techniques
EDFA-Based Chaotic Optical Communication Systems
All-Optical Chaotic Optical Communication Systems
Optoelectronic Chaotic Optical Communication Systems
Optical-Chaos-Based Ultra-Fast Physical Random Bit Generators for Secure Communications
Analog Signal Generation
Single-Bit Sampling Systems
Multi-Bit Sampling Systems
Random Bit Generation and Verification
Chaos-Based TRNGs Applied to Cryptography
Conclusions
References
Performance Evaluation of Chaotic and Conventional Encryption on Portable and Mobile Platforms
Introduction
Chaotic and Conventional Encryption Schemes
Chaotic Encryption System
Advanced Encryption Standard (AES)
Performance Evaluation
Methodology
Results
Final Remarks
References
Author Index