Deterministic Chaos in Digital Cryptography

This thesis studies the application of deterministic chaos to digital cryptography. Cryptographic systems such as pseudo-random generators (PRNG), block ciphers and hash functions are regarded as a dynamic system (X, j), where X is a state space (Le. message space) and f : X -+ X is an iterated function. In both chaos theory and cryptography, the object of study is a dynamic system that performs an iterative nonlinear transformation of information in an apparently unpredictable but deterministic manner. In terms of chaos theory, the sensitivity to the initial conditions together with the mixing property ensures cryptographic confusion (statistical independence) and diffusion (uniform propagation of plaintext and key randomness into cihertext). This synergetic relationship between the properties of chaotic and cryptographic systems is considered at both the theoretical and practical levels: The theoretical background upon which this relationship is based, includes discussions on chaos, ergodicity, complexity, randomness, unpredictability and entropy. Two approaches to the finite-state implementation of chaotic systems (Le. pseudo-chaos) are considered: (i) floating-point approximation of continuous-state chaos; (ii) binary pseudo-chaos. An overview is given of chaotic systems underpinning cryptographic algorithms along with their strengths and weaknesses. Though all conventional cryposystems are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are sufficient to guarantee cryptographic strength and security. A dynamic system is said to have an analytical solution Xn = (xo) if any trajectory point Xn can be computed directly from the initial conditions Xo, without performing n iterations. A chaotic system with an analytical solution may have a unpredictable multi-valued map Xn+l = f(xn). Their floating-point approximation is studied in the context of pseudo-random generators. A cryptographic software system E-Larm ™ implementing a multistream pseudo-chaotic generator is described. Several pseudo-chaotic systems including the logistic map, sine map, tangent- and logarithm feedback maps, sawteeth and tent maps are evaluated by means of floating point computations. Two types of partitioning are used to extract pseudo-random from the floating-point state variable: (i) combining the last significant bits of the floating-point number (for nonlinear maps); and (ii) threshold partitioning (for piecewise linear maps). Multi-round iterations are produced to decrease the bit dependence and increase non-linearity. Relationships between pseudo-chaotic systems are introduced to avoid short cycles (each system influences periodically the states of other systems used in the encryption session). An evaluation of cryptographic properties of E-Larm is given using graphical plots such as state distributions, phase-space portraits, spectral density Fourier transform, approximated entropy (APEN), cycle length histogram, as well as a variety of statistical tests from the National Institute of Standards and Technology (NIST) suite. Though E-Larm passes all tests recommended by NIST, an approach based on the floating-point approximation of chaos is inefficient in terms of the quality/performance ratio (compared with existing PRNG algorithms). Also no solution is known to control short cycles. In conclusion, the role of chaos theory in cryptography is identified; disadvantages of floating-point pseudo-chaos are emphasized although binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite

Dynamic block encryption with self-authenticating key exchange

One of the greatest challenges facing cryptographers is the mechanism used for key exchange. When secret data is transmitted, the chances are that there may be an attacker who will try to intercept and decrypt the message. Having done so, he/she might just gain advantage over the information obtained, or attempt to tamper with the message, and thus, misguiding the recipient. Both cases are equally fatal and may cause great harm as a consequence. In cryptography, there are two commonly used methods of exchanging secret keys between parties. In the first method, symmetric cryptography, the key is sent in advance, over some secure channel, which only the intended recipient can read. The second method of key sharing is by using a public key exchange method, where each party has a private and public key, a public key is shared and a private key is kept locally. In both cases, keys are exchanged between two parties. In this thesis, we propose a method whereby the risk of exchanging keys is minimised. The key is embedded in the encrypted text using a process that we call `chirp coding', and recovered by the recipient using a process that is based on correlation. The `chirp coding parameters' are exchanged between users by employing a USB flash memory retained by each user. If the keys are compromised they are still not usable because an attacker can only have access to part of the key. Alternatively, the software can be configured to operate in a one time parameter mode, in this mode, the parameters are agreed upon in advance. There is no parameter exchange during file transmission, except, of course, the key embedded in ciphertext. The thesis also introduces a method of encryption which utilises dynamic blocks, where the block size is different for each block. Prime numbers are used to drive two random number generators: a Linear Congruential Generator (LCG) which takes in the seed and initialises the system and a Blum-Blum Shum (BBS) generator which is used to generate random streams to encrypt messages, images or video clips for example. In each case, the key created is text dependent and therefore will change as each message is sent. The scheme presented in this research is composed of five basic modules. The first module is the key generation module, where the key to be generated is message dependent. The second module, encryption module, performs data encryption. The third module, key exchange module, embeds the key into the encrypted text. Once this is done, the message is transmitted and the recipient uses the key extraction module to retrieve the key and finally the decryption module is executed to decrypt the message and authenticate it. In addition, the message may be compressed before encryption and decompressed by the recipient after decryption using standard compression tools

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product - CrypsticTM - which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed

Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Gramatická evoluce v jazyce nezávislém na výpočetní platformě

Import 05/08/2014The thesis aims on implementation of grammar evolution in a platform-independent language. Grammar evolution is an advanced optimization technique from a field of evolutionary algorithms. Its range of applications is very wide and covers many engineering, economical and other fields of science. The thesis is divided into three parts. The first one is rather theoretical and describes the principles of grammar evolution and evolutionary algorithms in general. The second part describes my own implementations of grammar evolution and the experiments for which I have used them. The last part concludes achieved results and also proposes the ways of further research of the topic.Předmětem této diplomové práce je implementace gramatické evoluce v jazyce nezávislém na platformě. Gramatická evoluce je pokročilá optimalizační technika, která spadá do oblasti evolučních algoritmů. Možnosti jejího využití jsou široké a pokrývají spoustu odvětví inženýrských, ekonomických a dalších oborů. Práce je rozdělena do tří částí. První část je teoretická a pojednává o principech gramatické evoluci a evolučních algoritmů obecně. Druhá část popisuje mé implementace programů, které jsem v rámci této diplomové práce vytvořil a experimenty, které jsem s nimi prováděl. Poslední část obsahuje shrnutí této práce a nabízí možnosti dalšího vývoje.460 - Katedra informatikyvýborn

Cryptography and Its Applications in Information Security

Nowadays, mankind is living in a cyber world. Modern technologies involve fast communication links between potentially billions of devices through complex networks (satellite, mobile phone, Internet, Internet of Things (IoT), etc.). The main concern posed by these entangled complex networks is their protection against passive and active attacks that could compromise public security (sabotage, espionage, cyber-terrorism) and privacy. This Special Issue “Cryptography and Its Applications in Information Security” addresses the range of problems related to the security of information in networks and multimedia communications and to bring together researchers, practitioners, and industrials interested by such questions. It consists of eight peer-reviewed papers, however easily understandable, that cover a range of subjects and applications related security of information

A new class of efficient piecewise nonlinear chaotic maps for secure cryptosystems

In this paper we construct a new class of nonlinear chaotic maps for secure cryptosystems. These maps can overcome the security holes brought by the "piecewise linearity" of the previous Piecewise Linear Chaotic Maps (PWLCM) due to a fact that the chaotic sequences generated by the derived iterative system based on the proposed maps are proved to have perfect dynamic properties, such as uniform invariant distribution, d-like autocorrelation function etc. Furthermore, the relative quantized two-value sequences also have perfect secure statistical characteristics. In terms of computing speed, the proposed maps have faster speed than the recently proposed nonlinear "piecewise-square-root" maps (PSRM), and they actually have equivalently the same computing speed with the linear PWLCM