Chaos synchronization and its application to secure communication

Chaos theory is well known as one of three revolutions in physical sciences in 20th-century, as one physicist called it: Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurable process; and chaos eliminates the Laplacian fantasy of deterministic predictability". Specially, when chaos synchronization was found in 1991, chaos theory becomes more and more attractive. Chaos has been widely applied to many scientific disciplines: mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics. One of most important engineering applications is secure communication because of the properties of random behaviours and sensitivity to initial conditions of chaos systems. Noise-like dynamical behaviours can be used to mask the original information in symmetric cryptography. Sensitivity to initial conditions and unpredictability make chaotic systems very suitable to construct one-way function in public-key cryptography. In chaos-based secure communication schemes, information signals are masked or modulated (encrypted) by chaotic signals at the transmitter and the resulting encrypted signals are sent to the corresponding receiver across a public channel (unsafe channel). Perfect chaos synchronization is usually expected to recover the original information signals. In other words, the recovery of the information signals requires the receiver's own copy of the chaotic signals which are synchronized with the transmitter ones. Thus, chaos synchronization is the key technique throughout this whole process. Due to the difficulties of generating and synchronizing chaotic systems and the limit of digital computer precision, there exist many challenges in chaos-based secure communication. In this thesis, we try to solve chaos generation and chaos synchronization problems. Starting from designing chaotic and hyperchaotic system by first-order delay differential equation, we present a family of novel cell attractors with multiple positive Lyapunov exponents. Compared with previously reported hyperchaos systems with complex mathematic structure (more than 3 dimensions), our system is relatively simple while its dynamical behaviours are very complicated. We present a systemic parameter control method to adjust the number of positive Lyapunov exponents, which is an index of chaos degree. Furthermore, we develop a delay feedback controller and apply it to Chen system to generate multi-scroll attractors. It can be generalized to Chua system, Lorenz system, Jerk equation, etc. Since chaos synchronization is the critical technique in chaos-based secure communication, we present corresponding impulsive synchronization criteria to guarantee that the receiver can generate the same chaotic signals at the receiver when time delay and uncertainty emerge in the transmission process. Aiming at the weakness of general impulsive synchronization scheme, i.e., there always exists an upper boundary to limit impulsive intervals during the synchronization process, we design a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS). IISS can not only be flexibly applied to the scenario where the control window is restricted but also improve the security of chaos-based secure communication via reducing the control window width and decreasing the redundancy of synchronization signals. Finally, we propose chaos-based public-key cryptography algorithms which can be used to encrypt synchronization signals and guarantee their security across the public channel

New hyperchaotic system with single nonlinearity, its electronic circuit and encryption design based on current conveyor

Nowadays, hyperchaotic system (HCSs) have been started to be used in engineering applications because they have complex dynamics, randomness, and high sensitivity. For this purpose, HCSs with different features have been introduced in the literature. In this work, a new HCS with a single discontinuous nonlinearity is introduced and analyzed. The proposed system has one saddle focus equilibrium. When the dynamic properties and bifurcation graphics of the system are analyzed, it is determined that the proposed system exhibits the complex phenomenon of multistability. Moreover, analog electronic circuit design of the proposed system is performed with positive second-generation current conveyor. In addition, an encryption circuit is designed to demonstrate that the proposed system can be used in various engineering applications

Enabling Space-Air integration: A Satellite-UAV networking authentication scheme

One of the goals of sixth-generation mobile networks (6G) is to achieve a larger network coverage area. Satellite networks enable global coverage and aerial nodes such as Unmanned Aerial Vehicle (UAV) can serve as a supplement to ground networks in remote environments. Therefore, 6G networks are gradually evolving towards Space-Air-Ground integrated networks. The combination of UAV networks and satellite networks is a research hotspot in the field of Space-Air integrated networks. However, the combination of UAV networks and satellite networks currently faces many challenges in terms of security. The characteristics of large propagation delay and unstable communication links in satellite networks make them vulnerable to various attacks, including eavesdropping, tampering, and impersonation. Meanwhile, existing research on UAV networks mainly focuses on UAV-Ground networking authentication mechanisms, which are not suitable for resource-constrained nodes in the Space-Air integration scenario. Therefore, based on elliptic curve public key cryptography and Chebyshev polynomial, we propose a secure networking authentication scheme for satellite nodes and UAV nodes in the Space-Air integration scenario. The security analysis indicates that our scheme possesses security attributes such as mutual authentication, key agreement, identity anonymity, unlinkability, perfect forward-backward security, and resistance against various protocol attacks, among other security properties. Performance analysis also indicates certain advantages of our scheme over existing schemes in terms of signaling, bandwidth, and computational overhead

Estudio de mapeos caóticos discretos y su aplicación en criptografía

"La seguridad de la información digital cada vez tiene más auge, debido al creciente uso de dispositivos móviles, además del incremento de operaciones realizadas a través de internet. Esto representa un gran reto ya que para lograr la confidencialidad, integridad y autentificación es necesario el uso de mecanismos especializados, una forma de proporcionar estos servicios es por medio de la criptografía, sin embargo, la creciente demanda requiere de nuevos algoritmos que sean más rápidos y a su vez más seguros. Una opción para lograr estos objetivos es la criptografía basada en sistemas caóticos. Este trabajo de tesis se presenta en tres partes, en la primera parte se muestran los conceptos y definiciones básicas de las ¿áreas de criptografía y sistemas dinámicos, así como las herramientas que se tienen para estudiar cada uno de estos sistemas. Además se da una visión general de estas áreas así como una clasificación, de tal forma que nos enfocaremos en cifrados en flujo y en sistemas dinámicos de tiempo discreto. Cabe señalar que los sistemas dinámicos estudiados en este trabajo a diferencia del mapeo logístico y casa de campaña son multi-modales, los cuales presentan ciertas ventajas en comparación con los mapeos uni-modales. Posteriormente se analizan las similitudes y diferencias que se encuentran en estas dos áreas, dando lugar a la criptografía caótica, la cual ha sido objeto de estudio por diversos grupos de investigación en los últimos años. En la segunda parte de este trabajo se proponen metodologías para construir dos generadores pseudo-aleatorios, los cuales son la parte fundamental en el uso de cifrados en flujo, por un lado se propone el uso de valores positivos y negativos en el parámetro de bifurcación del mapeo logístico en conjunto con retardos, de esta forma es posible construir un generador que muestra resultados satisfactorios a las pruebas estadísticas de aleatoriedad propuestas por el NIST y además no es posible reconstruir el espacio fase. Por otro lado se presenta un generador basado en mapeos multi-modales el cual obtiene una secuencia binaria por medio de la combinación de diferentes modas, la principal ventaja radica en que solo es necesario definir un mapeo para obtener diferentes comportamientos, de igual forma este generador presenta resultados satisfactorios al ser evaluado por las pruebas estadísticas propuestas por el NIST.""The security of digital information is increasingly due to increasing use of mobile devices, in addition to the increase in transactions conducted via Internet. This represents a great challenge in order to achieve confidentiality, integrity and authentication is necessary use specialized mechanisms, a way of providing these services is through cryptography, however, the growing demand requires new algorithms that are faster and safe. One option to achieve these goals is chaos based cryptography. This thesis is presented in three parts, in the first part the basic concepts and definitions of the cryptography and dynamic systems as well as the tools to study each of these systems are shown. Furthermore an overview of these areas and a classification is given, we will focus on stream ciphers and discrete time dynamical systems. Note that the dynamical systems studied in this work unlike the logistic and tent map are multimodal, which have certain advantages compared with uni-modal maps. Afterwards the similarities and differences found in these two areas are analyzed, resulting in chaotic cryptography, which has been studied by several research groups in recent years. In the second part of this work we construct two pseudo-random generators, which are an essential part in the use of stream ciphers, in one hand we propose use positive and negative values in the bifurcation parameter of the logistic map together with delays, in this way it is possible to build a generator showing satisfactory results to statistical tests of randomness proposed by the NIST and it is not possible to reconstruct the phase space. On the other hand we present a generator based on multi-modal maps which produce a binary sequence obtained by combining different modal, the main advantage is that it is only necessary to define one map for different behaviors, similarly this generator presents satisfactory results when is evaluated by statistical tests proposed by the NIST.