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

FPGA based secure and noiseless image transmission using LEA and optimized bilateral filter

In today’s world, the transmission of secured and noiseless image is a difficult task. Therefore, effective strategies are important to secure the data or secret image from the attackers. Besides, denoising approaches are important to obtain noise-free images. For this, an effective crypto-steganography method based on Lightweight Encryption Algorithm (LEA) and Modified Least Significant Bit (MLSB) method for secured transmission is proposed. Moreover, a bilateral filter-based Whale Optimization Algorithm (WOA) is used for image denoising. Before image transmission, the secret image is encrypted by the LEA algorithm and embedded into the cover image using Discrete Wavelet Transform (DWT) and MLSB technique. After the image transmission, the extraction process is performed to recover the secret image. Finally, a bilateral filter-WOA is used to remove the noise from the secret image. The Verilog code for the proposed model is designed and simulated in Xilinx software. Finally, the simulation results show that the proposed filtering technique has superior performance than conventional bilateral filter and Gaussian filter in terms of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM)

The dynamics of complex systems. Studies and applications in computer science and biology

Our research has focused on the study of complex dynamics and on their use in both information security and bioinformatics. Our first work has been on chaotic discrete dynamical systems, and links have been established between these dynamics on the one hand, and either random or complex behaviors. Applications on information security are on the pseudorandom numbers generation, hash functions, informationhiding, and on security aspects on wireless sensor networks. On the bioinformatics level, we have applied our studies of complex systems to theevolution of genomes and to protein folding

On the Development of Novel Encryption Methods for Conventional and Biometric Images

Information security refers to the technique of protecting information from unauthorized access, use, disclosure, disruption and modification. Governments, military, corporations, financial institutions, hospitals, and private businesses amass a great deal of confidential information about their employees, customers, products, research, and financial status. Most of this information is now collected, processed and stored on electronic media and transmitted across networks to other computers. Encryption clearly addresses the need for confidentiality of information, in process of storage and transmission. Popular application of multimedia technology and increasingly transmission ability of network gradually leads us to acquire information directly and clearly through images and hence the security of image data has become inevitable. Moreover in the recent years, biometrics is gaining popularity for security purposes in many applications. However, during communication and transmission over insecure network channels it has some risks of being hacked, modified and reused. Hence, there is a strong need to protect biometric images during communication and transmission. In this thesis, attempts have been made to encrypt image efficiently and to enhance the security of biometrics images during transmission. In the first contribution, three different key matrix generation methods invertible, involuntary, and permutation key matrix generation have been proposed. Invertible and involuntary key matrix generation methods solves the key matrix inversion problem in Hill cipher. Permutation key matrix generation method increases the Hill system’s security. The conventional Hill cipher technique fails to encrypt images properly if the image consists of large area covered with same colour or gray level. Thus, it does not hide all features of the image which reveals patterns in the plaintext. Moreover, it can be easily broken with a known plaintext attack revealing weak security. To address these issues two different techniques are proposed, those are advanced Hill cipher algorithm and H-S-X cryptosystem to encrypt the images properly. Security analysis of both the techniques reveals superiority of encryption and decryption of images. On the other hand, H-S-X cryptosystem has been used to instil more diffusion and confusion on the cryptanalysis. FPGA implementation of both the proposed techniques has been modeled to show the effectiveness of both the techniques. An extended Hill cipher algorithm based on XOR and zigzag operation is designed to reduce both encryption and decryption time. This technique not only reduces the encryption and decryption time but also ensures no loss of data during encryption and decryption process as compared to other techniques and possesses more resistance to intruder attack. The hybrid cryptosystem which is the combination of extended Hill cipher technique and RSA algorithm has been implemented to solve the key distribution problem and to enhance the security with reduced encryption and decryption time. Two distinct approaches for image encryption are proposed using chaos based DNA coding along with shifting and scrambling or poker shuffle to create grand disorder between the pixels of the images. In the first approach, results obtained from chaos based DNA coding scheme is shifted and scrambled to provide encryption. On the other hand in the second approach the results obtained from chaos based DNA coding encryption is followed by poker shuffle operation to generate the final result. Simulated results suggest performance superiority for encryption and decryption of image and the results obtained have been compared and discussed. Later on FPGA implementation of proposed cryptosystem has been performed. In another contribution, a modified Hill cipher is proposed which is the combination of three techniques. This proposed modified Hill cipher takes advantage of all the three techniques. To acquire the demands of authenticity, integrity, and non-repudiation along with confidentiality, a novel hybrid method has been implemented. This method has employed proposed modified Hill cipher to provide confidentiality. Produced message digest encrypted by private key of RSA algorithm to achieve other features such as authenticity, integrity, and non-repudiation To enhance the security of images, a biometric cryptosystem approach that combines cryptography and biometrics has been proposed. Under this approach, the image is encrypted with the help of fingerprint and password. A key generated with the combination of fingerprint and password and is used for image encryption. This mechanism is seen to enhance the security of biometrics images during transmission. Each proposed algorithm is studied separately, and simulation experiments are conducted to evaluate their performance. The security analyses are performed and performance compared with other competent schemes

Encriptación sobre Capa Física para Ethernet Óptico de Alta Velocidad

INTRODUCCIÓN-------------------------Hoy en día, los enlaces ópticos con tasas de transmisión de hasta 100 Gbps y superiores son ya una realidad. Gracias a los avances logrados en las comunicaciones ópticas durante las últimas décadas es posible afrontar anchos de banda cada vez mayores, lo que satisface las demandas de las aplicaciones más exigentes [CIS16], como por ejemplo las basadas en cloud computing o big data. Por otro lado, la seguridad en la información sigue siendo un asunto de gran importancia en las comunicaciones ya que el volumen de amenazas en la red se ha incrementado durante los últimos años [CIS18]. Los fallos en la seguridad podrían llevar al mal funcionamiento de un servicio o la pérdida de confidencialidad en datos críticos de los clientes. En un sistema de comunicaciones por capas, como por ejemplo en el modelo OSI (Open System Interconnection) o TCP/IP (Transmission Control Protocol/Internet Protocol), se pueden llevar a cabo tanto ataques pasivos como activos en los diferentes niveles de la comunicación. Dependiendo de las capas de comunicación utilizadas, distintos mecanismos pueden ser adoptados para lograr la seguridad de la información. Por ejemplo, protocolos estandarizados tales como MACsec [IEE06] o IPsec [KEN05] son empleados normalmente en la capa 2 (capa de enlace de datos) y capa 3 (capa de red), respectivamente. En ambos casos la encriptación es llevada a cabo en cada trama o paquete de datos de forma individual. Para el caso particular de las redes ópticas, el análisis de las amenazas en su capa 1 (capa física) también es considerado crítico para garantizar unas comunicaciones seguras [SKO16], [FUR14]. En este caso se pueden destacar tres tipos de ataques: ataques de inserción de señal, ataques por splitting y ataques a las infraestructuras físicas. Los ataques por splitting son normalmente empleados para espionaje pasivo o para producir degradación en la señal [SKO16], estos se pueden llevar a cabo fácilmente gracias a técnicas de derivación en la fibra. De hecho, hoy en día ya existen métodos de bajo coste para interceptar la señal óptica gracias a dispositivos de acoplamiento óptico y conversores electroópticos sin la necesidad de interferir perceptiblemente en las comunicaciones [ZAF11]. Con el fin de tratar estas amenazas y proteger la confidencialidad de los datos en la capa física, varios mecanismos relacionados con tecnologías fotónicas han sido propuestos [FOK11], por ejemplo OCDM (Optical Code Division Multiplexing) [JI17], SCOC (Secure Communications using Optical Chaos) [HIZ10] o QKD (Quantum Key Distribution) [ELK13]. Otras técnicas, también relacionadas con protocolos de capa física, cifran la información a nivel de bit independientemente de la tecnología fotónica empleada, como la encriptación de los datos del payload en las tramas OTN (Optical Transport Network) [GUA16]. Algunas de las ventajas reivindicadas por estas técnicas de encriptación consisten en cifrar la información “al vuelo” introduciendo un overhead nulo en los datos y una latencia muy baja (en el rango de nanosegundos) en la información transmitida [GUA16]. De hecho, hoy en día ya están disponibles en el mercado equipos de comunicaciones OTN que realizan el cifrado a la velocidad de línea sin mermar el throughput, es decir consiguiendo un rendimiento de la transmisión del 100% [MIC16]. Esto contrasta con lo que hacen ciertos protocolos en otras capas de comunicación [KOL13], [XEN06]. Por ejemplo, IPsec generalmente introduce latencias en el rango de milisegundos. Además, el overhead introducido por IPsec durante el cifrado limita el rendimiento de transmisión a valores entre el 20% y el 90% de la máxima tasa de datos posible sin encriptación [TRO05], [KOL13]. Aparte de lograr la confidencialidad, alguno de los métodos mencionados anteriormente también es capaz de conseguir privacidad contra intrusos pasivos [FOK11], entendiendo esta como la amenaza cuando dichos intrusos pueden detectar simplemente la presencia de comunicaciones, aunque sean incapaces de descifrar el contenido de la información de las mismas. Esta habilidad puede ofrecer seguridad contra ataques basados en el análisis de los patrones del tráfico, que permitirían revelar información del comportamiento de una compañía o instalación. Dentro de los estándares de comunicaciones ópticas, Ethernet es uno de los más empleados hoy día. Un claro ejemplo es el acceso a las redes de transporte ópticas donde este estándar es utilizado normalmente cuando las tasas de acceso superan el gigabit por segundo. Tal y como se muestra en la Fig.1-1, algunas tecnologías de acceso en los tramos de última milla de las CEN (Carrier Ethernet Networks) son Ethernet sobre fibra (Fibra Directa con Ethernet, Ethernet sobre SONET/SDH, Ethernet sobre PON), Ethernet sobre PDH o Ethernet inalámbrico [MET09]. Dos de los estándares ópticos Ethernet más empleados hoy en día son los denominados 1000Base-X y 10GBase-R con tasas de transmisión de 1 Gbps y 10 Gbps, respectivamente.OBJETIVOS-------------------En el caso de las comunicaciones sobre Ethernet óptico no existe ningún mecanismo que logre la mencionada privacidad al mismo tiempo que la confidencialidad, sin que además introduzca un overhead o latencias indeseadas. El objetivo de esta tesis es el de proporcionar soluciones a dos de los estándares ópticos Ethernet más empleados, tales como 1000Base-X o 10GBase-R, logrando las características citadas anteriormente. En general los principales aspectos que se pretenden desarrollar en esta tesis son los siguientes: • Realizar propuestas viables de modificación de ambos estándares, 1000Base-X y 10GBase-R, de forma que se pueda llevar a cabo la encriptación en la capa física. • Lograr la compatibilidad de las nuevas arquitecturas de encriptación con dichos estándares de forma que el hardware electrónico más dependiente del medio de transmisión, como los módulos ópticos SFP, los SERDES o los circuitos de recuperación de reloj y datos, no necesite modificaciones adicionales. • Realizar un estudio de los posibles esquemas de encriptación por streaming que sean capaces de cifrar datos a velocidades superiores a 1 Gbps y adaptarlos a las arquitecturas propuestas. • Estudiar posibles mecanismos para llevar a cabo la sincronización de los módulos de encriptación entre dos terminales remotos.• Lograr que las soluciones propuestas lleven a cabo la encriptación introduciendo la menor latencia posible, al menos en un orden de magnitud igual o inferior al de soluciones en otros estándares de comunicaciones como OTN. • Llevar a cabo un análisis de la seguridad de las soluciones propuestas, incluyendo el estudio de la capacidad de privacidad en las comunicaciones. • Proponer un esquema de chequeo de integridad, autenticación y refresco de claves a nivel de capa física. • Llevar a cabo la implementación y verificación física de las soluciones propuestas.PUBLICACIONES----------------------------[PER19a] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Chaotic Encryption Applied to Optical Ethernet in Industrial Control Systems". IEEE Transactions on Instrumentation and Measurement, 68(12):4876–4886, Dec 2019. [PER19b] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Physical Layer Encryption for Industrial Ethernet in Gigabit Optical Links". IEEE Transactions on Industrial Electronics, 66(4):3287–3295, April 2019. [PER19c] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Chaotic Encryption for 10-Gb Ethernet Optical Links". IEEE Transactions on Circuits and Systems I: Regular Papers, 66(2):859–868, Feb. 2019. [PER19d] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Self-Synchronized Encryption for Physical Layer in 10Gbps Optical Links". IEEE Transactions on Computers, 68(6):899–911, June 2019. [PER19e] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Self-Synchronized Encryption Using an FPE Block Cipher for Gigabit Ethernet". In 2019 15th Conference on Ph.D Research in Microelectronics and Electronics (PRIME), pages 81–84, Lausanne, Switzerland, July 2019. [PER20a] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "A New Method for Format Preserving Encryption in High-Data Rate Communications". IEEE Access, 8:21003–21016, 2020. [PER20b] A. Pérez-Resa, M. Garcia-Bosque, C. Sánchez-Azqueta, and S. Celma. "Self-synchronized Encryption for Physical Layer in 1Gbps Ethernet Optical Links". IEEE Access, Pending Acceptance.<br /

Cryptographic primitives on reconfigurable platforms.

Tsoi Kuen Hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 84-92).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Objectives --- p.3Chapter 1.3 --- Contributions --- p.3Chapter 1.4 --- Thesis Organization --- p.4Chapter 2 --- Background and Review --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Cryptographic Algorithms --- p.6Chapter 2.3 --- Cryptographic Applications --- p.10Chapter 2.4 --- Modern Reconfigurable Platforms --- p.11Chapter 2.5 --- Review of Related Work --- p.14Chapter 2.5.1 --- Montgomery Multiplier --- p.14Chapter 2.5.2 --- IDEA Cipher --- p.16Chapter 2.5.3 --- RC4 Key Search --- p.17Chapter 2.5.4 --- Secure Random Number Generator --- p.18Chapter 2.6 --- Summary --- p.19Chapter 3 --- The IDEA Cipher --- p.20Chapter 3.1 --- Introduction --- p.20Chapter 3.2 --- The IDEA Algorithm --- p.21Chapter 3.2.1 --- Cipher Data Path --- p.21Chapter 3.2.2 --- S-Box: Multiplication Modulo 216 + 1 --- p.23Chapter 3.2.3 --- Key Schedule --- p.24Chapter 3.3 --- FPGA-based IDEA Implementation --- p.24Chapter 3.3.1 --- Multiplication Modulo 216 + 1 --- p.24Chapter 3.3.2 --- Deeply Pipelined IDEA Core --- p.26Chapter 3.3.3 --- Area Saving Modification --- p.28Chapter 3.3.4 --- Key Block in Memory --- p.28Chapter 3.3.5 --- Pipelined Key Block --- p.30Chapter 3.3.6 --- Interface --- p.31Chapter 3.3.7 --- Pipelined Design in CBC Mode --- p.31Chapter 3.4 --- Summary --- p.32Chapter 4 --- Variable Radix Montgomery Multiplier --- p.33Chapter 4.1 --- Introduction --- p.33Chapter 4.2 --- RSA Algorithm --- p.34Chapter 4.3 --- Montgomery Algorithm - Ax B mod N --- p.35Chapter 4.4 --- Systolic Array Structure --- p.36Chapter 4.5 --- Radix-2k Core --- p.37Chapter 4.5.1 --- The Original Kornerup Method (Bit-Serial) --- p.37Chapter 4.5.2 --- The Radix-2k Method --- p.38Chapter 4.5.3 --- Time-Space Relationship of Systolic Cells --- p.38Chapter 4.5.4 --- Design Correctness --- p.40Chapter 4.6 --- Implementation Details --- p.40Chapter 4.7 --- Summary --- p.41Chapter 5 --- Parallel RC4 Engine --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Algorithms --- p.44Chapter 5.2.1 --- RC4 --- p.44Chapter 5.2.2 --- Key Search --- p.46Chapter 5.3 --- System Architecture --- p.47Chapter 5.3.1 --- RC4 Cell Design --- p.47Chapter 5.3.2 --- Key Search --- p.49Chapter 5.3.3 --- Interface --- p.50Chapter 5.4 --- Implementation --- p.50Chapter 5.4.1 --- RC4 cell --- p.51Chapter 5.4.2 --- Floorplan --- p.53Chapter 5.5 --- Summary --- p.53Chapter 6 --- Blum Blum Shub Random Number Generator --- p.55Chapter 6.1 --- Introduction --- p.55Chapter 6.2 --- RRNG Algorithm . . --- p.56Chapter 6.3 --- PRNG Algorithm --- p.58Chapter 6.4 --- Architectural Overview --- p.59Chapter 6.5 --- Implementation --- p.59Chapter 6.5.1 --- Hardware RRNG --- p.60Chapter 6.5.2 --- BBS PRNG --- p.61Chapter 6.5.3 --- Interface --- p.66Chapter 6.6 --- Summary --- p.66Chapter 7 --- Experimental Results --- p.68Chapter 7.1 --- Design Platform --- p.68Chapter 7.2 --- IDEA Cipher --- p.69Chapter 7.2.1 --- Size of IDEA Cipher --- p.70Chapter 7.2.2 --- Performance of IDEA Cipher --- p.70Chapter 7.3 --- Variable Radix Systolic Array --- p.71Chapter 7.4 --- Parallel RC4 Engine --- p.75Chapter 7.5 --- BBS Random Number Generator --- p.76Chapter 7.5.1 --- Size --- p.76Chapter 7.5.2 --- Speed --- p.76Chapter 7.5.3 --- External Clock --- p.77Chapter 7.5.4 --- Random Performance --- p.78Chapter 7.6 --- Summary --- p.78Chapter 8 --- Conclusion --- p.81Chapter 8.1 --- Future Development --- p.83Bibliography --- p.8

Research on digital image watermark encryption based on hyperchaos

The digital watermarking technique embeds meaningful information into one or more watermark images hidden in one image, in which it is known as a secret carrier. It is difficult for a hacker to extract or remove any hidden watermark from an image, and especially to crack so called digital watermark. The combination of digital watermarking technique and traditional image encryption technique is able to greatly improve anti-hacking capability, which suggests it is a good method for keeping the integrity of the original image. The research works contained in this thesis include: (1)A literature review the hyperchaotic watermarking technique is relatively more advantageous, and becomes the main subject in this programme. (2)The theoretical foundation of watermarking technologies, including the human visual system (HVS), the colour space transform, discrete wavelet transform (DWT), the main watermark embedding algorithms, and the mainstream methods for improving watermark robustness and for evaluating watermark embedding performance. (3) The devised hyperchaotic scrambling technique it has been applied to colour image watermark that helps to improve the image encryption and anti-cracking capabilities. The experiments in this research prove the robustness and some other advantages of the invented technique. This thesis focuses on combining the chaotic scrambling and wavelet watermark embedding to achieve a hyperchaotic digital watermark to encrypt digital products, with the human visual system (HVS) and other factors taken into account. This research is of significant importance and has industrial application value

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

Synthetic presentation of iterative asynchronous parallel algorithms.

Iterative asynchronous parallel methods are nowadays gaining renewed interest in the community of researchers interested in High Performance Computing (HPC), in the specific case of massive parallelism. This is because these methods avoid the deadlock phenomena and that moreover a rigorous load balancing is not necessary, which is not the case with synchronous methods. Such iterative asynchronous parallel methods are of great interest when there are many synchronizations between processors, which in the case of iterative methods is the case when convergence is slow. Indeed in iterative synchronous parallel methods, to respect the task sequence graph that defines in fact the logic of the algorithm used, processors must wait for the results they need and calculated by other processors; such expectations of the results emitted by concurrent processors therefore cause idle times for standby processors. It is to overcome this drawback that asynchronous parallel iterative methods have been introduced first for the resolution of large scale linear systems and then for the resolution of highly nonlinear algebraic systems of large size as well, where the solution may be subject to constraints. This kind of method has been widely studied worldwide by many authors. The purpose of this presentation is to present as broadly and pedagogically as possible the asynchronous parallel iterative methods as well as the issues related to their implementation and application in solving many problems arising from High Performance Computing. We will therefore try as much as possible to present the underlying concepts that allow a good understanding of these methods by avoiding as much as possible an overly rigorous mathematical formalism; references to the main pioneering work will also be made. After a general introduction we will present the basic concepts that allow to model asynchronous parallel iterative methods including as a particular case synchronous methods. We will then present the algorithmic extensions of these methods consisting of asynchronous sub-domain methods, asynchronous multisplitting methods as well as asynchronous parallel methods with flexible communications. In each case an analysis of the behavior of these methods will be presented. Note that the first kind of analysis allows to obtain an estimate of the asymptotic rate of convergence. The difficult problem of the stopping test of asynchronous parallel iterations will be also studied, both by computer sciences considerations and also by numerical aspects related to the mathematical analysis of the behavior of theses iterative parallel methods. The parallel asynchronous methods have been implemented on various architectures and we will present the main principles that made it possible to code them. These parallel asynchronous methods have been used for the resolution of several kind of mathematical problems and we will list the main applications processed. Finally we will try to specify in which cases and on which type of architecture these methods are efficient and interesting to use

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