Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography

Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed 16×16 S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks

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

Securing Digital Images through Simple Permutation-Substitution Mechanism in Cloud-Based Smart City Environment

Data security plays a significant role in data transfer in cloud-based smart cities. Chaotic maps are commonly used in designing modern cryptographic applications, in which one-dimensional (1D) chaotic systems are widely used due to their simple design and low computational complexity. However, 1D chaotic maps suffer from different kinds of attacks because of their chaotic discontinuous ranges and small key-space. To own the benefits of 1D chaotic maps and avoid their drawbacks, the cascading of two integrated 1D chaotic systems has been utilized. In this paper, we report an image cryptosystem for data transfer in cloud-based smart cities using the cascading of Logistic-Chebyshev and Logistic-Sine maps. Logistic-Sine map has been utilized to permute the plain image, and Logistic-Chebyshev map has been used to substitute the permuted image, while the cascading of both integrated maps has been utilized in performing XOR procedure on the substituted image. The security analyses of the suggested approach prove that the encryption mechanism has good efficiency as well as lower encryption time compared with other related algorithms

Proceedings of AUTOMATA 2011 : 17th International Workshop on Cellular Automata and Discrete Complex Systems

International audienceThe proceedings contain full (reviewed) papers and short (non reviewed) papers that were presented at the workshop

Autómatas celulares y aplicaciones

Un autómata celular es un modelo matemático para un sistema dinámico que evoluciona en pasos discretos. Este trabajo presenta una aplicación de los autómatas celulares para el cifrado de información y el reparto de secretos. Se detalla un ejemplo didáctico de su aplicación para el cifrado de secretos empleando imágenes digitales. El desarrollo de este trabajo ha servido como actividad académica dirigida a alumnado de Ingeniería en Informática, para fomentar su interés en la criptografía mediante herramientas matemáticas estudiadas a lo largo de su carrera

Image encryption framework based on multi-chaotic maps and equal pixel values quantization

Abstract The importance of image encryption has considerably increased, especially after the dramatic evolution of the internet and network communications, due to the simplicity of capturing and transferring digital images. Although there are several encryption approaches, chaos-based image encryption is considered the most appropriate approach for image applications because of its sensitivity to initial conditions and control parameters. Confusion and diffusion methods have been used in conventional image encryption methods, but the ideal encrypted image has not yet been achieved. This research aims to generate an encrypted image free of statistical information to make cryptanalysis infeasible. Additionally, the motivation behind this work lies in addressing the shortcomings of conventional image encryption methods, which have not yet achieved the ideal encrypted image. The proposed framework aims to overcome these challenges by introducing a new method, Equal Pixel Values Quantization (EPVQ), along with enhancing the confusion and diffusion processes using chaotic maps and additive white Gaussian noise. Key security, statistical properties of encrypted images, and withstanding differential attacks are the most important issues in the field of image encryption. Therefore, a new method, Equal Pixel Values Quantization (EPVQ), was introduced in this study in addition to the proposed confusion and diffusion methods to achieve an ideal image encryption framework. Generally, the confusion method uses Sensitive Logistic Map (SLM), Henon Map, and additive white Gaussian noise to generate random numbers for use in the pixel permutation method. However, the diffusion method uses the Extended Bernoulli Map (EBM), Tinkerbell, Burgers, and Ricker maps to generate the random matrix. Internal Interaction between Image Pixels (IIIP) was used to implement the XOR (Exclusive OR) operator between the random matrix and scrambled image. Basically, the EPVQ method was used to idealize the histogram and information entropy of the ciphered image. The correlation between adjacent pixels was minimized to have a very small value (×10−3). Besides, the key space was extended to be very large (2450) considering the key sensitivity to hinder brute force attacks. Finally, a histogram was idealized to be perfectly equal in all occurrences, and the resulting information entropy was equal to the ideal value (8), which means that the resulting encrypted image is free of statistical properties in terms of the histogram and information entropy. Based on the findings, the high randomness of the generated random sequences of the proposed confusion and diffusion methods is capable of producing a robust image encryption framework against all types of cryptanalysis attacks

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

User-controlled cyber-security using automated key generation

Traditionally, several different methods are fully capable of providing an adequate degree of security to the threats and attacks that exists for revealing different keys. Though almost all the traditional methods give a good level of immunity to any possible breach in security keys, the biggest issue that exist with these methods is the dependency over third-party applications. Therefore, use of third-party applications is not an acceptable method to be used by high-security applications. For high-security applications, it is more secure that the key generation process is in the hands of the end users rather than a third-party. Giving access to third parties for high-security applications can also make the applications more venerable to data theft, security breach or even a loss in their integrity. In this research, the evolutionary computing tool Eureqa is used for the generation of encryption keys obtained by modelling pseudo-random input data. Previous approaches using this tool have required a calculation time too long for practical use and addressing this drawback is the main focus of the research. The work proposes a number of new approaches to the generation of secret keys for the encryption and decryption of data files and they are compared in their ability to operate in a secure manner using a range of statistical tests and in their ability to reduce calculation time using realistic practical assessments. A number of common tests of performance are the throughput, chi-square, histogram, time for encryption and decryption, key sensitivity and entropy analysis. From the results of the statistical tests, it can be concluded that the proposed data encryption and decryption algorithms are both reliable and secure. Being both reliable and secure eliminates the need for the dependency over third-party applications for the security keys. It also takes less time for the users to generate highly secure keys compared to the previously known techniques.The keys generated via Eureqa also have great potential to be adapted to data communication applications which require high security

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas