Dynamic Analysis and FPGA Implementation of a Kolmogorov-Like Hyperchaotic System

Chaotic systems have high potential for engineering applications due to their extremely complex dynamics. In the paper, a five-dimensional (5D) Kolmogorov-like hyperchaotic system is proposed. First, the hyperchaotic property is uncovered, and numerical analysis shows that the system displays the coexistence of different kinds of attractors. This system presents a generalized form of fluid and forced-dissipative dynamic systems. The vector field of the hyperchaotic system is decomposed to inertial, internal, dissipative and external torques, respectively, and the energies are analyzed in detail. Then, the bound of the 5D dissipative hyperchaos is estimated with a constructed spherical function. Finally, the system passes the NIST tests and an FPGA platform is used to realize the hyperchaotic system.

Improved El Gamal public key cryptosystem using 3D chaotic maps

Digital information is any type of data that is stored electronically. These data need to protect its assets and unauthorized access to it and therefore need measures to protect digital privacy. This process is done in different ways, one of which is encryption. Encryption provides secure transfer of unauthorized data over insecure channels. In this paper a method is proposed to create the keys to the El Gamal PKC algorithm based on chaos theory. The proposed algorithm uses 3D chaos maps to create keys used in the encryption and decryption process using an El Gamal algorithm. The time spent encoding and decoding in milliseconds was calculated and compared with methods that used 1D and 2D chaotic maps. Also, the results obtained exceeded most of the statistical and NIST tests. The generated results are tested their reactions against many types of attacks. Then, the results showed that the proposed method had an excellent randomness efficiency for creating public and private keys for El Gamal's algorithm.

Adaptive key generation algorithm based on software engineering methodology

Recently, the generation of security keys has been considered for guaranteeing the strongest of them in terms of randomness. In addition, the software engineering methodologies are adopted to ensure the mentioned goal is reached. In this paper, an adaptive key generation algorithm is proposed based on software engineering techniques. The adopted software engineering technique is self-checking process, used for detecting the fault in the underlying systems. This technique checks the generated security keys in terms of validity based on randomness factors. These factors include the results of National Institute of standard Test (NIST) tests. In case the randomness factors are less than the accepted values, the key is regenerated until obtaining the valid one. It is important to note that the security keys are generated using shift register and SIGABA technique. The proposed algorithm is tested over different case studies and the results show the effective performance of it to produce well random generated keys.

Implementing a Symmetric Lightweight Cryptosystem in Highly Constrained IoT Devices by Using a Chaotic S-Box

In the Internet of Things (IoT), a lot of constrained devices are interconnected. The data collected from those devices can be the target of cyberattacks. In this paper, a lightweight cryptosystem that can be efficiently implemented in highly constrained IOT devices is proposed. The algorithm is mainly based on Advanced Encryption Standard (AES) and a new chaotic S-box. Since its adoption by the IEEE 802.15.4 protocol, AES in embedded platforms have been increasingly used. The main cryptographic properties of the generated S-box have been validated. The randomness of the generated S-box has been confirmed by the NIST tests. Experimental results and security analysis demonstrated that the cryptosystem can, on the one hand, reach good encryption results and respects the limitation of the sensor’s resources, on the other hand. So the proposed solution could be reliably applied in image encryption and secure communication between networked smart objects.

Enhancing advance encryption standard security based on dual dynamic XOR table and MixColumns transformation

An efficient approach to secure information is critically needed at present. Cryptography remains the best approach to achieve security. On this basis, the National Institute of Standards and Technology (NIST) selected Rijndael, which is a symmetric block cipher, as the advanced encryption standard (AES). The MixColumns transformation of this cipher is the most important function within the linear unit and the major source of diffusion. Dynamic MixColumns transformation can be used to enhance the AES security. In this study, a method to enhance the AES security is developed on the basis of two methods. The first method is an extension of a previous study entitled “A novel Approach for Enhancing Security of Advance Encryption Standard using Private XOR Table and 3D chaotic regarding to Software quality Factor.” In the current study, the fixed XOR operation in AES rounds is replaced with a dual dynamic XOR table by using a 3D chaotic map. The dual dynamic XOR table is based on 4 bits; one is used for even rounds, and the other is used for odd rounds. The second method is dynamic MixColumns transformation, where the maximum distance separable (MDS) matrix of the MixColumns transformation, which is fixed and public in every round, is changed with a dynamic MDS matrix, which is private, by using a 3D chaotic map. A 3D chaotic map is used to generate secret keys. These replacements enhance the AES security, particularly the resistance against attacks. Diehard and NIST tests, entropy, correlation coefficient, and histogram are used for security analysis of the proposed method. C++ is used to implement the proposed and original algorithms. MATLAB and LINX are used for the security analysis. Results show that the proposed method is better than the original AES.

A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation

This work proposes a modified logistic map based on the system previously proposed by Han in 2019. The constructed map exhibits interesting chaos related phenomena like antimonotonicity, crisis, and coexisting attractors. In addition, the Lyapunov exponent of the map can achieve higher values, so the behavior of the proposed map is overall more complex compared to the original. The map is then successfully applied to the problem of random bit generation using techniques like the comparison between maps, X O R , and bit reversal. The proposed algorithm passes all the NIST tests, shows good correlation characteristics, and has a high key space.

Modeling, Synchronization, and FPGA Implementation of Hamiltonian Conservative Hyperchaos

Conservative chaotic systems have potentials in engineering application because of their superiority over the dissipative systems in terms of ergodicity and integer dimension. In this paper, five-dimension Euler equations are constructed by integrating two of sub-Euler equations, which are contributory to the exploration of higher-dimensional systems. These Euler equations compose the conservative parts from their antisymmetric structure, which have been proved to be both Hamiltonian and Casimir energy conservative. Furthermore, a family of Hamiltonian conservative hyperchaotic systems are proposed by breaking the conservation of Casimir energy. The numerical analysis shows that the system displays some interesting behaviors, such as the coexistence of quasi-periodic, chaotic, and hyperchaotic behaviors. Adaptive synchronization method is used to realize the hyperchaos synchronization. Finally, the system passed the NIST tests successfully. Field programmable gate array (FPGA) platform is used to implement the proposed Hamiltonian conservative hyperchaos.

Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems

Since the conservative chaotic system (CCS) has no general attractors, conservative chaotic flows are more suitable for the chaos-based secure communication than the chaotic attractors. In this paper, two Hamiltonian conservative chaotic systems (HCCSs) are constructed based on the 4D Euler equations and a proposed construction method. These two new systems are investigated by equilibrium points, dynamical evolution map, Hamilton energy, and Casimir energy. They look similar, but it is found that one can be explained using Casimir power and another cannot be explained in terms of the mechanism of chaos. Furthermore, a pseudorandom signal generator is developed based on these proposed systems, which are tested based on NIST tests and implemented by using the field programmable gate array (FPGA) technique.

THE GENERATING RANDOM SEQUENCES WITH THE INCREASED CRYPTOGRAPHIC STRENGTH

Random sequences are used in various applications in construction of cryptographic systems or formations of noise-type signals. For these tasks there is used the program generator of random sequences which is the determined device. Such a generator, as a rule, has special requirements concerning the quality of the numbers formation sequence. In cryptographic systems, the most often used are linearly – congruent generators, the main disadvantage of which is the short period of formation of pseudo-random number sequences. For this reason, in the article there is proposed the use of chaos generators as the period of the formed selection in this case depends on the size of digit net of the used computing system. It is obvious that the quality of the chaos generator has to be estimated through a system of the NIST tests. Therefore, detailed assessment of their statistical characteristics is necessary for practical application of chaos generators in cryptographic systems. In the article there are considered various generators and there is also given the qualitative assessment of the formation based on the binary random sequence. Considered are also the features of testing random number generators using the system. It is determined that not all chaos generators meet the requirements of the NIST tests. The article proposed the methods for improving statistical properties of chaos generators. The method of comparative analysis of random number generators based on NIST statistical tests is proposed, which allows to select generators with the best statistical properties. Proposed are also methods for improving the statistical characteristics of binary sequences, which are formed on the basis of various chaos generators.

Influence of Neighborhood Forms on the Quality of Pseudorandom Number Generators' Work Based on Cellular Automata

The chapter analyzes modern methods for constructing pseudo-random number generators based on cellular automata. Also analyzes the influence of neighborhood forms on the evolution of the functioning of cellular automata, as well as on the quality of the formation of pseudo-random bit sequences. Based on the use of various forms of the neighborhood for the XOR function, the quality of generators was analyzed using graphical tests and NIST tests. As a result of experimental studies, the optimal dimension of cellular automata and the number of heterogeneous cells were determined, which make it possible to obtain a high-quality pseudo-random bit sequence. The obtained results allowed to formulate a method for constructing high-quality pseudo-random number generators based on cellular automata, as well as to determine the necessary initial conditions for generators. The proposed generators allow to increase the length of the repetition period of a pseudo-random bit sequence.