Chaos-based Random Number Generator Research Articles

A comparison of embedded and non-embedded FPGA implementations for fractional chaos-based random number generators

A comparison of embedded and non-embedded FPGA implementations for fractional chaos-based random number generators

DWT-SVD Based Watermarking for High-Resolution Medical Holographic Images

Watermarking is one of the most common techniques used to protect data’s authenticity, integrity, and security. The obfuscation in the frequency domain used in the watermarking method makes the watermarking stronger than the obfuscation in the spatial domain. It occupies an important place in watermarking works in imperceptibility, capacity, and robustness. Finding the optimal location to hide the watermarking is one of the most challenging tasks in these methods and affects the method’s performance. In this article, sample identification information is processed with the method of watermaking on the hiding environment created by using a chaos-based random number generator on biomedical data to provide solutions to problems such as visual attack, identity theft, and information confusion. In order to obtain biomedical data, a lensless digital in-line holographic microscopy (DIHM) setup was designed, and holographic data of human blood and cancer cell lines, which are widely used in the laboratory environment, were obtained. The standard USAF 1951 target was used to evaluate the resolution of our imaging setup. Various QR codes were generated for medical sample identification, and the captured medical data were processed by watermarking it with chaos-based random number generators. A new method using chaos-based discrete wavelet transform (DWT) and singular value decomposition (SVD) has been developed and applied to high-resolution data to eliminate the problem of encrypted data being directly targeted by third-party attacks. The performance of the proposed new watermarking method has been demonstrated by various robustness and invisibility tests. Experimental results showed that the proposed scheme reached an average PSNR value of 564588 dB and SSIM value of 0.9972 against several geometric and destructive attacks, which means that the proposed method does not affect the image quality and also ensures the security of the watermarking information. The results of the proposed method have shown that it can be used efficiently in various fields.

The Effect of Using Multi-Scroll Chaotic Systems on Chaos-Based Random Number Generators’ Performance

Chaotic and hyper-chaotic systems are used in various engineering applications such as encryption, communication, and artificial intelligence. Also, chaotic systems are widely used in chaos-based random number generator (RNG) designs as chaotic system signals are not periodic and produce different values continuously. Since multi-scroll chaotic systems (MSCSs) produce more than one scroll, the output values can take more different values than chaotic systems. In this study, the effects of different directional values and/or different numbers of scrolls of multi-scroll chaotic systems on chaos-based random number generators’ performance are investigated with NIST 800-22 (National Institute of Standards and Technology) and correlation coefficient tests. As a result of the research, it has been concluded that the use of multi-scroll chaotic systems with different directional values and/or different numbers of scrolls does not always have a direct positive effect on the performance of chaos-based random number generators. Thus, it is necessary to use a special pre-process method that will vary according to the multi-scroll chaotic system to be used for chaos-based RNG designs with good performance.

Design and implementation of a new memristive chaotic system with application in touchless fingerprint encryption

In this paper, a new memristive chaotic system was constructed from three-dimensional Lorenz-type system. The system has infinitely many equilibria and exhibits coexisting attractors. The dynamic evolution corresponds to the parameters and the coupling strength indicate that the system is easy to generate chaos. Also the bifurcation diagrams from different initial conditions determine the coexistence of multiple attractors. An electronic circuit is done for verifying the physically existence of the system. Based on this system, chaos-based random number generator and the corresponding randomness tests are studied. An algorithm for touchless fingerprint encryption is established. Some comparative tests illustrate the effectiveness of the algorithm.

Statistical RF/Analog Integrated Circuit Design Using Combinatorial Randomness for Hardware Security Applications

While integrated circuit technologies keep scaling aggressively, analog, mixed-signal, and radio-frequency (RF) circuits encounter challenges by creating robust designs in advanced complementary metal–oxide–semiconductor (CMOS) processes with the diminishing voltage headroom. The increasing random mismatch of smaller feature sizes in leading-edge technology nodes severely limit the benefits of scaling for (RF)/analog circuits. This paper describes the details of the combinatorial randomness by statistically selecting device elements that relies on the significant growth in subsets number of combinations. The randomness can be utilized to provide post-manufacturing reconfiguration of the selectable circuit elements to achieve required specifications for ultra-low-power systems. The calibration methodology is demonstrated with an ultra-low-voltage chaos-based true random number generator (TRNG) for energy-constrained Internet of things (IoT) devices in the secure communications.

Cryptanalysis of a random number generator based on continuous‐time chaos

This study presents the algebraic cryptanalysis of a continuous-time chaotic random number generator (RNG) based on a Zhongtang chaotic system. The chaos-based RNG provides key values for logic encryption, round key formation and the substitution box (S-box) generation steps in AES (advanced encryption standard). In this study, an attack method is proposed to exploit the weaknesses of the chaos-based RNG used in this cryptographic system. By observing a chaotic state variable and knowing the structure of the target RNG, output bit sequence of the target RNG is reproduced by a clone RNG used in master–slave synchronisation scheme. The feasibility of the attack system is confirmed through simulation and numerical results. Through this attack method, the same S-box parameters and key values can be obtained which can be used for decryption of the proposed encryption algorithm. This study targets a specific continuous-time chaos-based RNG and the associated cryptographic system as a case study. However, the cryptanalysis method described in this study is applicable to any continuous-time or discrete-time chaos-based RNGs. Therefore, this study highlights the security vulnerabilities of chaos-based RNGs and emphasises that deterministic chaos phenomena itself should not be considered as the actual source of randomness.

Security analysis of a random number generator based on a chaotic hyperjerk system

This paper analyzes the security of a random number generator (RNG) based on a 4-D chaotic hyperjerk system. An attack system is designed to reveal the security weaknesses of the proposed chaotic RNG. Knowing the structure of the RNG and observing one of the state variables of the chaotic system, convergence between attack and target systems is demonstrated by applying linear continuous coupling in master-slave synchronization scheme. Output bit sequence of the chaotic RNG is identically reproduced. The feasibility of the attack system is verified through numerical simulations. In this paper, a specific continuous-time chaos-based RNG is targeted as a case study. However, the cryptanalysis method presented in this paper is applicable to any continuous-time or discrete-time chaos-based RNGs. Therefore, this study highlights the security vulnerabilities of chaos-based RNGs and underlines that deterministic chaos itself cannot be considered as an entropy source for generation of random numbers.

A Low Power Circuit Design for Chaos-Key Based Data Encryption

Dynamic and non-linear systems have been used to generate random bits in high-security applications for decades. In this perspective, due to their stochastic characteristic, chaotic systems have been emerging as the natural choice for the generation of random bits. This paper presents the design and the implementation of a chaos-based true random number generator and a chaos-key based data encryption scheme for secure communications. The mathematical expression of the dynamic system is presented and analyzed to evaluate the possibility of chaos occurrence. Then, the chaotic system is realized at the circuit level using 130 nm CMOS technology to generate random bit sequences, which are utilized in data encryption. Chaotic signal outputs of the chaos-based random number generator circuit are sampled at a maximum frequency of 50 MHz, enabling a high throughput of random bits. The core of the chaotic circuit consumes $630~\mu \text{W}$ in static mode and a maximum of $660~\mu \text{W}$ in running mode. The chaos-based one-time pad encryption scheme using the chaos-key generator shows the advantages of using this random number generator in secure communications. In this context, the data secrecy is compared to the advanced encryption standard AES128. Moreover, the design is simulated in different working conditions such as voltage supply and temperature variations, where it is shown that the random bit output benefits from a high entropy per bit and passes the standard statistical test suite (NIST) for cryptographic applications.

A new chaotic oscillator containing generalised memristor, single op-amp and RLC with chaos suppression and an application for the random number generation

In this paper, a new chaotic oscillator consists of a single op-amp, two capacitors, one resistor, one inductor, and memristive diode bridge cascaded with an inductor is proposed. The proposed chaotic oscillator has a line of equilibria. In the new oscillator circuit, negative feedback, i.e. inverting terminal of the op-amp is used, and the non-inverting terminal is grounded. The new oscillator has chaotic, periodic, quasi-periodic behaviours, as seen from the Lyapunov spectrum plots. Some more theoretical and numerical tools are used to present the dynamical behaviours of the new oscillator like bifurcation diagram, phase plot. Further, a non-singular terminal sliding mode control (N-TSMC) is designed for the suppression of the chaotic states of the new oscillator. An application of the new oscillator is shown by designing a chaos-based random number generator. Raspberry Pi 3 is used for the realisation of the random number generator.

A new chaotic system with hidden attractor and its engineering applications: analog circuit realization and image encryption

In this article a simple chaotic flow with hidden attractor is proposed. Various dynamics of this new system such as periodic and chaotic oscillations can be achieved by setting bifurcation parameters in a proper value. Nowadays chaos based engineering applications like encryption and hiding data face some significant problems. Chaotic systems with hidden attractors, which our system belongs to them, may unfold some primary steps to solve these problems. As the first step, chaotic behavior of our proposed system has been realised in physical existence by using the Orcard-PSpise software. We have found a proper qualitative likeness between experimental and simulation result. Then, chaos-based random number generator design is carried out using the proposed chaotic system. The numbers obtained from the random number generator are applied to the NIST 800-22 tests, and all of the random numbers are passed through the all tests. A chaos-based encryption algorithm with a random number generator is developed and image encryption application is implemented. Encryption results are compared with the AES algorithm, and performance and security evaluation of the developed encryption algorithm is performed.

A novel hybrid encryption algorithm based on chaos and S-AES algorithm

In this study, a novel chaos-based hybrid encryption algorithm design for secure and effective image encryption is presented. To design the algorithm, the Zhongtang chaotic system has been selected because of its rich dynamic features and its dynamical analysis is performed. On the base of this system, a new chaos-based random number generator (RNG) is developed and usefulness of the designed RNG in an encryption process is shown over NIST 800-22 randomness tests. S-Box generation algorithm is designed, and the performance tests of S-Box are realized. By using the designed RNG and S-Box generation algorithms, the new hybrid image encryption algorithm based on AES (CS-AES) is developed. Image encryption applications are performed for comparison with other encryption algorithms in the literature to show its security level and efficiency. Security and performance analyses are made, and results are evaluated. So, it is proved that the proposed CS-AES algorithm is more secure and effective.

Complexity-enhanced polarization-resolved chaos in a ring network of mutually coupled vertical-cavity surface-emitting lasers with multiple delays.

The complexity properties of polarization-resolved chaotic signals generated in a ring network of vertical-cavity surface-emitting lasers (VCSELs) mutually coupled with multiple delays are investigated quantitatively by using the proposed mean permutation entropy (MPE). For direct comparison, the complexity of polarization-resolved chaos in a ring network of VCSELs coupled with single delay is also considered. The effects of injection current, coupling strength, and frequency detuning on the chaotic complexity for both a single-delay ring network (SDRN) and a multiple-delay ring network (MDRN) are evaluated quantitatively and compared by the MPE. The effects of internal parameters of VCSELs on the complexity are also discussed, and the correlation properties between different polarization-resolved modes are also analyzed. It is shown that the complexity of chaos in two polarization-resolved modes of VCSELs in MDRN is much higher than those in SDRN in a much wider parameter region. Besides, wider range of injection current, coupling strength, and frequency detuning can be tuned to achieve the enhancement of chaotic complexity in MDRN. These results provide an effective quantifier, the proposed MPE, to evaluate quantitatively the complexity of chaos generated in systems with multiple delays, and the multichannel complexity-enhanced polarization-resolved chaos generated in MDRN of mutually coupled VCSELs is extremely meaningful for the chaos-based random number generators.

A New Approach to Analysis and Design of Chaos-Based Random Number Generators Using Algorithmic Converter

This paper presents a new approach to analysis and design of ADC-based random number generators. To this end, different full-bit and half-bit redundant stages of algorithmic converter are used to design chaotic maps. It is shown that, in the redundant and nonredundant structures, output probability density function of the converter stages and their related chaotic functions always converge to uniformity. It is demonstrated that residues become independent and uniformly distributed. This fact leads to the randomness and uniformity of distribution of the random number generator output bits. Moreover, it is shown that some common chaotic maps that are employed in chaotic random number generators can be implemented using nonredundant and half-bit redundant stages of algorithmic converter. In this way, the capability of ADC-based generators in designing chaotic maps and producing random number sequences is illustrated. The validity of the proposed chaos-based random number generator is confirmed using NIST statistical tests even in the presence of nonidealities in algorithmic converter. Since the ADCs are mixed-signal integrated circuits and can be used in high-speed applications, the ADC-based random number generator has high throughput and is easily embeddable in all analog and digital circuits.

Attack on a Chaos-Based Random Number Generator Using Anticipating Synchronization

Chaotic systems have been used in random number generation, owing to the property of sensitive dependence on initial conditions and hence the possibility to produce unpredictable signals. Within the types of chaotic systems, those which are defined by only one delay-differential equation are attractive due to their simple model. On the other hand, it is possible to synchronize to the future states of a time-delay chaotic system by anticipating synchronization. Therefore, random number generator (RNG), which employs such a system, might not be immune to the attacks. In this paper, attack on a chaos-based random number generator using anticipating synchronization is investigated. The considered time-delay chaotic system produces binary signals, which can directly be used as a source of RNG. Anticipating synchronization is obtained by incorporating other systems appropriately coupled to the original one. Quantification of synchronization is given by the bit error between the streams produced by the original and coupled systems. It is shown that the bit streams generated by the original system can be anticipated by the coupled systems beforehand.

Construction of Markov Partitions in PL1D Maps

A method is described for the construction of parameters' subspaces where Markov partitions can be found. The method is illustrated on the three-region piecewise linear 1-D (3PL1D) map, which is a popular approach for the chaos-based random number generator (RNG). For Markov partitions, the 3PL1D chaotic maps behave as Markov sources, and analytical calculation of its information entropy is possible, as demonstrated in this brief. From the knowledge of the stochastic transition matrix of the Markov source, one can exactly measure the appropriateness of the RNG in a given area. For classical RNGs, one typically relies on statistical tests as a quality indicator. Mathematical calculation of the quality of an RNG based on the 3PL1D chaotic maps makes the statistical tests useful only in the postimplementation phase as a verification of the hardware implementation.

A novel iris and chaos-based random number generator

A novel kind of iris and chaotic-based random number generator (ICRNG) is developed from the unique randomness and unpredictability of iris. This method combines biometric feature extraction and random number generation in a novel way. Firstly, we get the non-deterministic source-iris image by iris acquisition equipment, then, we use chaotic function to eliminate the similar pattern in iris from the same person and get the unpredictable random sequence. We use auto-correlation function method and correlation coefficients method to show that ICRNG is linearly independent, then, we use BDS statistical test method to verify ICRNG is nonlinearly independent. Finally, the randomness of ICRNG is verified by histogram analysis, information analysis, sensitivity analysis, FIPS 140-2 tests and NIST SP 800-22 tests. Hence, ICRNG possess satisfactory performance and can be implemented on common PC platform.

Numerical verification of chaos-based random number generators by using bootstrap method

Two random number generation methods based on a double-scroll chaotic system are introduced. Numerical models for the proposed designs have been developed where bootstrap method is utilized which allows us to estimate the statistical characteristics of underlying chaotic signals. Offset compensation loops have been developed in order to maximize the statistical quality of the output sequence and to be robust against external interference and parameter variations. Numerical results, verifying the feasibilities and correct operations of the random number generators are given such that numerically generated binary sequences fulfill FIPS-140-2 statistical test suites for randomness without post-processing.

Chaos-based random number generators-part I: analysis [cryptography

This paper and its companion (Part II) are devoted to the analysis of the application of a chaotic piecewise-linear one-dimensional (PL1D) map as random number generator (RNG). Piecewise linearity of the map enables us to mathematically find parameter values for which a generating partition is Markov and the RNG behaves as a Markov information source, and then to mathematically analyze the information generation process and the RNG. In the companion paper we discuss practical aspects of our chaos-based RNGs.