Chaotic Pseudorandom Number Generator Research Articles

Novel, Fast, Strong, and Parallel: A Colored Image Cipher Based on SBTM CPRNG

Smartphones, digital cameras, and other imaging devices generate vast amounts of high-resolution colored images daily, stored on devices equipped with multi-core central processing units or on the cloud. Safeguarding these images from potential attackers has become a pressing concern. This paper introduces a set of six innovative image ciphers designed to be stronger, faster, and more efficient. Three of these algorithms incorporate the State-Based Tent Map (SBTM) Chaotic Pseudo Random Number Generator (CPRNG), while the remaining three employ a proposed modified variant, SBTMPi. The Grayscale Image Cipher (GIC), Colored Image Cipher Single-Thread RGB (CIC1), and Colored Image Cipher Three-Thread RGB (CIC3) showcase the application of the proposed algorithms. By incorporating novel techniques in the confusion and diffusion phases, these ciphers demonstrate remarkable performance, particularly with large colored images. The study underscores the potential of SBTM-based image ciphers, contributing to the advancement of secure image encryption techniques with robust random number generation capabilities.

Artificial Neural Network Chaotic PRNG and simple encryption on FPGA

Artificial Neural Networks (ANNs) are remarkably able to fit complex functions, making them useful in various applications and systems. This paper uses ANN to fit the Pehlivan–Uyaroglu Chaotic System (PUCS) to produce an Artificial Neural Network Chaotic Pseudo-Random Number Generator (ANNC-PRNG). The proposed PRNG imitates the PUCS chaotic system’s properties and attractor shape. The proposed ANNC-PRNG is implemented in a simple image encryption system on the Xilinx Kintex-7 Genesys 2 Field Programmable Gate Array (FPGA) board. Hardware realization of an ANN trained on chaotic time series has not been presented before. The proposed ANN can be used for different numerical methods or chaotic systems, including fractional-order systems while keeping the same resources despite the methods’ complexity or chaotic systems’ complexity. Extensive testing for the ANNC-PRNG was done to prove the randomness of the produced outputs. The proposed ANNC-PRNG and the encryption system passed various well-established security and statistical tests and produced good results compared to recent similar research. The encryption system is robust against different attacks. The proposed hardware architecture is fast as it reaches a maximum frequency of 12.553 MHz throughput of 301 Mbit/s.

Efficient and secure chaotic PRNG for color image encryption

Random number generation is considered a major problem for any digital color image cipher algorithm and secret communication protocol. Pseudo-random number generators (PRNGs) are used in many security applications because they afford both features, the randomness efficiency and quality of the PRNG. The paper proposes a new PRNG depending on a combination of the Secure Hash Algorithm (SHA-2(256)) with the results of three chaotic maps: the 2D Henon map, the 2D Kaplan-Yorke map, and the 2D Tinkerbell map. In the proposed chaotic generator, 6 initial floating-point numbers with 10−16 precision are inputs to SHA-2(256) for generating the initial values of the three chaotic maps. Then the chaotic maps are iterated to produce a binary sequence that is processed to enhance the sequence complexity based on binary XOR addition operation and 2D shifting scrambling method. The random binary sequences produced by the proposed PRNG algorithm were tested using several number of analyses like the national statistical test suite, correlation analyses, key space analyses, Sum of absolute analyses (SAD), key sensitivity analyses, and histogram analyses. The results proved that scrambling binary sequences have passed successfully the NIST tests where the ratio η of p-value concerns individual sequences between [0.9805, 0.9994], the correlation between the produced sequences is very small where the distributions of Pearson's correlation coefficients belong to [-0.03, 0.03] and the distributions of Hamming distance coefficients belonging to [0.49, 0.52], all the results of the SAD between [0.33237, 0.33451] which are almost close ideal values, and the key space of proposed PRNG is very large which is 2319. The proposed PRNG was applied as a random key generation algorithm on a new color image cipher algorithm, with strong permutation and substitution methods to encrypt and decrypt each image color channel. The practicableness of the algorithm was tested by different statistical and security analyses.

A chaotic PRNG tested with the heuristic Differential Evolution

A pseudo random number generator (PRNG) is built with a chaotic map without fixed points implemented using fixed-point arithmetic. The generated binary sequences by the PRNG pass all the TestU01 statistical tests to prove the randomness of the generated binary sequences. Three multimodal benchmark functions are optimized with the heuristic Differential Evolution (DE) using the proposed PRNG, and these are compared with the DE using the standard random function available in the C programming language. If the shuffling technique is added to the generated chaotic random sequences, both approaches give the same statistically solutions. A hardware design in FPGA of the PRNG also is shown.

Image encryption based on fractional chaotic pseudo-random number generator and DNA encryption method

Nonlinear dynamic systems and chaotic systems have been quite exhaustively researched in the domain of cryptography. However, the possibility of using fractional chaotic systems in the cryptosystem design has been much less explored while it bears advantages such as enlarged keyspace and better resistance to attack compared to classical nonlinear systems. This paper, therefore, proposes a novel structure for the pseudo-random number generator based on 3 different fractional chaotic systems, namely fractional Chen system, Lu system, and fractional generalized double-humped logistic map. Then, the outputs of this fractional chaotic pseudo-random number generator are used as a keystream for an image encryption scheme. The confusion layer of the scheme is conducted by a dynamic DNA encoding and decoding method combined with a 2D cat map for the permutation in the DNA bases level. The diffusion layer is performed through the adoption of a 32 bits discrete logistic map. The performance and security analyses have been conducted for the above-designed cryptosystem, proving that the proposed cryptosystem is practical and efficient, and can be successfully implemented in image encryption.

Enhanced design and hardware implementation of a chaos-based block cipher for image protection

Nowadays chaos-based cryptography systems are widely used to protect sensitive data. A variety of chaos-based cryptosystems with software implementation has been published in the literature. However, due to the rapid growth of connected devices, the development of hardware secure and low-resource cryptographic systems is necessary. In this paper, we enhance the design of one of our software cryptosystems and then we address its FPGA-based implementation. The improvement in the design consists essentially to introduce an Initial Vector (IV) entry to the Chaotic Pseudo Random Number Generator (CPRNG) thus allowing to generate a new dynamic keys for the confusion layer (using a modified 2-D cat map) and diffusion layer (using a logistic map) with each new execution of the system. The CPRNG is formed by XORred a discrete Skew Tent Map (STM) with a discrete Piecewise Linear Chaotic Map (PWLCM). The proposed cryptosystem, which operates in Cipher Block Chaining (CBC) mode, is controlled by a Finite State Machine (FSM) to ensure that both the encryption and decryption are performed by the same reconfigurable architecture. The system is implemented on a Xilinx XC7Z020 ZYNQ FPGA platform. The results obtained in terms of hardware implementation costs (logic resources, throughput, and efficiency) and in terms of security against cryptographic attacks demonstrate the effectiveness of the proposed chaos-based cryptosystem.

Memristive Structure-Based Chaotic System for PRNG

This paper suggests an approach to generate pseudo-random sequences based on the discrete-time model of the simple memristive chaotic system. We show that implementing Euler’s and Runge–Kutta’s methods for the simulation solutions gives the possibility of obtaining chaotic sequences that maintain general properties of the original chaotic system. A preliminary criterion based on the binary sequence balance estimation is proposed and applied to separate any binary representation of the chaotic time sequences into random and non-random parts. This gives us the possibility to delete obviously non-random sequences prior to the post-processing. The investigations were performed for arithmetic with both fixed and floating points. In both cases, the obtained sequences successfully passed the NIST SP 800-22 statistical tests. The utilization of the unidirectional asymmetric coupling of chaotic systems without full synchronization between them was suggested to increase the performance of the chaotic pseudo-random number generator (CPRNG) and avoid identical sequences on different outputs of the coupled systems. The proposed CPRNG was also implemented and tested on FPGA using Euler’s method and fixed-point arithmetic for possible usage in different applications. The FPGA implementation of CPRNG supports a generation speed up to 1.2 Gbits/s for a clock frequency of 50 MHz. In addition, we presented an example of the application of CPRNG to symmetric image encryption, but nevertheless, one is suitable for the encryption of any binary source.

A Novel 3D Chaotic System With Line Equilibrium: Multistability, Integral Sliding Mode Control, Electronic Circuit, FPGA Implementation and Its Image Encryption

This paper announces a novel three-dimensional chaotic system with line equilibrium and discusses its dynamic properties such as Lyapunov exponents, phase portraits, equilibrium points, bifurcation diagram, multistability and coexisting attractors. New synchronization results based on integral sliding mode control (ISMC) are also derived for the new chaotic system with line equilibrium. In addition, an electronic circuit implementation of the new chaotic system with line equilibrium is reported and a good qualitative agreement is exhibited between the MATLAB simulations of the theoretical model and the MultiSim results. We also display the implementation of the Field-Programmable Gate Array (FPGA) based Pseudo-Random Number Generator (PRNG) by using the new chaotic system. The throughput of the proposed FPGA based new chaotic PRNG is 462.731 Mbps. Randomness analysis of the generated numbers has been performed with respect to the NIST-800-22 tests and they have successfully passed all of the tests. Finally, an image encryption algorithm based on the pixel-level scrambling, bit-level scrambling, and pixel value diffusion is proposed. The experimental results show that the encryption algorithm not only shuffles the pixel positions of the image, but also replaces the pixel values with different values, which can effectively resist various attacks such as brute force attack and differential attack.

Hardware Efficient Pseudo-Random Number Generator Using Chen Chaotic System on FPGA

This paper introduces an FPGA implementation of a pseudo-random number generator (PRNG) using Chen’s chaotic system. This paper mainly focuses on the development of an efficient VLSI architecture of PRNG in terms of bit rate, area resources, latency, maximum length sequence, and randomness. First, we analyze the dynamic behavior of the chaotic trajectories of Chen’s system and set the parameter’s value to maintain low hardware design complexity. A circuit realization of the proposed PRNG is presented using hardwired shifting, additions, subtractions, and multiplexing schemes. The benefit of this architecture, all the binary multiplications (except [Formula: see text] and [Formula: see text] operations are performed using hardwired shifting. Moreover, the generated sequences pass all the 15 statistical tests of NIST, while it generates pseudo-random numbers at a uniform clock rate with minimum hardware complexity. The proposed architecture of PRNG is realized using Verilog HDL, prototyped on the Virtex-5 FPGA (XC5VLX50T) device, and its analysis has been done using the Matlab tool. Performance analysis confirms that the proposed Chen chaotic attractor-based PRNG scheme is simple, secure, and hardware efficient, with high potential to be adopted in cryptography applications.

Design of pseudo-random number generator from turbulence padded chaotic map

Transmission of the information in any form requires security. Security protocols used for communication rely on the use of random numbers. Pseudo-random numbers are required with good statistical properties and efficiency. The use of a single chaotic map may not produce enough randomness. The turbulence is padded into the existing map to improve its chaotic behaviour and increase the periodicity. A Pseudo-random number generator (PRNG) with this architecture is devised to generate random bit sequences from secret keys. The statistical properties of newly constructed PRNG are tested with NIST SP 800–22 statistical test suite and were shown to have good randomness. To ensure its usability in cryptographic applications, we analysed the size of its key space, key sensitivity, and performance speed. The test results show that the newly designed PRNG has a 3.6% increase in key space and a 5% increase in its performance speed compared to existing chaotic PRNGs. The novel PRNG with faster performance is found suitable for lightweight cryptographic applications.

Symmetric Cryptography With a Chaotic Map and a Multilayer Machine Learning Network for Physiological Signal Infosecurity: Case Study in Electrocardiogram

Digital physiological signals in telecare medicine information systems have been widely applied in remote medical applications, such as telecare, tele-examination, and telediagnosis, via computer networking transmission or wireless communication. However, these medical records need to ensure authorization demands in the channel model for human body communication and remote medical servers and enhance the confidentiality, recoverability, and availability of transmission data. Hence, this study proposes a symmetric cryptography scheme with a chaotic map and a multilayer machine learning network (MMLN) to achieve physiological signal infosecurity. A chaotic pseudorandom number generator within specific control parameters can dynamically produce unordered sequence numbers to set the secret keys for a regular secret key update, thereby improving the security of private cipher codes. The chaotic map is quickly iterated to produce a pseudorandom key stream for real-time applications, and the private cipher codes are selected using the initial and specific control parameters at the data emitter and receiver ends. A general regression neural network is used to map the high-dimensional input–output pair of cipher codes for substitution and permutation processes. Its adaptive MMLN with an optimization algorithm can rapidly train the random cipher code protocol to achieve an encryptor and a decryptor for a regular encrypted communication. Using the Massachusetts Institute of Technology–Beth Israel Hospital (MIT–BIH) Arrhythmia Database, 100 electrocardiogram fragments are used to verify the proposed model, and the peak signal-to-noise ratio (PSNR) as a quantitative quality metric is used to evaluate the visual quality after encryption and decryption processes for further diagnosis applications. Experimental results show that the proposed scheme has a higher mean PSNR (35.26 ± 3.77 dB) and shorter mean executing time (0.16 ± 0.01 s) compared with traditional cryptography protocol schemes.

A novel secure chaos-based pseudo random number generator based on ANN-based chaotic and ring oscillator: design and its FPGA implementation

This paper presents a novel, real time, high speed and robust chaos-based pseudo random number generator (PRNG) design using the structures of artificial neural network (ANN)-based 2D chaotic oscillator and ring oscillator. In this study, four different robust PRNGs have been implemented using four different approaches (TS-55, Elliott-93, Elliott-2, Cordic-LUT) of TanSig activation functions (TSAF) that have been used in the design of ANN-based 2D chaotic oscillators. The designs have been coded in VHDL using IEEE-754–1985 number standard. The PRNGs have been synthesized for Virtex-6 FPGA chip using Xilinx ISE Design Tools. After Place&Route operation, FPGA chip statistics and maximum operating frequencies have been presented. The maximum operating frequencies of the proposed PRNGs range between 184 and 241 MHz. The 1 Mbit of bit streams generated by PRNGs have been subjected to NIST-800–22 randomness tests. Among 4 different proposed PRNGs, the proposed PRNGs that designed using the Elliott-93 and Cordic-LUT approaches have successfully passed all NIST-800–22 tests and have a bit production rate of 241 Mbps. The proposed secure hybrid chaos-based PRNG structures were compared with similar studies conducted in the literature in recent years. According to the results, the proposed FPGA-based secure new chaotic PRNG structures are useful in cryptographic applications.

PUF-Based Secure Chaotic Random Number Generator Design Methodology

Pseudorandom number generators (PRNGs) play a pivotal role in generating key sequences of cryptographic protocols. Among different schemes, a simple chaotic PRNG (CPRNG) exhibits the property of being extremely sensitive to the initial seed and, hence, unpredictable. However, CPRNG is vulnerable if the initial seed is compromised. In this brief, we propose a novel physical unclonable function-based CPRNG (PUF-CPRNG), where the initial seed is secured by generating it from PUF. Furthermore, the proposed PUF-CPRNG includes dynamic refreshing logic to ensure that the random numbers generated are nonperiodic. To further secure the PUF-CPRNG, the feedback values of CPRNG are fed from PUF. An hardware architecture for the proposed methodology has been designed, and the proof of concept implementation was carried out using Xilinx Virtex-7 field-programmable gate array (FPGA). The proposed PUF-CPRNG passes the statistical test NIST 800-22, ENT, and correlation analysis.

Design of the nonlinear look-up table in the chaotic pseudorandom number generator based on augmented Lorenz map

Design of the nonlinear look-up table in the chaotic pseudorandom number generator based on augmented Lorenz map

Multiplierless chaotic Pseudo random number generators

This paper presents a multiplierless based FPGA implementation for six different chaotic Pseudo Random Number Generators (PRNGs) that are based on: Chua, modified Lorenz, modified Rössler, Frequency Dependent Negative Resistor (FDNR) oscillator, and other two systems that are modelled using the simple jerk equation. These chosen systems can be employed in high speed applications because they don’t utilize any hardware multiplier. The proposed PRNGs have been implemented using VHDL, synthesized on Xilinx, using the FPGA: XC5VLX50T, and tested using the NIST statistical suite. Furthermore, a comparison has been established between the performance of all the PRNGs, regarding the implementation area, speed, and the statistical randomness quality. It has been found that the modified Lorenz PRNG has the best randomness quality and the best hardware performance as it can pass all the NIST tests while operating at 298.597 MHz and utilizing only 0.23% and 0.62% from the FPGA’s slice registers and Look-Up-Tables (LUTs) respectively.

A secure image encryption scheme based on cellular automata and chaotic skew tent map

This paper presents a highly secure image encryption scheme for secure image communication and storage. The scheme is based on a chaotic skew tent map and cellular automata (CA). The chaotic skew tent map is used as the initial vector generator for the CA which needs a 128 bit initial bit sequence to generate pseudo random number sequence (PRNS). Using the PRNS, the plain image pixels are first permuted to remove the high correlation among the adjacent pixels in the image. Then the permuted image is encrypted based on a single random number generated by the chaotic skew tent map. The chaotic skew tent map has a very large key space, on the other hand, CA generates PRNS faster than a chaotic pseudo random number generator (PRNG). Therefore, a combination of both chaotic map and CA gives a system with higher key space and faster PRNS generator. The experimental results show a good encryption effects which are capable to resist any kind of known attacks.

New pseudo-random number generator based on improved discrete-space chaotic map

In this paper, a new pseudo-random number generator (PRNG) based on improved onedimensional discrete-space chaotic map is proposed. Like the original, the improved map relies on bijective mapping of permutations and natural numbers. Instead of using standard Lehmer code, we use a mapping computable in linear time, which significantly speeds up the PRNG. Results of NIST 800-22 test suite and TestU01 test suite confirm that the proposed approach can be used for generation of pseudo-random numbers. Due to discrete nature of used chaotic map, the proposed PRNG is not influenced by dynamical degradation and has virtually unlimited key space. Proposed approach has much better ratio between required memory and security level than previous secure one-dimensional discrete-space chaotic PRNGs. Also, proposed PRNG is much faster than other secure PRNGs of the same type. Satisfactory speed and small memory requirements indicate that proposed PRNG has properties desirable for use in devices with limited memory space, such as wireless sensor networks.

Differential Evolution and Deterministic Chaotic Series: A Detailed Study

This research represents a detailed insight into the modern and popular hybridization of deterministic chaotic dynamics and evolutionary computation. It is aimed at the influence of chaotic sequences on the performance of four selected Differential Evolution (DE) variants. The variants of interest were: original DE/Rand/1/ and DE/Best/1/ mutation schemes, simple parameter adaptive jDE, and the recent state of the art version SHADE. Experiments are focused on the extensive investigation of the different randomization schemes for the selection of individuals in DE algorithm driven by the nine different two-dimensional discrete deterministic chaotic systems, as the chaotic pseudorandom number generators. The performances of DE variants and their chaotic/non-chaotic versions are recorded in the one-dimensional settings of 10D and 15 test functions from the CEC 2015 benchmark, further statistically analyzed.

Reconfigurable chaotic pseudo random number generator based on FPGA

This paper presents an FPGA Pseudo Random Number Generator (PRNG) that is based on the Lorenz and Lü chaotic systems. These two systems are used to generate four different 3D chaotic attractors. One attractor is generated from Lorenz while the other three attractors are generated from Lü. The output attractor of the proposed PRNG can be reconfigured during real time operation using an efficient hardwired shifting and multiplexing scheme. Furthermore, in order to exploit the proposed reconfiguration feature, the proposed PRNG has been embedded in an FPGA cascaded encryption processor that ciphers the input data from one up to four times successively. In each ciphering operation the PRNG is set to a new configuration and is initialized according to a part of the encryption key. The size of the encryption key can be varied according to the number of required ciphering operations. The proposed PRNG has been realized using VHDL, synthesized on Xilinx using the FPGA device XC5VLX50T, and analyzed using MATLAB and the NIST statistical suite. The proposed PRNG has utilized only 1.4% from the FPGA’s slices, achieved an operating frequency up to 78 MHz, and successfully passed all the NIST statistical tests.

A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption

In this work, we propose a novel 3D chaotic map obtained by coupling the piecewise and logistic maps. Showing excellent properties, like a high randomness, a high complexity and a very long period, this map has enabled us to implement and investigate a new chaotic pseudo-random number generator (CPRNG). The produced pseudo-random numbers exhibit a uniform distribution and successfully pass the NIST SP 800-22 randomness tests suite. In addition, an application in the field of color image encryption is proposed where the encryption key is strongly correlated with the plain image and is then used to perform the confusion and diffusion stages. Furthermore, the ability to expand the size of our map has an impact on the complexity of the system and increases the size of the key space, making our cryptosystems more efficient and safer. We also give some statistical tests and computer simulations which confirm that the proposed algorithm has a high level of security.