Digitized Chaos for Pseudo-random Number Generation in Cryptography

We present a new way of testing Random Number Generators (RNGs). Our approach allows to test Pseudo Random Number Generators (PRNGs) including Cryptographically Secure Pseudo Random Number Generators (CSPRNGs). The paper describes how to use machine learning for this. To construct a tester we compare the properties of three most common learning techniques to find the one most suitable one for testing RNGs. By analyzing the system during training and regarding the expected behavior of random numbers, we define an optimizer for learning RNGs. Based on the results and regarding the behavior of the machine learning algorithm, we define a rating for RNGs. On a state-of-the-art GPU cluster, we evaluate the full tester for multiple PRNGs. Additionally, we compare the results with the results from the commonly used test suite dieharder. The results prove that the developed tester is suitable for testing random numbers. In comparison to dieharder, it is even more powerful and able to replace it. Our tester could disclose weaknesses in PRNGs that are wrongly considered as CSPRNG. This could increase the security of many cryptographic protocols based on random numbers.

Random number generation is a fundamental aspect of computer science, cryptography, simulations, and statistical sampling. This paper explores the definitions, classifications, and implementations of random and pseudo-random number generators (RNGs and PRNGs). We examine true random number generators (TRNGs), which derive randomness from physical phenomena, and pseudo-random number generators (PRNGs), which use deterministic algorithms to produce sequences that mimic randomness. Case studies, including Random.org, HotBits, laser-based RNGs, and the Linux random number generator, illustrate practical implementations. We also discuss vulnerabilities, security considerations, and the importance of entropy in generating unpredictable sequences.

Cryptographic Pseudorandom Number Generators (CPRNG) play a very crucial role in Internet of Things (IoT) security. Cryptographic protocols require random numbers for nonces, salts, and key generation. However, developing secure and lightweight CPRNG is strenuous. Insecure source of randomness can evolve in vulnerabilities and can jeopardize security mechanisms. As the number of IoT devices are expected to exceed over billions, the demand for distributed CPRNG increases. Manually configuring random numbers in large numbers of IoT devices is practically challenging and insecure. In this paper, we propose a cryptographically secure pseudorandom number generator based on sensor data as source of randomness. The appealing characteristic of a sensor data based random number generator is that sensor can possibly generate infinite data. Thus, having longer period and perhaps higher entropy. We also present proof-of-concept of potential usage of sensor data as a source of randomness. Furthermore, the mechanism is evaluated with the NIST statistical suite.

The requirement of encryption is everywhere whether data is being transmitted or being stored in some devices. Random numbers can be used in data encryption. Every IoT device which is connected to a network needs secure and low cost techniques for encryption. In modern day the introduction of cryptocurrency wallet and other wallet services need more secure and random key for encryption which cannot be generated through algorithm-based Pseudo Random Number Generator (PRNG). The advanced video games require true random numbers. The connected portable IoT devices also transfer sensitive data. So, a low cost and simple circuit of True Random Number Generator (TRNG) effectuate the requirements. A non-deterministic signal or a noise signal is a source of true randomness. Detection of non-deterministic signal using sensors is a simple approach which is used in this paper to generate True Random Numbers. The TRNG proposed in this paper have simple hardware setup which includes an Arduino Uno board, LDR sensor and sound sensor. A simple modular equation and EXOR logic is used as processing algorithm. The random number generated through this setup passes all the tests of randomness given in the NIST-STS test.

Random numbers are widely used in various applications. In the majority of cases, a pseudo-random number generator is used since true random number generators are slow and they are barely suitable for the hardware implementation. In this paper, we present new architecture of URNG (uniform random number generator) employing Leap-Ahead LFSR architecture for hardware implementation. In particular, the proposed URNG consists of two more segmented Leap-Ahead LFSRs to overcome the drawback of the conventional URNG employing Leap-Ahead architecture, that is, the sharp decrease of a maximum period of the generated random numbers. Thus, the proposed URNG with segmented LFSR architecture can generate multiple bits random number in a cycle without the frequent diminishing of maximum period of the generated random numbers. We prove the efficiency of the proposed segmented LFSR-architecture through the mathematical analysis. The simulation results show that the proposed URNG employing segmented Leap-Ahead LFSR architecture can be increased 2.5 times of the maximum period of generated random numbers compared to the URNG using the conventional Leap-Ahead architecture.

Pseudo random number generators (PRNG) play a key role in various security and cryptographic applications where the performance of these applications is directly related to the quality of generated random numbers. The design of such random number generators is a challenging task. In this paper, we propose an application of Hopfield Neural Networks (HNN) as pseudo random number generator. This is done based on a unique property of HNN, i.e., its unpredictable behavior under certain conditions. We compare the main features of ideal random number generators with those of PRNG based on Hopfield Neural Networks. We use a battery of statistical tests developed by National Institute of Standards and Technology (NIST) to measure the performance, and to evaluate the quality of the proposed Hopfield random number generator.

This paper presents a method to hide three binary images in a grayscale image with same resolution. Pseudo Random Number Generator(PRNG) produces the random numbers that rearranges the binary values. PRNG algorithm is unique and the strength of random numbers generated are equal to random numbers generated without a seed value. Each binary image pixel values are rearranged through three random number series and it is hidden in a grayscale image through Ultra Unique Numbers (UUN). By comparing both concealed image and original image, modification among the image is identified. To identify concealed secret binary information in a grayscale image at the destination, UUN is reapplied. PRNG is used to rearrange the binary values for transforming the binary images. The main aim of this paper is to increase the embedding capacity of carter image without degrading the quality of the secret information with high Peak Signal Noise Ratio(PSNR).

In today’s world, advancement of Information Technology has been simultaneously followed by cyber crimes resulting in offensive and distressful digital contents. Threat to the digital content has initiated the need for application of forensic activities in digital field seeking evidence against any type of cyber crimes for the sake of reinforcement of the law and order. Digital Forensics is an interdisciplinary branch of computer science and forensic sciences, rapidly utilizing the recovery and/or investigation works on digital data explored in electronic memory based devices with reference to any cyber based unethical, illegal, and unauthorized activities. A typical digital forensic investigation work follows three steps to collect evidence(s): content acquisition, content analysis and report generation. In digital content analysis higher amount of data volumes and human resource(s) exposure to distressing and offensive materials are of major concerns. Lack of technological support for processing large amount of offensive data makes the analytical procedure quite time consuming and expensive. Thus, it results in a degradation of mental health of concerned investigators. Backlog in processing time by law enforcement department and financial limitations initiate huge demand for digital forensic investigators turning out trustworthy results within reasonable time. Forensic analysis is performed on randomly populated sample, instead of entire population size, for faster and reliable analysis procedure of digital contents. Present work reports about an efficient design methodology to facilitate random sampling procedure to be used in digital forensic investigations. Cellular Automata (CA) based approach has been used in our random sampling method. Equal Length Cellular Automata (ELCA) based pseudo-random pattern generator (PRPG) has been proposed in a cost effective manner utilizing the concept of random pattern generator. Exhibition of high degree randomness has been demonstrated in the field of randomness quality testing. Concerned cost effectiveness refers to time complexity, space complexity, design complexity and searching complexity. This research includes the comparative study for some well known random number generators, e.g., recursive pseudo-random number generator (RPRNG), atmospheric noise based true-random number generator (TRNG), Monte-Carlo (M-C) pseudo-random number generator, Maximum Length Cellular Automata (MaxCA) random number generator and proposed Equal Length Cellular Automata (ELCA) random number generator.Resulting sequences for all those above mentioned pattern generatorshave significant improvement in terms of randomness quality. Associated fault coverage is being improved using iterative methods. Emphasis on cost effectiveness has been initiated for proposed random sampling in forensic analysis.

Pseudo random number generators (PRNGs) are crucial for numerous applications in HPC ranging from molecular dynamics to quantum chemistry, and hydrodynamics. These applications require high throughput and good statistical quality from the PRNGs - especially for parallel computing where long pseudo-random sequences can be exhausted rapidly. Although a handful PRNGs have been adapted to parallel computing, they do not fully exploit the features of wide-SIMD many-core processors and GPU accelerators in modern supercomputers. Multiple Recursive Generators (MRGs) are a family of random number generators based on higher order recursion, which provide statistically high-quality random number sequences with extremely long-recurrence lengths, and deterministic jump-ahead for effective parallelism. We reformulate the MRG8 (8th-order recursive implementation) for Intel's KNL and NVIDIA's P100 GPU - named MRG8-AVX512 and MRG8-GPU respectively. Our optimized implementation generates the same random number sequence as the original well-characterized MRG8. We evaluated MRG8-AVX512 and MRG8-GPU together with vender tuned random number generators for Intel KNL and GPU. MRG8-AVX512 achieves a substantial 69% improvement compared to Intel's MKL, and MRG8-GPU shows a maximum 3.36x speedup compared to NVIDIA's cuRAND library.

True random number generators (TRNG) are important counterparts to pseudorandom number generators (PRNG), especially for high security applications such as cryptography. They produce unpredictable, non-repeatable random sequences. However, most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs. These generators usually require post-processing algorithms to eliminate biases but in turn, reduces performance. In this paper, a new post-processing method based on hyperchaos is proposed for software-based TRNGs which not only eliminates statistical biases but also provides amplification in order to improve the performance of TRNGs. The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input changes, diffusion, and confusion capabilities to achieve these goals. Quantized bits of a physical entropy source are used to perturb the parameters of a hyperchaotic map, which is then iterated to produce a set of random output bits. To depict the feasibility of the proposed post-processing algorithm, it is applied in designing TRNGs based on digital audio. The generators are analyzed to identify statistical defects in addition to forward and backward security. Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput, which in turn reflects on the effectiveness of the proposed post-processing method.

Present day's data security plays a vital role in digital human life. Data is a valuable asset to any organization and hence its security from external attacks is very important. Information security is not only an important aspect but essential, to secure data from unapproved access. Data encryption, decryption and key management are the key factors in data protection. It is very important to have the right data security solution to meet the challenging threats. Cryptosystem implementation and random number generators are crucial for Cryptosystem applications such as security applications, space applications, military applications and smart cards et al. In this paper, we present the implementation of hybrid cryptosystem based on the True Random number Generator, pseudo Random number Generator and whitening the data by using the ASIC design flow.

The article is dedicated to a detailed review of pseudorandom number generators (PRNGs), their operating principles, features, advantages, limitations, and various implementation methods. Pseudorandom number generators have become an integral part of modern information security, leveraging advanced cryptographic algorithms to ensure reliability and resistance to attacks. Pseudorandom numbers are widely used in cryptography, simulation, computer games, and many other fields. The main goal of the article is to analyze various methods of generating pseudorandom numbers, their features, advantages, and disadvantages, as well as to study their impact on cryptographic strength. The article begins with the basic principles of PRNG operation, focusing on linear congruential generators (LCGs) as the simplest example. Although LCGs are easy to implement, they have significant limitations in the context of cryptographic security, such as short periods and relative predictability. For higher security requirements, cryptographically secure pseudorandom number generators (CSPRNGs) based on block ciphers, hash functions, or other complex mathematical algorithms are recommended. Additional attention is given to generators such as ChaCha20 and NORX, which demonstrate high speed and resistance to cryptanalytic attacks. Theoretical cryptographic strength is also analyzed for generators based on modified algorithms, such as BBS and BM, supported by the complexity of computational problems. In conclusion, the article emphasizes the critical importance of understanding the operation of various PRNGs for information security professionals, as the choice of generator can significantly impact the overall security level of a system. A comparison of the efficiency and cryptographic strength of different pseudorandom number generation methods is presented in a table, supplemented by program algorithms, their characteristics, and examples of their use in cryptography.

With1 the advent of quantum computers, encryption technologies such as RSA and ECC, which currently protect data integrity, are at risk of being compromised with ease. This development poses significant threats to the security of cloud computing and data centers. Additionally, the Random Number Generators (RNGs) that form the foundation of existing encryption systems may also become predictable under quantum computer attacks, necessitating the introduction of new RNGs. This paper introduces four widely used Pseudorandom Number Generators (PRNGs) and three Quantum Random Number Generators (QRNGs), evaluating their randomness, speed, and data range using TestU01 and other analytical tools. The evaluation results demonstrate that the strengths and weaknesses of RNGs differ in terms of speed, randomness, and implementation complexity, emphasizing the importance of selecting the appropriate RNG based on the priority factors of each service.

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required “coin” parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

Currently, True Random Number Generation (TRNG) is relatively slow, utilizing natural, physical processes as its entropy source. Other types of random numbers, such as Pseudo-Random Numbers, lack true randomness as eventually they repeat, but can be generated with great speed. The main idea of the work presented in this paper is to introduce parallel random number generation as a scalable means of increasing the rate of true random number generation in hardware to match and surpass that of Pseudo-Random Number Generators (PRNGs). Using a Raspberry Pi platform, this work will combine two (2) standard TRNGs to form one (1) unified, Parallel - True Random Number Generator (P-TRNG), with more than twice the output performance rate of its component TRNGs, and with demonstrated scalability.