Segmented Leap-Ahead LFSR Architecture for Uniform Random Number Generator

Random numbers play a key-role in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly combined together: True Random Number Generators (TRNGs), and Pseudo Random Number Generators (PRNGs). The former are devices that exploit truly stochastic physical phenomena [2, 3, 4, 5, 6], such as the electronic noise or the chaotic dynamics of certain nonlinear systems: for these devices the output sequences have an intrinsic degree of unpredictability, that is measured referring to the theoretical tools provided by Information Theory (e.g., in terms of the Shannon entropy) [7,4]. On the other hand, PRNGs are deterministic periodic finite state machines whose aim is to emulate, within the period, the random behavior of a truly random source of numbers. From a theoretical point of view, due to their deterministic nature, PRNGs are potentially predictable by observing their generated sequences [8, 9, 10, 1]. Nevertheless, in literature some families of PRNGs are classified to be ‘secure’, meaning that their algorithmic structure involves calculations that in average, referring to the prediction task, require an amount of computation time that is asymptotically unfeasible with the size of the problem, when referring to both the computational equipment at disposal and the known computing fastest algorithms [1,11]. It is worth noting that a given generator, even if belonging to an asymptotically secure family of PRNGs, can generate short periodic (and unsecure) sequences for several values of the initial seed. Therefore, apart from the cryptographic robustness of their algorithmic structure, a cryptographic PRNG must generate sequences that are acceptable from a statistical point of view, i.e., that pass a certain number of standard statistical tests [1, 12].

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.

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.

A facility for generating sequences of pseudorandom numbers is a fundamental part of computer simulation systems. Furthermore, multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform random-number generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. Simple procedure calls allow the user to make any generator “jump” ahead/back v steps (random numbers). Implementation issues are discussed. An efficient and portable code is also provided to implement the package. The basic underlying generator CMRG (combined Multiple Recursive Generator) combines two multiple recursive random number generators with a period length of approximately 2191 (˜ 3.1× 1057), good speed, and excellent theoretical properties.

A facility for generating sequences of pseudorandom numbers is a fundamental part of computer simulation systems. Furthermore, multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform random-number generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. Simple procedure calls allow the user to make any generator “jump” ahead/back v steps (random numbers). Implementation issues are discussed. An efficient and portable code is also provided to implement the package. The basic underlying generator CMRG (combined multiple recursive generator) combines two multiple recursive random number generators with a period length of approximately 2191 (≈ 3.1× 1057), good speed, and excellent theoretical properties.

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.

The Ziggurat algorithm is an efficient way for building a Gaussian random number generator (GRNG), which is useful in many scientific and engineering applications. As the classic ziggurat-based GRNG includes nonlinear operations in judging the wedge and tail regions, which is complicated and resource consuming. An improved ziggurat algorithm is proposed by optimizing the accepting model with piecewise linear fitting, replacing the nonlinear operations with linear ones. The improved GRNG works with a 33% decrease of resource and has no significant performance loss. In addition, the uniform random number generator (URNG) in GRNG is implemented by metastability-based ring oscillators with XOR trees, which is the state-of-the-art technique for generating true random numbers in fully digital ways. FPGA results show that the proposed GRNG generates good normal distribution samples with a smooth power spectrum.

Random numbers are a fundamental resource in science and engineering, and are also widely used in many fields, such as simulation, cryptography, lotteries, fundamental science. There are algorithmically generated numbers that look like random numbers but are not truly random. These pseudo random numbers are generated from a computer, using deterministic algorithms. Because, we cannot use pseudo random generators in situations, where true randomness is necessary, we use true random number generators. In this case, we use unpredictable random events as a random source. Quantum random number generators (QRNG) output true random numbers based on inherent randomness in quantum measurements. Our goal is to generate fast random numbers at a lower cost. At the same time, a high level of randomness is essential. We present the improved novel quantum random number generator, which is based the on time of arrival QRNG. It is rather efficient, as it uses the simple version of the detectors with rather few requirements. The novel QRNG produces more than one random bit per each photon detection.

A true random number generator (TRNG) is suitable for generating secure keys and nonces. TRNGs implemented in IoT devices must be small in scale and have low power consumption. The random number sequence generated by TRNG needs to have high entropy immediately after startup and a stable state. In this paper, three types of ring oscillator type TRNGs, TERO-based, COSO-based, and STR-based TRNG, are implemented on Zynq-7010. When these TRNGs are implemented as a single entropy source, it is challenging to implement them because it is necessary to evaluate the layout and wiring for each FPGA. This paper proposes a TRNG configuration, which exclusively ORs the outputs of multiple entropy sources. We show that this configuration can reduce the implementing difficulty and realize high entropy. For the random number sequence evaluation, we use the statistical test of NIST SP800-90B and BSI AIS 20/31. In addition, the random number sequence immediately after the startup is also statistically evaluated. As a result, our proposed TRNGs generate high entropy random numbers and are easy to implement on FPGA when we implement TRNGs with eight single entropy sources for TERO-based TRNG, 48 for COSO-based TRNG, and two for STR-based TRNG, respectively.

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.

Random numbers are widely used in the cryptography and security systems. However, most of the true random number generators (TRNG) which use physical randomness are with high complexity and high power consumption. This paper proposes a new TRNG circuit using magnetic tunnel junction (MTJ). As one of the reliability issues in MTJ based circuit, the stochastic switching behavior provides a perfect physical source of randomness. The functionality of proposed design is validated by transient simulations with 28nm fully depleted silicon-on-insulator (FDSOI) technology and an accurate MTJ compact model. Simulation results show that our design can generate accurate random bitstream stably. The reliability analysis concerning process variation of MTJs and transistors proves the good variability tolerance of our TRNG design. Furthermore, our design can output stable random bitstream around 30 tuning steps.

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.

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.

An ideal image compression technique for image data archival, retrieval and distribution would be one with the asymmetrical computational requirements of vector quantization (VQ), but without the complications arising from VQ codebooks. Codebook generation and maintenance are stumbling blocks which have limited the use of VQ as a practical image compression algorithm. Model-based VQ (MVQ), a variant of VQ described here, has the computational properties of VQ but does not require explicit codebooks. The codebooks are internally generated using mean removed error and human visual system (HVS) models. The error model assumed is the Laplacian distribution with mean, (lambda) , computed from a sample of the input image. A Laplacian distribution with mean, (lambda) , is generated with a uniform random number generator. These random numbers are grouped into vectors. These vectors are further conditioned to make them perceptually meaningful by filtering the DCT coefficients from each vector. The DCT coefficients are filtered by multiplying by a weight matrix that is found to be optimal for human perception. The inverse DCT is performed to produced the conditioned vectors for the codebook. The only image dependent parameter used in the generation of codebook is the mean, (lambda) , that is included in the coded file to repeat the codebook generation process for decoding.

Random numbers are needed in many areas: cryptography, Monte Carlo computation and simulation, industrial testing and labeling, hazard games, gambling, etc. Our assumption has been that random numbers cannot be computed; because digital computers operate deterministically, they cannot produce random numbers. Instead, random numbers are best obtained using physical (true) random number generators (TRNG), which operate by measuring a well-controlled and specially prepared physical process. Randomness of a TRNG can be precisely, scientifically characterized and measured. Especially valuable are the information-theoretic provable random number generators (RNGs), which, at the state of the art, seem to be possible only by exploiting randomness inherent to certain quantum systems. On the other hand, current industry standards dictate the use of RNGs based on free-running oscillators (FRO) whose randomness is derived from electronic noise present in logic circuits and which cannot be strictly proven as uniformly random, but offer easier technological realization. The FRO approach is currently used in 3rd- and 4th-generation FPGA and ASIC hardware, unsuitable for realization of quantum RNGs. In this chapter we compare weak and strong aspects of the two approaches. Finally, we discuss several examples where use of a true RNG is critical and show how it can significantly improve security of cryptographic systems, and discuss industrial and research challenges that prevent widespread use of TRNGs.