FPGA based RNG for random WOB method in unit cube capacitance calculation

Random number generators for large-scale parallel Monte Carlo simulations on FPGA

In order to scale down a circuit size for hardware realization of neural network systems, there are many researches on a conventional pulse model neuron, in which, a conventional numerical calculation is replaced by a stochastic calculation. In the conventional stochastic calculation, LFSR (linear feedback shift register) has been used as a random number generator. In general, a good randomness is required for an exact calculation result. However, since the random numbers which are generated by LFSR is lacking in the randomness, there is a problem which affects an accuracy of the conventional stochastic calculation which uses LFSR for generating the random numbers. In our work, in order to improve the accuracy of the conventional stochastic calculation, we propose to use GLFSR (generalized-LFSR) which generates the random numbers which are rich in randomness as the random number generator for the stochastic calculation. The accuracy of the stochastic calculation is also evaluated using a standard deviation value (SD) and a maximum error. As a result, the proposed stochastic calculation which using GLFSR as the random number generator shows a highest accuracy of the calculation result.

Today, cryptographic security depends primarily on having strong keys and keeping them secret. The keys should be produced by a reliable and robust to external manipulations generators of random numbers. To hamper different attacks, the generators should be implemented in the same chip as a cryptographic system using random numbers. It forces a designer to create a random number generator purely digitally. Unfortunately, the obtained sequences are biased and do not pass many statistical tests. Therefore an output of the random number generator has to be subjected to a transformation called post-processing. In this paper the hash function SHA-256 as post-processing of bits produced by a combined random bit generator using jitter observed in ring oscillators (ROs) is proposed. All components – the random number generator and the SHA-256, are implemented in a single Field Programmable Gate Array (FPGA). We expect that the proposed solution, implemented in the same FPGA together with a cryptographic system, is more attack-resistant owing to many sources of randomness with significantly different nominal frequencies.

Random number generators represent basic cryptographic primitives. They are widely used in modern security schemes including security protocols, computer security and password sources. In some algorithms (e.g. DSA) or protocols (e.g. zero-knowledge), random numbers are intrinsic to the computation [3]. In all these applications, strength of security depends greatly on the quality of randomness of the source. Pseudo random number generators (PRNGs) play an important role in cryptographic applications, as the security of these systems depends on the assumption that future values in the random sequence can be unpredictable. A linear feedback shift register (LFSR), in effect, implements a binary polynomial generator. These generators find common use for PRNGs. However, the random sequence generated by LFSR can not guarantee the unpredictability in secure system. We have used genetic algorithm to improve LFSR and proposed a novel random number generator with complex architecture and longer period.

The way of measuring diameter by use of measuring bow height and chord length is commonly adopted for the large diameter work piece. In the process of computing the diameter of large work piece, measurement uncertainty is an important parameter and is always employed to evaluate the reliability of the measurement results. Therefore, it is essential to present reliable methods to evaluate the measurement uncertainty, especially in precise measurement. Because of the limitations of low convergence and unstable results of the Monte-Carlo (MC) method, the quasi-Monte-Carlo (QMC) method is used to estimate the measurement uncertainty. The QMC method is an improvement of the ordinary MC method which employs highly uniform quasi random numbers to replace MC's pseudo random numbers. In the process of evaluation, first, more homogeneous random numbers (quasi random numbers) are generated based on Halton's sequence. Then these random numbers are transformed into the desired distribution random numbers. The desired distribution random numbers are used to simulate the measurement errors. By computing the simulation results, measurement uncertainty can be obtained. An experiment of cylinder diameter measurement and its uncertainty evaluation are given. In the experiment, the guide to the expression of uncertainty in measurement method, MC method, and QMC method are validated. The result shows that the QMC method has a higher convergence rate and more stable evaluation results than that of the MC method. Therefore, the QMC method can be applied effectively to evaluate the measurement uncertainty.

RNGAVXLIB: Program library for random number generation, AVX realization

Thermal-pulse method is a powerful tool for measuring space charge distributions in polymer films. The data analysis for thermal-pulse method involves the Fredholm integral equation of the first kind, which requires an appropriate numerical procedure to obtain a solution. Various numerical techniques, including scale transformation and regulation method, are proposed. Of those numerical methods, the scale transformation (ST) is the simplest and the most widely used method. However, it presents a high spatial resolution only near the sample surface. Monte Carlo (MC) method is one of the recently proposed ways to solve the equation numerically and has been successfully applied to the analysis of laser intensity modulation method data, which also involves the Fredholm integral equation of the first kind. In this paper we attempt to analyze thermal-pulse data in frequency domain with the MC method and discuss its effectiveness based on some numerical simulations. The simulation results indicate that the electric field profiles can be effectively extracted by the MC method. The computed profiles by the MC method consist well with the supposed distributions in the entire thickness of the sample, while the profiles reconstructed by the ST method fit very well to the supposed one at the vicinity of the target surface and distort sharply along the direction of the thermal pulse propagation in the sample bulk. On the other hand, the oscillations in the computed results by the MC method could deteriorate its accuracy in this study. The influence of noise level on the analysis based on the MC method is also tested by the use of the simulated data. The results show that the computed profiles would become more fluctuant as the noise level increases. This problem can be solved by selecting a larger value of tolerance during the singular value decomposition procedure. Thus, the value of tolerance is considered to be one of the key parameters in this algorithm, which is actually hard to determine. Additionally, the experimental data obtained from a polypropylene film under applied electric field are analyzed to illustrate the feasibility of MC method to be applied to the thermal-pulse experimental data. The results also show that the spatial accuracy by the MC method in the entire sample thickness is higher than by the ST method, which verifies that the MC method is more suitable for detecting the electric field distribution in the deep bulk of the sample. Owing to noise and error, the accuracy of MC calculation depends on the chosen tolerance value, which is now considered to be an obstacle in applying this method to the practical thermal-pulse measurement.

This paper presents the FPGA (Field Programmable Gate Array) implementation and the coupling analysis of a metastability-based random number generator (RNG). The metastability is acquired through exploiting transient effect ring oscillators (TEROs) and the random bit generation is accomplished through irregular sampling of regular waveform method. As the proposed RNG is made up of only digital logic gates, it is prototyped on a Xilinx ZedBoard Zynq-7000 evaluation platform. It is demonstrated that the RNG output bitstream satisfies NIST 800-22 statistical tests of randomness without any need for post-processing and the proposed RNG can provide high data throughput. Furthermore, the proposed RNG uses less number of components compared to previously reported TERO based RNGs, thus enabling lower power consumption and smaller footprint. Additionally, the proposed RNG is subjected to correlation based cryptanalysis study. In classical ring oscillator (RO) based RNGs, the ring oscillators are required to be placed at a distance from each other to avoid locking phenomenon that may occur due to coupling between adjacent ROs. This study demonstrates that unlike classical RO based RNGs, the proposed RNG is insensitive to locking phenomenon and TERO structures are not required to be placed way from each other. Therefore, the proposed method lead to a more compact RNG design compared to classical RO based RNGs.

Much scientific work has focused on the generation of random numbers as well as the distribution of said random numbers for use as a cryptographic key. However, emphasis is often placed on one of the two to the exclusion of the other, but both are often simultaneously important. Here we present a simple hybrid free-space link scheme for both the generation and secure distribution of (pseudo-)random numbers between two remote parties, drawing the randomness from the stochastic nature of atmospheric turbulence. The atmosphere is simulated using digital micro-mirror devices for efficient, all-digital control. After outlining one potential algorithm for extracting random numbers based on finding the centre-of-mass (COM) of turbulent beam intensity profiles, the statistics of our experimental COM measurements is studied and found to agree well with the literature. After implementing the scheme in the laboratory, Alice and Bob are able to establish a string of correlated random bits with an 84% fidelity. Finally, we make a simple modification to the original setup in an attempt to thwart the hacking attempts of an eavesdropper, Eve, who has access to the free-space portion of the link. We find that the fidelity between Eve’s key and that of Alice/Bob is 54%, only slightly above the theoretical minimum. Atmospheric turbulence could hence be leveraged as an added security measure, rather than being seen as a drawback.

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.

This paper presents the FPGA (Field Programmable Gate Array) implementation and coupling analysis of a metastability-based random number generator (RNG). The metastability is obtained by using transient effect ring oscillators (TEROs) and the RNG uses regular sampling of irregular waveform method. As the proposed RNG is designed with digital logic gates only, it is implemented on a Xilinx ZedBoard Zynq-7000 evaluation platform. The output bitstream satisfies NIST 800-22 statistical tests of randomness without any need for postprocessing at a high bit rate. The proposed RNG uses less number of components compared to previously reported TERO based RNGs, thus suggesting lower power consumption and area. Additionally, correlation-based cryptanalysis study is conducted on the proposed RNG. In classical ring oscillator (RO) based RNGs, the ring oscillators need to be located at a distance from each other to avoid coupling between adjacent ROs. This study demonstrates that unlike classical RO based RNGs, the proposed RNG is able to guarantee high stability. It is insensitive to the locking phenomenon, hence leading to more compact RNG design.

Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even the most robust implementation of a cipher. Due to their intrinsic close relationship with analogue parameters of the circuit, True Random Number Generators are usually tailored on specific silicon technology and are not easily scalable on programmable hardware, without affecting their entropy. On the other hand, programmable hardware and programmable System on Chip are gaining large adoption rate, also in security critical application, where high quality random number generation is mandatory. The work presented herein describes the design and the validation of a digital True Random Number Generator for cryptographically secure applications on Field Programmable Gate Array. After a preliminary study of literature and standards specifying requirements for random number generation, the design flow is illustrated, from specifications definition to the synthesis phase. Several solutions have been studied to assess their performances on a Field Programmable Gate Array device, with the aim to select the highest performance architecture. The proposed designs have been tested and validated, employing official test suites released by NIST standardization body, assessing the independence from the place and route and the randomness degree of the generated output. An architecture derived from the Fibonacci-Galois Ring Oscillator has been selected and synthesized on Intel Stratix IV, supporting throughput up to 400 Mbps. The achieved entropy in the best configuration is greater than 0.995.

This paper proposes a hardware oriented dropout algorithm for an efficient field-programmable gate array (FPGA) implementation. Dropout is a regularization technique, which is commonly used in neural networks such as multilayer perceptrons (MLPs), convolutional neural networks (CNNs), among others. To generate a dropout mask to randomly drop neurons during training phase, random number generators (RNGs) are usually used in software implementations. However, RNGs consume considerable FPGA resources in hardware implementations. The proposed method is able to minimize the resources required for FPGA implementation of dropout by performing a simple rotation operation to a predefined dropout mask. We apply the proposed method to MLPs and CNNs and evaluate them on MNIST and CIFAR-10 classification. In addition, we employ the proposed method in GoogLeNet training using own dataset to develop a vision system for home service robots. The experimental results demonstrate that the proposed method achieves the same regularized effect as the ordinary dropout algorithm. Logic synthesis results show that the proposed method significantly reduces the consumption of FPGA resources in comparison to the ordinary RNG-based approaches.

In the context of growing the adoption of advanced sensors and systems for active vehicle safety and driver assistance, an increasingly important issue is the security of the information exchanged between the different sub-systems of the vehicle. Random number generation is crucial in modern encryption and security applications as it is a critical task from the point of view of the robustness of the security chain. Random numbers are in fact used to generate the encryption keys to be used for ciphers. Consequently, any weakness in the key generation process can potentially leak information that can be used to breach even the strongest cipher. This paper presents the architecture of a high performance Random Number Generator (RNG) IP-core, in particular a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) IP-core, a digital hardware accelerator for random numbers generation which can be employed for cryptographically secure applications. The specifications used to develop the proposed project were derived from dedicated literature and standards. Subsequently, specific architecture optimizations were studied to achieve better timing performance and very high throughput values. The IP-core has been validated thanks to the official NIST Statistical Test Suite, in order to evaluate the degree of randomness of the numbers generated in output. Finally the CSPRNG IP-core has been characterized on relevant Field Programmable Gate Array (FPGA) and ASIC standard-cell technologies.

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.