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

In this paper we consider a side-channel attack on a chaos-based random number generator (RNG) based on power consumption analysis. The aim of this attack is to verify if it is possible to retrieve information regarding the internal state of the chaotic system used to generate the random bits. In fact, one of the most common arguments against this kind of RNGs is that, due to the deterministic nature of the chaotic circuit on which they rely, the system cannot be truly unpredictable. Here we analyze the power consumption profile of a chaos-based RNG prototype we designed in 0.35 mum CMOS technology, showing that for the proposed circuit the internal state (and therefore the future evolution) of the system cannot be determined with a side-channel attack based on a power analysis. This property makes the proposed RNG perfectly suitable for high-security cryptographic applications.

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 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.

Monte Carlo (MC) method is widely used in resolving mathematical problems that are too complicated to solve analytically. The method involves with sampling process of the random numbers and probability to estimate the result. As MC method depending on a large number of good quality random numbers to produce a high accuracy result, developing a good random number generator (RNG) is vital. Most of random number generators are developed in software based, with the improvement of Field Programmable Gate Arrays (FPGA) density and speed in recent days, implementing random number generator (RNG) directly into hardware is feasible. Random Walk on the Boundary (WOB) is one of MC methods that applied to calculate the unit cube capacitance. The unique requirement of this method is the random numbers produced by RNG must fall within the Gaussian distribution and the maximum decimal values in the range of [0, 1]. Thus, in this paper we presented a novel hardware RNG for Random WOB method to calculate unit cube capacitance in FPGA. The RNG is implemented in floating-point base, using the combination of Cellular Automata Shift Register (CASR) and Linear Feedback Shift Register (LFSR) then channeled through Box-Muller transformation. There is linear approximation in computing logarithmic function applied in Box-Muller transformation. Based on statistical tests, the random numbers generated is nearly 97.5% resembling the standard normal distribution.

Random number generators are integral components to Monte Carlo codes. They provide the pseudorandom number sequence used to actually sample the distributions of interest. As a result, they are one of the most important components to the software. The current recommended MCNP random number generator is a 63-bit linear congruential generator (LCG). This generator is quite fast, but it has some drawbacks. First, it only has a period of 2⁶³. Due to the necessarily non-optimal usage of random numbers to ensure parallel reproducibility, this amount is too few to guarantee random number sequences are not reused in all configurations the code runs under. As simulation size increases, users will need to be aware of the limitations of the generator and tune configuration variables to best suit their simulations, or they will need to assume that reuse is not negatively affecting their answers. Neither of these are optimal. Second, small LCGs are fairly weak in bit generation quality, and this can have an unknown impact on the quality of the simulation. This paper is an investigation into whether or not more modern random number generators can supersede the current ones. The goal is to find a generator that is similar or superior in speed to the LCGs, has a state space large enough to make strong guarantees about random number reuse, and passes all modern random number test suites. If such a generator is found, it would eliminate the need for the user to even be aware of the limitations of the random number generator and would simplify the use of the code. This paper will be broken into several parts. Sec. 2 will discuss the evolution of the random number generator within the MCNP code. Sec. 3 will go over what a Monte Carlo code needs from a generator to be reproducible and portable and how the current generator behaves in that light. Sec. 4 goes through how each generator was tested. Finally, Sec. 5 will discuss improvements that could be made to the code.

Nowadays, we can enjoy many internet applications including online lotteries and games. The results of lotteries, card games, dice throwing and so on, depend upon the values of random numbers generated under some rules. However, we cannot verify the correctness for the given random numbers, that means, we have no means to convince ourselves that the given random numbers have indeed been correctly generated, using a pre-determined algorithm, and without being intentionally perverted by anyone. We say that such random number generation can provide ‘transparency’. It is quite important that random numbers given online can convince us that those are correctly generated. In other words, the transparency of online random number generation is quite important. Sako et. al. [5] have given a random number generation scheme applicable to the game ‘Backgammon’, in which transparency of blockchain enables us to verify the correctness for used random numbers after the game ended. In that scheme, however, the server has to be a trusted party, and it means dishonest generation of random numbers is possible by making one player and the server corrupted. In this paper, we present a transparent random number generation scheme. To be sure that a few trusted parties appears in the description of the scheme, but by implementing such trusted ones with public blockchain actually operated, our scheme can generate transparent random numbers without requiring any trusted parties.

RNGAVXLIB: Program library for random number generation, AVX realization

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 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.

The importance of random number generators (RNGs) to various computing applications is well understood. To ensure a quality level of output, high-entropy sources should be utilized as input. However, the algorithms used have not yet fully evolved to utilize newer technology. Even the Android pseudo RNG (APRNG) merely builds atop the Linux RNG to produce random numbers. This paper presents an exploratory study into methods of generating random numbers on sensor-equipped mobile and Internet of Things devices. We first perform a data collection study across 37 Android devices to determine two things-how much random data is consumed by modern devices, and which sensors are capable of producing sufficiently random data. We use the results of our analysis to create an experimental framework called SensoRNG, which serves as a prototype to test the efficacy of a sensor-based RNG. SensoRNG employs collection of data from on-board sensors and combines them via a lightweight mixing algorithm to produce random numbers. We evaluate SensoRNG with the National Institute of Standards and Technology statistical testing suite and demonstrate that a sensor-based RNG can provide high quality random numbers with only little additional overhead.

Random number generators (RNG) are a fundamental hardware component in modern cryptographic systems [1]. The generation of random numbers can be subdivided into two classes, pseudo-RNGs and hardware RNGs. In pseudo-RNGs software algorithms are implemented on deterministic hardware but are dependent on a set of initial values or “seed”, which reduces the security. In contrast, hardware RNGs generate random numbers from a naturally occurring physical phenomenon, such as thermal noise. However, implementations often suffer from large silicon footprints due to the need to create resistor-amplifier-ADC chains [2] or bias removal circuits [3]. In this work, we experimentally demonstrate a compact and scalable 1T1R based RNG by harnessing the inherent stochasticity in the insulator-to-metal phase transition (IMT) in vanadium dioxide (VO 2 ).

CHAPTER 12 - SIMULATIONS WITH RANDOM NUMBERS

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.

We present a generator producing unique and truly random bit sequences based on the measurement of the quantum uncertainty of a continuous variable vacuum state. Vacuum states have the advantage of being inherently pure states, i.e. they cannot be tempered with by an adversary and are easily detectable. Therefore, they are an ideal resource for a quantum RNG. Our RNG consists of a simple homodyne detection system.

Randomness is a critical issue in peer-to-peer networks because random numbers allow us to fairly select the candidates, resolve the lotteries, select block producers, etc. The difficulty is that each participant wants to verify that the random number was randomly generated, this led to the invention of verifiable random functions (VRF). The VRF is a pseudo-random function that provides a solution to blockchain-based random number generation. This paper focuses on the implementation of an elliptic curve-based VRF introduced by NIST called ECVRF-secp256r1 in Solidity. The algorithm verifies the randomness on-chain, tests the gas consumption at each stage, and compares it to the ECVRF-secp256k1.