True Random Number Generators

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.

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 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.

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 ).

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.

A physical random number generator, which generates truly random number trains by using the randomness of physical phenomena, is widely used in the field of cryptographic applications. We have developed an ultra high-speed superconductive physical random number generator that can generate random numbers at a frequency of more than 10 GHz by utilizing the high-speed operation and high-sensitivity of superconductive integrated circuits. In this study, we have statistically evaluated the quality of the random number trains generated by the superconductive physical random number generator. The performances of the statistical tests were based on a test method provided by National Institute of Standards and Technology (NIST). These statistical tests comprised several fundamental tests that were performed to evaluate the random number trains for their utilization in practical cryptographic applications. We have generated 230 random number trains consisting of 20,000-bits by using the superconductive physical random number generator fabricated by the SRL 2.5 kA/cm 2 Nb standard process. The generated random number trains passed all the fundamental statistical tests. This result indicates that the superconductive random number generator can be sufficiently utilized in practical applications.

The requirement of physical true random number generator and the difference between the true random number and pseudo-random number are presented. The recent experiements of true ran-dom number generator, expetically, the various schemes of true random number generator based on lasers, are summarized. Also, we report the progress of the thoretical and experimental research on physical true random number generator in our group.

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.

Quantum random numbers play a crucial role in diverse applications, including cryptography, simulation, and artificial intelligence. In contrast to predictable algorithm-based pseudo-random numbers, quantum physics provides new avenues for generating theoretically true random numbers by exploiting the inherent uncertainty contained in quantum phenomena. Here, we propose and demonstrate a quantum random number generator (QRNG) using a prepared broadband squeezed state of light, where the randomness of the generated numbers entirely originates from the quantum noise introduced by squeezing operation rather than vacuum noise. The relationship between entropy rate and squeezing level is analyzed. Furthermore, we employ a source-independent quantum random number protocol to enhance the security of the random number generator.

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.

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.

The generation of random numbers is crucial for practical implementations of cryptographic algorithms. In this sense, hardware security modules (HSMs) include true random number generators (TRNGs) implemented in hardware to achieve good random number generation. In the case of cryptographic algorithms implemented on FPGAs, the hardware implementation of RNGs is limited to the programmable cells in the device. Among the different proposals to obtain sources of entropy and process them to implement TRNGs, those based in ring oscillators (ROs), operating in parallel and combined with XOR gates, present good statistical properties at the cost of high area requirements. In this paper, these TRNGs are revisited, showing a method for area optimization independently of the FPGA technology used. Experimental results show that three ring oscillators requiring only three LUTs are enough to build a TRNG on Artix 7 devices from Xilinx with a throughput of 33.3 Kbps, which passes NIST tests. A throughput of 50 Kbps can be achieved with four ring oscillators, also requiring three LUTs in Artix 7 devices, while 100 Kbps can be achieved using an structure with four ring oscillators requiring seven LUTs.

Quantum random number generators (QRNGs) can generate true random numbers and have significant applications in quantum communication, numerical computation, and model simulation. However, the rate of random number generation based on photon detection is constrained by the maximum count rate of a single-photon detector. Therefore, improving the efficiency of random number generation for individual photon detection events becomes an optional way to increase the rate of random number generation. In this paper, multidimensional photon detection is implemented to enhance single-photon detection events, thereby providing a new, to the best of our knowledge, technical development strategy for high-speed random number generators. The temporal and spatial coherence of coherent-state photons is utilized as a valuable quantum resource, enabling us to achieve the simultaneous extraction of time-space measurement collapsed randomness for single-photon detection events using a chip-scale CMOS-integrated single-photon avalanche diode array. The efficiency of random number generation for single-photon detection events is effectively improved. In our experiments, up to 20 bits can be extracted from an individual photon detection event, and the rate of random number generation reaches up to 2.067 Gbps.

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.

This paper shows the research on hardware random number generator (HRNG). As truly random numbers are strongly required in encryption and computer simulation areas, developing a simple and inexpensive HRNG has significant value. The whole system is divided into the noise generating module and the processing module. After the numbers are generated, a randomness test has been carried out which indicates that the random numbers generated are truly random. It is concluded that the final product of this HRNG meets the requirements of the objectives.