Certified Quantum Random-Number Generator Based on Single-Photon Entanglement

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.

Quantum random number generators (QRNG) represent an advanced solution for randomness generation, which is essential in every cryptographic application. In this context, integrated arrays of single-photon detectors have promising applications as QRNGs based on the spatial detection of photons. For the employment of QRNGs in cryptography, it is necessary to have efficient methods to evaluate the so-called quantum min-entropy that corresponds to the amount of the true extractable quantum randomness from the QRNG. Here, we present an efficient method that allows the estimation of the quantum min-entropy for a multi-detector QRNG. In particular, we consider a scenario in which an attacker can control the efficiency of the detectors and knows the emitted number of photons. Eventually, we apply the method to a QRNG with 103 detectors.

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.

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 quantum random number generator (QRNG) based on a silicon nanocrystals (Si-NCs) light emitting device (LED) coupled with a silicon single photon avalanche photodiode (Si-SPAD) is presented. A simple setup is used for the generation of random bits. The modeled approach assures a negligible bias on datasets of ∼100 Mbits length. The raw data pass all the statistical tests in the National Institute of Standards and Technology (NIST) suite without any post-processing operations. The bit-rate of 0.6 Mbps is achieved. The information-theoretically provable randomness extractor of Toeplitz-hashing function is applied to longer datasets (∼1 Gbits) to extract the randomness, to minimize the bias, and consequently pass all the NIST tests. Stabilizing the temperature, resetting the applied current to the LED, or a feedback system can also be used as parameter control solutions to generate good quality, long datasets of random numbers suitable for cryptographic applications.

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.

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.

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 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.

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.

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.

We demonstrate a 6 Gbps real-time optical quantum random number generator by measuring vacuum fluctuation. To address the common problem that speed gap exists between fast randomness generation and slow randomness extraction in most high-speed real-time quantum random number generator systems, we present an optimized extraction algorithm based on parallel implementation of Toeplitz hashing to reduce the influence of classical noise due to the imperfection of devices. Notably, the real-time rate of randomness extraction we have achieved reaches the highest speed of 12 Gbps by occupying less computing resources, and the algorithm has the ability to support hundreds of Gbps randomness extraction. By assuming that the eavesdropper with complete knowledge of the classical noise, our generator has a randomness generation speed of 6.83 Gbps and this supports the generation of 6 Gbps information-theoretically provable quantum random numbers, which are output in real-time through peripheral component interconnect express interface.

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 ).

Harnessing quantum processes is an efficient method to generate truly indeterministic random numbers, which are of fundamental importance for cryptographic protocols, security applications or Monte-Carlo simulations. Recently, quantum random number generators based on continuous variables have gathered a lot of attention due to the potentially high bit rates they can deliver. Especially quadrature measurements on shot-noise limited states have been studied in detail as they do not offer any side information to potential adversaries under ideal experimental conditions. However, they may be subject to additional classical noise beyond the quantum limit, which may become a source of side information for eavesdroppers. While such eavesdropping attacks have been investigated in theory in some detail, experimental studies are still rare. We experimentally realize a continuous variable eavesdropping attack, based on heterodyne detection, on a trusted quantum random number generator and discuss the limitations for secure random number generation that arise.