Real-time vacuum-state quantum random-number generator on a chip

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.

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 numbers are a fundamental ingredient for many applications including simulation, modelling and cryptography. Sound random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. We demonstrate a real-time self-testing source independent quantum random number generator (QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source; only the detection device is trusted. We use a homodyne detection to alternatively measure the Q and P conjugate quadratures of our source. Using the entropic uncertainty relation, measurements on P allow us to estimate a bound on the min-entropy of Q conditioned on any classical or quantum side information that a malicious eavesdropper may detain. This bound gives the minimum number of secure bits we can extract from the Q measurement. We discuss the performance of different estimators for this bound. We operate this QRNG with a squeezed state and we compare its performance with a QRNG using thermal states. The real-time bit rate was 8.2 kb/s when using the squeezed source and between 5.2-7.2 kb/s when the thermal state source was used.

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.

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.

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.

The vital characteristic of randomness is unpredictability. Thus any regularity will compromise the application of random numbers. Quantum random number generators (QRNGs) can provide intrinsic unpredictable randomness based on the nature of quantum physics, while pseudo-random number generator can not due to the origination of deterministic algorithms or physical processes. However, commonly used traditional test suits are rigorously to test the statistical properties, and the unpredictability of random numbers is still difficult to test. To verify which sources of random numbers are truly unpredictable, in this paper, we propose a new randomness testing method with the artificial neural network (ANN). Random number sequences generated by four different kinds of sources are tested, which are the natural number λ, the linear congruence generator (LCG) pseudo-random algorithm, the Mersenne Twister (MT) pseudorandom algorithm and the QRNG based on vacuum noise, respectively. The testing results indicate that the random sequences from natural number λ and LCG fail to pass our randomness test, while the other two kinds of sequences pass the test successfully due to the relatively simple structure of our ANN. As the complexity of the ANN and the amount of computing power involved increasing, this test method has potential to predict the MT random numbers, and it is also expected that the quantum random numbers can not pass the test with unpredictability no matter how complex the ANN is.

Quantum entanglement represents an ideal resource to guarantee the security of random numbers employed in many scientific and cryptographic applications. However, entanglement-based certified random number generators are particularly challenging to implement. Here, we demonstrate a certified quantum random number generator based on momentum-polarization entangled single-photon states. The use of single-photon entanglement allows an attenuated laser source to be employed and a simple setup where only linear optical components are utilized. For the latter, a semi-device-independent modeling of the photonic quantum random number generator is developed, which certifies a minimum entropy of $(2.5\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, corresponding to a generation rate of 4.4 kHz. At the expenses of a higher level of trust in the system, the certified minimum entropy can be increased to $(30.1\ifmmode\pm\else\textpm\fi{}0.5)\mathrm{%}$, implying a generation rate of 52.7 kHz. Our results show that a simple optical implementation combined with an accurate modeling provide an entanglement-based high-security quantum random number generator using imperfect devices.

This paper presents a novel approach to enhancing the security and reliability of drone communications through the integration of Quantum Random Number Generators (QRNG) in Frequency Hopping Spread Spectrum (FHSS) systems. We propose a multi-drone framework that leverages QRNG technology to generate truly random frequency hopping sequences, significantly improving resistance against jamming and interception attempts. Our method introduces a concurrent access protocol for multiple drones to share a QRNG device efficiently, incorporating robust error handling and a shared memory system for random number distribution. The implementation includes secure communication protocols, ensuring data integrity and confidentiality through encryption and Hash-based Message Authentication Code (HMAC) verification. We demonstrate the system’s effectiveness through comprehensive simulations and statistical analyses, including spectral density, frequency distribution, and autocorrelation studies of the generated frequency sequences. The results show a significant enhancement in the unpredictability and uniformity of frequency distributions compared to traditional pseudo-random number generator-based approaches. Specifically, the frequency distributions of the drones exhibited a relatively uniform spread across the available spectrum, with minimal discernible patterns in the frequency sequences, indicating high unpredictability. Autocorrelation analyses revealed a sharp peak at zero lag and linear decrease to zero values for other lags, confirming a general absence of periodicity or predictability in the sequences, which enhances resistance to predictive attacks. Spectral analysis confirmed a relatively flat power spectral density across frequencies, characteristic of truly random sequences, thereby minimizing vulnerabilities to spectral-based jamming. Statistical tests, including Chi-squared and Kolmogorov-Smirnov, further confirm the unpredictability of the frequency sequences generated by QRNG, supporting enhanced security measures against predictive attacks. While some short-term correlations were observed, suggesting areas for improvement in QRNG technology, the overall findings confirm the potential of QRNG-based FHSS systems in significantly improving the security and reliability of drone communications. This work contributes to the growing field of quantum-enhanced wireless communications, offering substantial advancements in security and reliability for drone operations. The proposed system has potential applications in military, emergency response, and secure commercial drone operations, where enhanced communication security is paramount.

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.

To realize a vacuum-fluctuation-based quantum random number generator (QRNG), various implementations can be explored to improve efficiency and practicality. In this study, we employed a multi-mode (MM) laser as the local oscillator in a vacuum-fluctuation QRNG and compared its performance with that of a conventional single-mode (SM) laser. Despite experiencing frequency-mode hopping, the MM laser successfully interfered with the vacuum state, similar to the SM reference. The common-mode rejection ratio of the balanced homodyne detection setup exceeded 35 dB for all laser sources. The digitized raw data were processed with a cryptographic hash function to generate full-entropy data. These outputs passed both the independent and identically distributed test recommended in NIST SP 800-90B and the statistical test suite under the SP 800-22 guideline, confirming their quality as quantum random numbers. Our results demonstrate that full-entropy data derived from either SM or MM lasers are applicable to systems requiring high-quality randomness, such as quantum key distribution. This study represents the first demonstration of an MM-laser-based vacuum-fluctuation QRNG, achieving a generation rate of 10 Gbps and indicating potential for compact and practical implementation.

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 TRNG (True Random Number Generator) is an important component for security in mobile computing and IoT. This paper presents an light-weight FPGA implementation of a previously proposed latch-based TRNG, while keeping the quality of generated random numbers. By accumulating the generated random numbers fifteen times with an XOR operation for each output word, the proposed TRNG with 16 latches passed the NIST SP 800-22 test suite, whereas the original TRNG required 248 latches. An important finding of this work is that the quality of random sequence is greatly improved by XOR-ing temporally interleaved series of bits.

Printed electronics (PE) is a fast-growing field with promising applications in wearables, smart sensors, and smart cards, since it provides mechanical flexibility, and low-cost, on-demand, and customizable fabrication. To secure the operation of these applications, true random number generators (TRNGs) are required to generate unpredictable bits for cryptographic functions and padding. However, since the additive fabrication process of the PE circuits results in high intrinsic variations due to the random dispersion of the printed inks on the substrate, constructing a printed TRNG is challenging. In this article, we exploit the additive customizable fabrication feature of inkjet printing to design a TRNG based on electrolyte-gated field-effect transistors (EGFETs). We also propose a printed resistor tuning flow for the TRNG circuit to mitigate the overall process variation of the TRNG so that the generated bits are mostly based on the random noise in the circuit, providing a true random behavior. The simulation results show that the overall process variation of the TRNGs is mitigated by 110 times, and the generated bitstream of the tuned TRNGs passes the National Institute of Standards and Technology - Statistical Test Suite. For the proof of concept, the proposed TRNG circuit was fabricated and tuned. The characterization results of the tuned TRNGs prove that the TRNGs generate random bitstreams at the supply voltage of down to 0.5 V. Hence, the proposed TRNG design is suitable to secure low-power applications in this domain.

Random numbers are widely used in cryptographic algorithms and protocols. A faulty true random number generator (TRNG) may open a door into a system in spite of cryptographic protection. It is therefore important to design TRNGs so that they can be tested at different stages of their lifetime to assure their trustworthiness. In this paper, we propose a method for designing physical unclonable function (PUF)-based TRNGs which can be tested in-field by known answer tests. We present a prototype FPGA implementation of the proposed TRNG based on an arbiter PUF which passes all NIST 800-22 statistical tests and has the minimal entropy of 0.918 estimated according to NIST 800-90B recommendations. This is a nontrivial achievement given that arbiter PUFs are notoriously hard to place in a symmetric manner in FPGAs.