A Peripheral-Free True Random Number Generator Based on Integrated Circuits Enabled by Atomically Thin Two-Dimensional Materials.

True random number generators (TRNG) are important counterparts to pseudorandom number generators (PRNG), especially for high security applications such as cryptography. They produce unpredictable, non-repeatable random sequences. However, most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs. These generators usually require post-processing algorithms to eliminate biases but in turn, reduces performance. In this paper, a new post-processing method based on hyperchaos is proposed for software-based TRNGs which not only eliminates statistical biases but also provides amplification in order to improve the performance of TRNGs. The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input changes, diffusion, and confusion capabilities to achieve these goals. Quantized bits of a physical entropy source are used to perturb the parameters of a hyperchaotic map, which is then iterated to produce a set of random output bits. To depict the feasibility of the proposed post-processing algorithm, it is applied in designing TRNGs based on digital audio. The generators are analyzed to identify statistical defects in addition to forward and backward security. Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput, which in turn reflects on the effectiveness of the proposed post-processing method.

The explosive growth of Internet of Things (IoT) devices has demanded the urgency of robust data security to protect private information. The random numbers generated by pseudo‐random number generators (PRNGs) play a crucial role in cryptographic algorithms. However, these sequences have become increasingly predictable due to advances in computing power and machine learning. Therefore, the development of true random number generators (TRNGs), which exploit the intrinsic hardware‐level randomness as an entropy source, is important for future data security. In this study, we present TRNG circuits that harness the inherent stochasticity of a multilayer hBN volatile memristor. The fabricated device exhibits highly stable threshold switching with low set/hold voltages and a significantly high on/off ratio. We implement a spike generator by integrating the threshold switching memristor with passive components. Digitization with a fixed‐reference comparator directly converts output spikes into bitstreams that successfully pass NIST randomness tests without postprocessing. The practical utility of the TRNG is demonstrated through XOR‐based encryption and decryption of black‐and‐white and grayscale images, resulting in noise‐like encrypted data and perfect recovery of the originals using identical keys. These results establish 2D hBN‐based threshold switching memristors as compelling hardware entropy sources for secure, next‐generation electronic systems.

True random number generators (TRNG) are widely used to generate encryption keys in information security systems [1]–[2]. In TRNG, entropy source is a critical module who provides the source of randomness of output bit stream. The unavoidable electrical noise in circuit becomes an ideal entropy source due to its unpredictability. Among the methods of capturing electrical noise, ring oscillator-based entropy source makes the TRNG most robust to deterministic noise and 1/f noise which means the strongest anti-interference capability, so it is simple in structure and easy to integrate [3]. Thus, great research attention has focused on ring oscillator-based TRNGs [3] –[7]. In [4], a high-speed TRNG with 100Mbps output bit rate was proposed, but it took up too much power and area. A TRNG based on tetrahedral ring oscillator was proposed in [5]. Its power consumption was very low but the output bit rate was also very low. A ring oscillator-based TRNG with low output bit rate but high power was proposed in [7]. In a word, none of the above architectures achieve an appropriate compromise between bit rate and power consumption. This work presents a new feedback architecture of TRNG based on tetrahedral ring oscillator. The output random bit stream generates a relative random control voltage that acts on the transmission gates in oscillator through a feedback loop, thus increasing phase jitter of the oscillator and improving output bit rate. Furthermore, an XOR chain-based post-processing unit is added to eliminate the statistical deviations and correlations between raw 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.

We describe a methodology and standard of proof for experimental claims of quantum random-number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations, lower bounds on the quantum contribution to the average min-entropy can be derived from measurements on the QRNG output. Given these bounds, randomness extractors allow generation of nearly perfect ``$\ensuremath{\epsilon}$-random'' bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the $\ensuremath{\epsilon}$ randomness of these sequences. We demonstrate the methodology by application to phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness source. All other factors, including classical phase noise, amplitude fluctuations, digitization errors, and correlations due to finite detection bandwidth, are treated with paranoid caution, i.e., assuming the worst possible behaviors consistent with observations. A data-constrained numerical optimization of the distribution of untrusted parameters is used to lower bound the average min-entropy. Under this paranoid analysis, the QRNG remains efficient, generating at least 2.3 quantum random bits per symbol with 8-bit digitization and at least 0.83 quantum random bits per symbol with binary digitization at a confidence level of 0.999 93. The result demonstrates ultrafast QRNG with strong experimental guarantees.

A reconfigurable PUF structure with dual working modes based on entropy separation model

Random numbers play a key-role in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly combined together: True Random Number Generators (TRNGs), and Pseudo Random Number Generators (PRNGs). The former are devices that exploit truly stochastic physical phenomena [2, 3, 4, 5, 6], such as the electronic noise or the chaotic dynamics of certain nonlinear systems: for these devices the output sequences have an intrinsic degree of unpredictability, that is measured referring to the theoretical tools provided by Information Theory (e.g., in terms of the Shannon entropy) [7,4]. On the other hand, PRNGs are deterministic periodic finite state machines whose aim is to emulate, within the period, the random behavior of a truly random source of numbers. From a theoretical point of view, due to their deterministic nature, PRNGs are potentially predictable by observing their generated sequences [8, 9, 10, 1]. Nevertheless, in literature some families of PRNGs are classified to be ‘secure’, meaning that their algorithmic structure involves calculations that in average, referring to the prediction task, require an amount of computation time that is asymptotically unfeasible with the size of the problem, when referring to both the computational equipment at disposal and the known computing fastest algorithms [1,11]. It is worth noting that a given generator, even if belonging to an asymptotically secure family of PRNGs, can generate short periodic (and unsecure) sequences for several values of the initial seed. Therefore, apart from the cryptographic robustness of their algorithmic structure, a cryptographic PRNG must generate sequences that are acceptable from a statistical point of view, i.e., that pass a certain number of standard statistical tests [1, 12].

Currently, True Random Number Generation (TRNG) is relatively slow, utilizing natural, physical processes as its entropy source. Other types of random numbers, such as Pseudo-Random Numbers, lack true randomness as eventually they repeat, but can be generated with great speed. The main idea of the work presented in this paper is to introduce parallel random number generation as a scalable means of increasing the rate of true random number generation in hardware to match and surpass that of Pseudo-Random Number Generators (PRNGs). Using a Raspberry Pi platform, this work will combine two (2) standard TRNGs to form one (1) unified, Parallel - True Random Number Generator (P-TRNG), with more than twice the output performance rate of its component TRNGs, and with demonstrated scalability.

Quantum random number generator (QRNG) allows obtaining true random bit sequences. In QRNG based on quantum nature of vacuum, optical beam splitter with two inputs and two outputs is normally used. We compare mathematical descriptions of spatial beam splitter and fiber Y-splitter in the quantum model for QRNG, based on homodyne detection. These descriptions were identical, that allows to use fiber Y-splitters in practical QRNG schemes, simplifying the setup. Also we receive relations between the input radiation and the resulting differential current in homodyne detector. We experimentally demonstrate possibility of true random bits generation by using QRNG based on homodyne detection with Y-splitter.

By measuring the amplified spontaneous emission (ASE) noise of the superluminescent light emitting diodes, we propose and realize a quantum random number generator (QRNG) featured with practicability. In the QRNG, after the detection and amplification of the ASE noise, the data acquisition and randomness extraction which is integrated in a field programmable gate array (FPGA) are both implemented in real-time, and the final random bit sequences are delivered to a host computer with a real-time generation rate of 1.2 Gbps. Further, to achieve compactness, all the components of the QRNG are integrated on three independent printed circuit boards with a compact design, and the QRNG is packed in a small enclosure sized 140 mm × 120 mm × 25 mm. The final random bit sequences can pass all the NIST-STS and DIEHARD tests.

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.

Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We demonstrate that a quantum computer can serve as a high-quality, weakly random source for a generalized user-defined probability mass function (PMF). Specifically, QC measurement implements the process of variate sampling according to a user-specified PMF resulting in a word comprised of electronic bits that can then be processed by an extractor function to address inaccuracies due to non-ideal quantum gate operations and other system biases. We introduce an automated and flexible method for implementing a TRNG as a programmed quantum circuit that executes on commercially-available, gate-model quantum computers. The user specifies the desired word size as the number of qubits and a definition of the desired PMF. Based upon the user specification of the PMF, our compilation tool automatically synthesizes the desired TRNG as a structural OpenQASM file containing native gate operations that are optimized to reduce the circuit's quantum depth. The resulting TRNG provides multiple bits of randomness for each execution/measurement cycle; thus, the number of random bits produced in each execution is limited only by the size of the QC. We provide experimental results to illustrate the viability of this approach.

We present a circuit technique to extract true random numbers from carrier capture and emission in oxide traps in the emerging redox-based resistive memory (ReRAM). This phenomenon that appears as small changes in current magnitude passing through the device is known as random telegraph noise (RTN) and is increasingly becoming a source of reliability issues in nanometer-scale devices. We demonstrate a circuit that exploits TRN suitable for a true random number generator (TRNG) in security applications, where the system is secure from different adversarial attacks, including side-channel monitoring and machine learning analysis. We experimentally characterize RTN in ReRAMs and extract its dependency to temperature, voltage, and area. We introduce an RTN harvesting circuit to mitigate sensitivities to temperature fluctuations, injected supply noise, and power signal monitoring. We reduced bias and imbalance in data due to high-speed sampling via von Neumann whitening. The circuit is compared to conventional non-differential readout approach. Our approach shows a 7.26 times improvement in autocorrelation and significant resilience against the injected supply noise. We also demonstrate the TRNG’s quality and robustness using statistical tests and machine learning attacks. The output of the generator satisfies statistical tests for randomness and is immune to modeling attacks based on the machine learning methods.

The Internet of Things (IoT) now underpins critical systems like healthcare monitors, smart home, smart grids, automotive V2V & V2X networks, and industrial controls but it still relies on classical cryptography, whose security assumptions are vulnerable to quantum computers. A large quantum computer could run Shor’s algorithm to break RSA/ECC and use Grover’s algorithm to accelerate brute-forcing of symmetric keys, undermining the confidentiality and authentication of data in these IoT applications. Researchers have proposed quantum cryptographic solutions. Quantum key distribution (QKD) and quantum random number generators (QRNGs) exploit quantum mechanics to detect eavesdropping and deliver provably secure key material. For example, chip-scale QRNGs can be embedded in IoT sensors to generate true random keys, boosting resistance to brute-force attacks. These quantum techniques provide information-theoretic secrecy, for instance, QKD-generated keys have been used to authenticate smart-grid SCADA. However, most IoT devices are resource-constrained, making direct deployment of conventional QKD hardware challenging. Post-quantum cryptography (PQC) complements quantum methods by providing algorithms such as lattice-based, hash-based that resist quantum attacks on existing hardware. Standardized PQC can be deployed via software updates on legacy IoT nodes, enabling scalable and quantum-safe security within current constraints. Researchers are exploring lightweight PQC for connected cars and e-health sensors. Hybrid approaches combining QKD/QRNG with PQC offer a layered defense. Since QKD protocols are regarded as ‘future-proof’ and PQC standards mature, their combined use will be essential for robust, quantum-safe IoT security. Miniaturizing quantum components such as integrated QKD/QRNG modules and optimizing lightweight PQC schemes for low-power IoT devices are future research directions to secure IoT networks.

In this paper, we propose and demonstrate a novel technique for true random number generator (TRNG) application using GeSe-based Ovonic threshold switching (OTS) selector devices. The inherent variability in OTS threshold voltage results in a bimodal distribution of on/off states which can be easily converted into digital bits. The experimental evaluation shows that the proposed TRNG enables the generation of high-quality random bits that passed 12 tests in the National Institute of Standards and Technology statistical test suite without complex external circuits for post-processing. The randomness is further evidenced by the prediction rate of ∼50% using machine learning algorithm. Compared with the TRNGs based on non-volatile memories, the volatile nature of OTS avoids the reset operation, thus further simplifying the operation and improving the generation frequency.