True Random Number Generator Research Articles

De-Correlation and De-Bias Post-Processing Circuits for True Random Number Generator

De-Correlation and De-Bias Post-Processing Circuits for True Random Number Generator

Laser-engraved holograms as entropy source for random number generators

Our study introduces a novel approach to true random number generation (TRNG) using speckle patterns generated by laser-engraved holograms on carbon fiber-reinforced polymer (CFRP) composite substrates. Unlike previous methods, our approach simplifies the process by generating the necessary image dataset from a single microscope image of the engraved hologram. We achieve a high extraction ratio of 76 %, demonstrating the effectiveness of our TRNG. Moreover, our method successfully passes rigorous statistical tests proposed by the National Institute of Standards and Technology (NIST), indicating its suitability for cryptographic and secure system applications. This work offers promising implications for enhancing security in various domains, from secure communication networks to IoT devices.

Quantum Physical Unclonable Function Based on Multidimensional Fingerprint Features of Single Photon Emitters in Random AlN Nanocrystals

AbstractPhysical unclonable function (PUF) has emerged as a unique physical'fingerprint' that is inherently difficult to replicate. It shows tremendous application value in various hardware security areas such as identity authentication, chip anticounterfeiting, communication encryption, blockchain, etc. However, with the rapid development of 3D nanoprinting, classical PUFs constructed with disordered micro‐nanostructures face tremendous threats from physical cloning attacks. Herein, this study proposes and demonstrates the utilization of room‐temperature single‐photon emitters derived from atomic defects in randomly distributed pyramidal aluminum nitride (AlN) nanocrystals as a novel quantum PUF to resist physical cloning attacks. The fabrication of this quantum PUF on silicon (Si) wafers enables seamless integration with silicon photonic integrated circuits. The multidimensional fingerprint features of the single‐photon emitters are highly sensitive to the lattice parameters of the uneven AlN nanocrystals. Furthermore, each single photon emitter can work as a quantum random number generator to ensure the fundamental unpredictability of PUFs. The subatomic precision requirement coupled with unpredictable quantum emission behavior makes it practically impossible to attack the proposed quantum PUF, providing a promising solution for information security in the post‐quantum era.

Scenarios for Optical Encryption Using Quantum Keys

Optical communications providing huge capacity and low latency remain vulnerable to a range of attacks. In consequence, encryption at the optical layer is needed to ensure secure data transmission. In our previous work, we proposed LightPath SECurity (LPSec), a secure cryptographic solution for optical transmission that leverages stream ciphers and Diffie–Hellman (DH) key exchange for high-speed optical encryption. Still, LPSec faces limitations related to key generation and key distribution. To address these limitations, in this paper, we rely on Quantum Random Number Generators (QRNG) and Quantum Key Distribution (QKD) networks. Specifically, we focus on three meaningful scenarios: In Scenario A, the two optical transponders (Tp) involved in the optical transmission are within the security perimeter of the QKD network. In Scenario B, only one Tp is within the QKD network, so keys are retrieved from a QRNG and distributed using LPSec. Finally, Scenario C extends Scenario B by employing Post-Quantum Cryptography (PQC) by implementing a Key Encapsulation Mechanism (KEM) to secure key exchanges. The scenarios are analyzed based on their security, efficiency, and applicability, demonstrating the potential of quantum-enhanced LPSec to provide secure, low-latency encryption for current optical communications. The experimental assessment, conducted on the Madrid Quantum Infrastructure, validates the feasibility of the proposed solutions.

Security primitives for memoryless IoT devices based on Physical Unclonable Functions and True Random Number Generators

The article describes various security primitives for significantly resource-constrained devices, such as sensors or sensor networks, IoT devices, wearables, etc. — i.e., devices without programmable memory. It is dedicated to parts which cannot handle complex algorithms of modern secure cryptography, cannot be equipped with programmable memories, or their circuits or data in permanent memories can be easily reverse-engineered. Instead, all security techniques (e.g., identification, authentication, and encryption) are based on modern hardware cryptography, mainly: physical unclonable functions (PUFs) and true random number generators (TRNGs). The paper addresses numerous issues from untraceable identification to mutual authentication to one-time pad encryption. The communication security is considered to be a trade-off between the device’s resources (processing ability, energy consumption, implementation size, response time), preparation complicity (initialization time, size of a server data storage) and the security capabilities and protection levels. Primitives can be included into the communication protocol based on particular needs and available hardware resources.

Silicon-based quantum random number generator with untrusted sources and uncharacterized measurements

Random numbers are essential resources in science and engineering, with indispensable applications in simulation, cybersecurity, and finance. Quantum random number generators (QRNGs), based on the principles of quantum mechanics, ensure genuine randomness and unpredictability. Silicon photonics enables the large-scale deployment of integrated QRNGs due to its low cost, miniaturization, and compatibility with CMOS technology. However, current integrated QRNGs are typically based on perfect or partially perfect device models, deviating from real-world devices, which compromises the unpredictability of quantum random numbers. In this study, we implemented a silicon-based QRNG that makes no assumptions about the source and only uses trusted but uncharacterized measurement devices. In experimental demonstration, we show that our setup can generate secure random numbers with different choices of intensities of laser light, and achieve an optimized random number generation rate of up to 4.04 Mbps. Our work significantly advances the security, practicality, and commercial development of QRNGs by employing imperfect devices.

Investigating device-independent quantum random number generation

Quantum random number generation (QRNG) is a resource that is a necessity in the field of cryptography. However, its certification has been challenging. In this article, we certify randomness with the aid of quantum entanglement in a device independent setting, where we choose two-photon interference for source characterisation. The CHSH inequality violation and quantum state tomography are used as independent checks on the measurement devices. These measures ensure the unpredictability of quantum random number generation. This work can be easily extended to faster randomness expansion protocols.

Evaluating integration methods of a quantum random number generator in OpenSSL for TLS

The rapid advancement of quantum computing poses a significant threat to conventional cryptography. Whilst post-quantum cryptography (PQC) stands as the prevailing trend for fortifying the security of cryptographic systems, the coexistence of quantum and classical computing paradigms presents an opportunity to leverage the strengths of both technologies, for instance, nowadays the use of Quantum Random Number Generators (QRNGs)–considered as True Random Number Generators (TRNGs)–opens up the possibility of discussing hybrid systems. In this paper, we evaluate both aspects, on the one hand, we use hybrid TLS (Transport Layer Security) protocol that leverages the widely used secure protocol on the Internet and integrates PQC algorithms, and, on the other hand, we evaluate two approaches to integrate a QRNG, i.e., Quantis PCIe-240M, in OpenSSL 3.0 to be used by TLS. Both approaches are compared through a Nginx Web server, that uses OpenSSL’s implementation of TLS 1.3 for secure web communication. Our findings highlight the importance of optimizing such integration method, because while direct integration can lead to performance penalties specific to the method and hardware used, alternative methods demonstrate the potential for efficient QRNG deployment in cryptographic systems.

Correlation avoidance in single-photon detecting quantum random number generators by dead time overestimation

In the case of quantum random number generators based on single-photon arrivals, the physical properties of single-photon detectors, such as time-tagger clocks and dead time, influence the stochastic properties of the generated random numbers. This can lead to unwanted correlations among consecutive samples.We present a method based on extending the insensitive periods after photon detections. This method eliminates the unwanted stochastic effects at the cost of reduced generation speed. We calculate performance measures for our presented method and verify its correctness with computer simulations and measurements conducted on an experimental setup. Our algorithm has low complexity, making it convenient to implement in QRNG schemes, where the benefits of having uncorrelated output intervals exceed the disadvantages of the decreased rate.

Partial loopholes free device-independent quantum random number generator using IBM's quantum computers

Abstract Random numbers form an intrinsic part of modern day computing with applications in a wide variety of fields, and quantum systems due to their intrinsic randomness form a suitable candidate for generation of true random numbers that can also be certified. In this work, we have demonstrated the use of cloud based quantum computers to develop a partially loophole free device-independent quantum random number generator (QRNG). The generated random numbers have been tested for their source of origin through experiments based on the testing of Clauser, Horne, Shimony, and Holt (CHSH) inequality through available IBM quantum computers. The performance of each quantum computer against the CHSH test has been plotted and characterized. Further, efforts have been made to close as many loopholes as possible to produce device-independent quantum random number generators. This study will help provide new directions for the development of self-testing and semi-self-testing random number generators using quantum computers.

Lightweight High‐Throughput TRNG Based on Single‐Node Boolean Chaotic Structure

ABSTRACTWith the rise of the Internet and electronic devices, the security of network information is gaining attention, and the true random number generator (TRNG) is playing an increasingly crucial role in information security. TRNG, based on Boolean chaotic entropy source, has drawn significant interest due to its uncomplicated circuit design and minimal hardware resource usage. However, most existing structures consist of two‐input or three‐input logic devices, forming a complex multinode, geometrically symmetric Boolean chaotic network using multiple logic devices. This network configuration results in increased complexity and reduced throughput. This study introduces an entropy source based on Boolean chaos utilizing single‐node and four‐input XOR gates, which can be easily placed and routed on Xilinx Artix‐7 FPGA. It requires only 29 LUTs and 5 DFFs without any postprocessing, achieving a throughput of up to 700 Mb/s. The output of TRNG has successfully passed various tests including the autocorrelation test, NIST SP800‐22, NIST SP800‐90B, AIS‐31, and TESTU01 tests with favorable results. Furthermore, by applying a three‐stage XOR chain postprocessing on Xilinx Spartan‐6 FPGA and Xilinx Virtex‐6 FPGA, it has passed the NIST SP800‐22 and NIST SP800‐90B tests at 300 Mb/s. The structure was also tested using Xilinx Virtex‐6 FPGA under different temperature and voltage conditions, passing the NIST SP800‐90B IID test.

True Random Number Generator Based on Chaotic Oscillation of a Tunable Double-Well MEMS Resonator.

Chaotic systems have aroused interest across various scientific disciplines such as physics, biology, chemistry, and meteorology. The deterministic but unpredictable nature of a chaotic system is an ideal feature for random number generation. Microelectromechanical systems (MEMS) are a promising technology that effectively harnesses chaos, offering advantages such as a compact footprint, scalability, and low power consumption. This paper presents a true random number generator (TRNG) based on a double-well MEMS resonator integrated with an actuator and position sensor. The potential energy landscape of the proposed MEMS resonator is actively tunable with a direct current voltage. Experimental demonstrations of tunable bistability and chaotic resonance are reported in this paper. A chaotic time sequence is generated through piezoresistive sensing of the position of the MEMS resonator once it is driven into the chaotic regime. Subsequently, the randomness of the bit sequence, achieved by applying the exclusive or function to a digital chaotic sequence and its delayed differential is confirmed to meet the National Institute of Standards and Technology specifications. Moreover, the throughput and energy efficiency of the proposed MEMS-based TRNG can be adjusted from 50 kb s-1 and 0.44 pJ per bit at a low energy barrier to 167 kb s-1 and 6.74 pJ per bit at a high energy barrier by changing the MEMS device's potential well. The tunability of the proposed double-well MEMS resonator not only offers continuous adjustments in the energy efficiency of TNRG but also unveils vast and diverse research opportunities in analog computing, encryption, and secure communications.

Imperfect Measurement Devices Impact the Security of Tomography‐Based Source‐Independent Quantum Random Number Generator

AbstractSource‐independent quantum random number generators (SI‐QRNGs) can generate secure random numbers with untrusted and uncharacterized sources. Recently, a tomography‐based SI‐QRNG protocol has garnered significant attention for its higher randomness generation rate[Phys. Rev. A 99, 022328 (2019)], achieved through measurements utilizing three mutually unbiased bases. However, imperfect and inadequately characterized measurement devices would impact the security and performance of this protocol. In this work, considering the imperfect basis modulation, afterpulse effect and detection efficiency mismatch, it is demonstrated that the imperfect measurement devices would reduce the extractable randomness and lead to the incorrect estimation of the conditional min‐entropy. Additionally, the influences of the finite‐size effect and the performances of the protocol based on different parameter estimation methods are investigated and compared. To guarantee the security of generated random numbers, accurate conditional min‐entropy estimation methods that are compatible with imperfect factors are also developed. The work emphasizes the significance of considering the imperfections in measurement devices and establishing tighter bounds for parameter estimation, especially in high‐speed systems, thereby enhancing the robustness and performance of the protocol.

Leveraging quantum uncertainty: Quantum randomness through the lens of classical communication networks

The generation of random numbers and the study of its properties have been an elusive field for a fair portion of the century. The application of random numbers is employed in many use cases such as cryptography, neural networks, numerical simulation, and gambling. The performance of each of these use cases is profoundly impacted by the employed random numbers; henceforth, the quality of randomness is of critical importance when it comes to their usage. A poorly generated random number can make a security system vulnerable, or any numerical or statistical evaluation misleading. Although various modes of classical random number generators exist and still function to provide strong cryptographic properties, emergence of quantum mechanical randomness has shed light on a novel path of generating certified randomness which supersedes the classical counterpart in terms of security. Harnessing quantum mechanical phenomena enables generation of true random numbers which can be certified and further implemented to elevate the net quality of the specific use cases. In this work, we generate and analyze random numbers from three different sources — 50: 50 beam splitter (BS), quantum key distribution (QKD) setup with classical post-processing scheme, and a commercially available quantum random number generator (QRNG) (ID Quantique (IDQ)). The quality of the generated random numbers from the various sources is checked in statistical tests and compared. Further on, we have developed a system which implements the QRNG-based random numbers to facilitate message authentication code (MAC) and one time password (OTP) protocols, demonstrating a communication network application. In this manner we discuss about a network which integrates quantum mechanics to the current classical networking approaches to enhance certain aspects of the networking protocol — in this case, the security.

TRNG Entropy Model in the Presence of Flicker FM Noise

Flicker Frequency Modulated (FM) noise, which influences free-running Ring Oscillators (ROs), can make a substantial contribution to the entropy generated by RO-based True Random Number Generators (TRNGs). While current TRNG stochastic models predominantly concentrate on white FM noise, the addition of flicker FM noise could remarkably enrich the analysis of the TRNG entropy production rate. This paper introduces an entropy model for TRNGs, employing Gaussian processes, to estimate entropy generation from both white FM and flicker FM noise. We analytically derive the flicker FM noise Auto-Correlation Function (ACF), enabling assessment of entropy contributions conditioned on partial knowledge of the TRNG’s internal state. Utilizing the developed model with commonly reported noise magnitudes found in literature, it is determined that flicker FM noise holds the potential to substantially enhance the TRNG’s entropy rate. However, due to considerable variation in reported magnitudes across limited available research on flicker FM noise, it cannot yet be universally accepted as a dependable source of TRNG entropy.

Machine Learning-Based Randomness Analysis For a Auantum Random Number Generator

Abstract Random numbers are critical to information security. Quantum random numbers are theoretically truly random and unpredictable. However, the measurement process of a quantum random number generator (QRNG) can be affected by environmental disturbances that compromise the integrity of the generated random numbers. A machine learning model is proposed to assess the stochasticity of the continuous variable QRNG under the influence of vacuum noise. The model is designed to detect the correlation between the randomness of the QRNG being corrupted under the influence of classical noise (electrical noise). In addition, our model detects a decrease in the randomness of the QRNG random numbers when the electrical noise intensity increases to a certain correlation. The results show that machine learning (ML) can be used as a measure of the quality of QRNG.

Metalens array for quantum random number

Quantum random number generation (QRNG) leveraging intrinsic quantum uncertainty has attracted significant interest in the field of integrated photonic architecture, with applications in quantum cryptography, tests of quantum nonlocality, and beyond. The demand for compact, low-energy consumption, robust, fast, and cost-effective QRNGs integrated into photonic chips is highlighted, whereas most previous works focused on bulk optics. Here, based on the metalens array entangled source, we experimentally realized a miniaturized, high-dimensional quantum random number generator via a meta-device without post-randomness extraction. Specifically, the device has a high-density output with 100 channels per square millimeter. This chip-scale quantum randomness source can obtain random number arrays without post-randomness extraction and enable compact integration for quantum applications needing secure keys or randomness. Our approach demonstrates potential in secure key generation and randomness for quantum applications.

True random number generation based on temporal fluctuations of abalone shell coherent random lasers.

The output modes of random lasers exhibit randomness, making them a potential high-quality physical entropy source for generating random numbers. In this paper, we controlled a low-cost and easily fabricated abalone shell random laser, generating forward and backward coherent random lasers simultaneously in a single channel, resulting in highly diverse mode variations. After post-processing steps such as third-order difference calculations and exclusive-or (XOR) logic operations, we generated a random number sequence for the first time, to the best of our knowledge, based on the temporal fluctuations of biomimetic random laser coherent modes. The instantaneous generation rate reached a preliminary 40 Gbps. Moreover, the random bits satisfy requirements such as random distribution, independence, and absence of bias, successfully passing the NIST SP800-22 standard test, confirming the high quality of the random number sequence.

Hardware-Efficient Configurable Ring-Oscillator-Based Physical Unclonable Function/True Random Number Generator Module for Secure Key Management.

The use of physical unclonable functions (PUFs) linked to the manufacturing process of the electronic devices supporting applications that exchange critical data over the Internet has made these elements essential to guarantee the authenticity of said devices, as well as the confidentiality and integrity of the information they process or transmit. This paper describes the development of a configurable PUF/TRNG module based on ring oscillators (ROs) that takes full advantage of the structure of modern programmable devices offered by Xilinx 7 Series families. The proposed architecture improves the hardware efficiency with two main objectives. On the one hand, we perform an exhaustive statistical characterization of the results derived from the exploitation of RO configurability. On the other hand, we undertake the development of a new version of the module that requires a smaller amount of resources while considerably increasing the number of output bits compared to other proposals previously reported in the literature. The design as a highly parameterized intellectual property (IP) module connectable through a standard interface to a soft- or hard-core general-purpose processor greatly facilitates its integration into embedded solutions while accelerating the validation and characterization of this element on the same electronic device that implements it. The studies carried out reveal adequate values of reliability, uniqueness, and unpredictability when the module acts as a PUF, as well as acceptable levels of randomness and entropy when it acts as a true random number generator (TRNG). They also illustrate the ability to obfuscate and recover identifiers or cryptographic keys of up to 4096 bits using an implementation of the PUF/TRNG module that requires only an array of 4×4 configurable logic blocks (CLBs) to accommodate the RO bank.

A True Random Number Generator Design Based on the Triboelectric Nanogenerator with Multiple Entropy Sources.

The triboelectric nanogenerator (TENG) has the potential to serve as a high-entropy energy harvester, enabling the self-powered operation of Internet of Things (IoT) devices. True random number generator (TRNG) is a common feature of encryption used in IoT data communication, ensuring the security of transmitted information. The benefits of multiplexing TENG and TRNG in resource-constrained IoT devices are substantial. However, current designs are limited by the usage scenarios and throughput of the TRNG. Specifically, we propose a structurally and environmentally friendly design based on the contact-separation structure, integrating heat fluctuation and charge decay as entropy sources. Furthermore, filtering and differential algorithms are recommended for data processing based on TENG characteristics to enhance randomness. Finally, a TENG-based TRNG is fabricated, and its performance is verified. Test results demonstrate a random number throughput of 25 Mbps with a randomness test pass rate approaching 99%, demonstrating suitability for resource-constrained IoT applications.