True Random Number Generator Research Articles

A High-Speed FPGA-Based True Random Number Generator Using Metastability With Clock Managers

True random number generators (TRNGs) are fundamentals in many important security applications. Though they exploit randomness sources that are typical of the analog domain, digital-based solutions are strongly required especially when they have to be implemented on Field Programmable Gate Array (FPGA)-based digital systems. This brief describes a novel methodology to easily design a TRNG on FPGA devices. It exploits the runtime capability of the Digital Clock Manager (DCM) hardware primitives to tune the phase shift between two clock signals. The presented auto-tuning strategy automatically sets the phase difference of two clock signals in order to force on one or more flip-flops (FFs) to enter the metastability region, used as a randomness source. Moreover, a novel use of the fast carry-chain hardware primitive is proposed to further increase the randomness of the generated bits. Finally, an effective on-chip post-processing scheme that does not reduce the TRNG throughput is described. The proposed TRNG architecture has been implemented on the Xilinx Zynq XC7Z020 System on Chip (SoC). It passed all the National Institute of Standards and Technology (NIST) SP 800–22 statistical tests with a maximum throughput of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$300 \times 10^{6}$ </tex-math></inline-formula> bit per second. The latter is considerably higher than the throughput of other previously published DCM-based TRNGs.

Amorphous indium–gallium–zinc–oxide memristor arrays for parallel true random number generators

True random number generators (TRNGs) can generate unpredictable binary bitstream by exploiting the intrinsic stochasticity in physical variables. In a threshold switching memristor, the stochastic forming/rupture of conducting pathway has been proved to be a good random source, while further improvement of high randomness and throughput is still a challenge. Here, a crossbar array of amorphous indium–gallium–zinc–oxide (a-IGZO)-based threshold switching memristors was designed for high-throughput TRNGs. The intrinsic stochasticity of Ag conductive filament in IGZO memristor and the stochastic sneak paths in the crossbar array are the two sources of randomness in our TRNGs. In our design, one input pulse train can produce multi-channel random bits, which enables a high scalability for such TRNGs. In addition, the average energy consumption of the TRNGs can be further reduced by increasing the integration scale of the memristors. Such IGZO-based TRNGs are of great significance for security applications.

Phase randomness in a semiconductor laser: Issue of quantum random-number generation

Gain-switched lasers are in demand in numerous quantum applications, particularly, in systems of quantum key distribution and in various optical quantum random number generators. The reason for this popularity is natural phase randomization between gain-switched laser pulses. The idea of such randomization has become so familiar that most authors use it without regard to the features of the laser operation mode they use. However, at high repetition rates of laser pulses or when pulses are generated at a bias current close to the threshold, the phase randomization condition may be violated. This paper describes theoretical and experimental methods for estimating the degree of phase randomization in a gain-switched laser. We consider in detail different situations of laser pulse interference and show that the interference signal remains quantum in nature even in the presence of classical phase drift in the interferometer provided that the phase diffusion in a laser is efficient enough. Moreover, we formulate the relationship between the previously introduced quantum reduction factor and the leftover hash lemma. Using this relationship, we develop a method to estimate the quantum noise contribution to the interference signal in the presence of phase correlations. Finally, we introduce a simple experimental method based on the analysis of statistical interference fringes, providing more detailed information about the probabilistic properties of laser pulse interference.

Stochastic current response in diffusive memristor for security applications

Among various emerging information encryption technologies, diffusive memristors play an important role in such hardware security applications due to their volatile characteristics and intrinsic stochasticity. Here, we propose a true random number generator (TRNG) based on the random distributed current response of Ag/phenylalanine dipeptide microrod (FF MR)/Ag diffusive memristor which passes all National Institute of Standards and Technology tests. The key innovation of this method is that the degree of randomness of the output bits can be controlled by adjusting the reference voltage (Vref) where ideal 50% average uniformity of the generated random bits can be achieved. Furthermore, we used the true random number generated by TRNG as the cryptographic key to constructing a data encryption system and experimentally demonstrated the fully functional implementation of the encryption process. Through scanning electron microscopy and line scan energy dispersion spectrum analysis of the device, the confinement effect of FF MR on the Ag conductive filaments was verified, ensuring the reliable operation of TRNG and the entire encryption system.

Design and Implementation of a flexible Multi-purpose Cryptographic System on low cost FPGA

The design of cryptographic hardware that supports multiple cryptographic primitives is common in literature. In this work, a new design is presented consisting of a multi-purpose cryptographic system featuring both 128-bit pipelined AES-CORE (Advanced Encryption Standard) for high-speed symmetric encryption and a Keccak hash core on a low-cost FPGA. The KECCAK-CORE’s security and performance parameters are tunable in the sense that capacity, bitrate, and the number of rounds can be user-defined. Such flexibility enables the core to suit a large range of security requirements. The structure of Keccak’s sponge construction is exploited to enable different modes of operation. An example application outlined in this work is Pseudo Random Number Generation (PRNG). With few adjustments, the KECCAK-CORE was also operated as a post-processing unit for True Random Number Generation (TRNG) that uses the analog Lorenz chaotic circuit as a physical entropy source. The multi-purpose design was implemented in VHDL targeting an IntelFPGA Cyclone-V FPGA. For AES symmetric encryption, a maximum throughput of 31.1Gbps was achieved and a logic usage of 25146LEs (23% of the FPGA) in the case of the pipelined variant of AES-CORE. For the KECCAK-CORE, maximum throughput figures of 5.81, 8.4, and 11Gbps were achieved for the three SHA-3 variants 512, 384, and 256-bit respectively, with an area usage of 8947LEs (8%). The system as a whole occupies an area of 26909LEs (26%). The random sequences generated by the system operating in PRNG and TRNG post- processing modes successfully passed the National Institute of Standards and Technology (NIST) statistical test suite (NIST SP 800-22). The information entropy analysis performed on the post-processed TRNG sequences indicates an average of 0.935.

Strategies for ultra-fast bit generation of two-terminal threshold switch-based true random number generator using drift-free Ge-doped SiO2 threshold switch device

To achieve fast random bit generation under 50 ns per bit by employing the threshold voltage (Vth) variation of a simple two-terminal threshold switch (TS) device, we have confirmed that Vth drift-free switching characteristics, along with large Vth variation and fast switching speed, are key factors for implementing true random number generator (TRNG) devices. We analyzed the drift-switching characteristics of various TS devices together with our innovative oxide TS device for TRNG applications. Our findings show that stochastic switching is degraded by the Vth drift characteristics of a conventional ovonic threshold switch (OTS) for fast random bit generation. Conversely, the drift-free insulating-to-metal transition (IMT)-based TS device has very tight Vth variation, which is not suitable as a dynamic entropy source for TRNG. However, the Ge-doped SiO2-based TS device operates with drift-free and large Vth variation switching characteristics. Finally, we successfully demonstrated the potential of a Ge:SiO2-based TS device for TRNG application pertaining to fast random bit generation under 50 ns per bit without a complex circuit system.

Optimization of Random Telegraph Noise Characteristics in Memristor for True Random Number Generator

Memristor devices can be utilized for various computing applications, and stochastic computing is one of them. The intrinsic stochastic characteristics of the memristor cause unpredictable current fluctuations by the capture and emission of electrons in a trap site. Herein, a true random number generator (TRNG) using the random telegraph noise (RTN) of the memristor as an entropy source is proposed. TiOx/Al2O3memristors are fabricated, and the capture time probability of the RTN characteristics is modulated to 50% with varying read‐voltage and device conductance state. In addition, the TRNG operations with the RTN current signals as entropy sources are experimentally demonstrated with a customized breadboard, and the randomness is verified with the National Institute of Standards and Technology (NIST) tests.

Provably-secure quantum randomness expansion with uncharacterised homodyne detection

Quantum random number generators (QRNGs) are able to generate numbers that are certifiably random, even to an agent who holds some side information. Such systems typically require that the elements being used are precisely calibrated and validly certified for a credible security analysis. However, this can be experimentally challenging and result in potential side-channels which could compromise the security of the QRNG. In this work, we propose, design and experimentally demonstrate a QRNG protocol that completely removes the calibration requirement for the measurement device. Moreover, our protocol is secure against quantum side information. We also take into account the finite-size effects and remove the independent and identically distributed requirement for the measurement side. More importantly, our QRNG scheme features a simple implementation which uses only standard optical components and are readily implementable on integrated-photonic platforms. To validate the feasibility and practicability of the protocol, we set up a fibre-optical experimental system with a home-made homodyne detector with an effective efficiency of 91.7% at 1550 nm. The system works at a rate of 2.5 MHz, and obtains a net randomness expansion rate of 4.98 kbits/s at 1010 rounds. Our results pave the way for an integrated QRNG with self-testing feature and provable security.

Jitter-based Adaptive True Random Number Generation Circuits for FPGAs in the Cloud

In this article, we present and evaluate a true random number generator (TRNG) design that is compatible with the restrictions imposed by cloud-based Field Programmable Gate Array (FPGA) providers such as Amazon Web Services (AWS) EC2 F1. Because cloud FPGA providers disallow the ring oscillator circuits that conventionally generate TRNG entropy, our design is oscillator-free and uses clock jitter as its entropy source. The clock jitter is harvested with a time-to-digital converter (TDC) and a controllable delay line that is continuously tuned to compensate for process, voltage, and temperature variations. After describing the design, we present and validate a stochastic model that conservatively quantifies its worst-case entropy. We deploy and model the design in the cloud on 60 EC2 F1 FPGA instances to ensure sufficient randomness is captured. TRNG entropy is further validated using NIST test suites, and experiments are performed to understand how the TRNG responds to on-die power attacks that disturb the FPGA supply voltage in the vicinity of the TRNG. After introducing and validating our basic TRNG design, we introduce and validate a new variant that uses four instances of a linkable sampling module to increase the entropy per sample and improve throughput. The new variant improves throughput by 250% at a modest 17% increase in CLB count.

A dynamically reconfigurable entropy source circuit for high-throughput true random number generator

—True random number generator is an important hardware security primitive. Entropy source is the key to the design of a high-throughput true random number generator. To improve the throughput of a true random number generator while maintaining low hardware overhead, a novel entropy source circuit using ring oscillator with dynamically reconfigurable delay chain is proposed in this paper. The proposed entropy source exploits both signal jitter and circuit metastability. It consists of a seventh-order cycle shift register, seven 2-1MUXs and a core loop delay chain that is composed of inverters in series. Under the control of a high-frequency clock, the cycle shift register generates state transitions to control the output of MUXs, which in turn changes the number of inverters connected in the delay chain, switching the operation of the ring between steady and oscillating states. The outputs of five entropy sources are sampled and further XOR-ed with D flip-flops at a sampling clock of 400 MHz to obtain true random numbers. The proposed TRNG is implemented on the Xilinx Virtex-6 FPGA. The random numbers are captured in real-time using the Xilinx ChipScope and the TRNG is tested using the standard test specifications. The experimental results show that when working under a throughput of 400 Mbps, the proposed TRNG passes the NIST SP800-22 and the NIST SP800–90 B tests with a passing rate greater than 98% and a minimum entropy index per bit greater than 0.99. It also passes the relevant performance tests including autocorrelation test, restart test, deviation test, and temperature and voltage fluctuation test, and it has low hardware overhead.

Cosmic coding and transfer for ultra high security near-field communications

By using true random number (TRN) generators, encoding with the highest security can be realized. However, a completely secure strategy to transfer these TRNs has not yet been devised. Quantum key distribution (QKD) has attempted to establish secure key distribution methodology of this kind; however, several quantum cracking strategies have been predicted and experimentally demonstrated. In this work, COSMOCAT was invented as a solution for next-generation ultrahigh security near-field communications. With COSMOCAT, TRNs are generated from naturally occurring and ubiquitous cosmic-ray muons and the generated cosmic keys are distributed by these muons with an unprecedented level of security. The successful results of this experiment indicate that our prototype and the new key-generation-and-distribution standard can be utilized for practical encoding and near-field data transfer at rates of 10-100 Mbps. It is anticipated that COSMOCAT will be one of key techniques for future high security, near-field communication management.

Optical quantum random number generators: a comparative study

Quantum random number generators give the opportunity to, in theory, obtain completely unpredictable numbers only perturbed by the noise in the measurement. The obtained data can be digitalized and processed so that it gives as a result a uniform sequence of binary random numbers without any relation with the classical noise in the system. In this work we analyze the performance of optical QRNGs with three different arrangements: a homodyne detector measuring vacuum fluctuations, a homodyne detector measuring amplified spontaneous emission from an EDFA and a spontaneous emission phase noise-based generator. The raw data from the experiments is processed using a Toeplitz extractor, giving as a result sequences of binary numbers capable of passing the NIST Statistical Test Suite.

Suitability of Generalized GAROs on FPGAs as PUFs or TRNGs Considering Spatial Correlations

In the last years, guaranteeing the security in IoT communications has become an essential task. In this paper, the bias of a wide set of oscillators has been studied to determine their suitability as both True Random Number Generators (TRNGs) and Physically Unclonable Functions (PUFs). For this purpose, a generic configurable structure has been proposed and implemented in an FPGA. With this implementation, by introducing some external signals it is possible to configure the system in different oscillator topologies. This way, we have managed to analyze 2730 oscillators composed by 7 Lookup Tables (LUTs) without having to resynthesize the code each time. The performed analysis has included conventional ring oscillators, Galois ring oscillators and newly proposed oscillator topologies. From this analysis we have concluded that none of these oscillators behave as an ideal TRNG but ring oscillators present the closest to an ideal behavior. Regarding their suitability as PUFs, some of the newly proposed oscillators in this paper present a high reproducibility, higher than that of conventional ring oscillator PUF (RO-PUF) and a high uniqueness. Furthermore, we have noticed that both their reproducibility and their uniqueness tend to improve when increasing the length of the oscillators, which opens the possibility of finding new oscillators with even better properties by studying oscillators of bigger lengths. Finally, by studying the spatial correlation of the bias of these oscillators, we have observed that they present a much lower spatial correlation compared to the ring oscillators, which opens the possibility of using these oscillators in PUF architectures that use more comparisons than typical RO-PUFs.

Low Power Scan-based Built-in Self-test Based on True Random Number Generator Using Multistage Feedback Ring Oscillator

Low Power Scan-based Built-in Self-test Based on True Random Number Generator Using Multistage Feedback Ring Oscillator

Inkjet-printed h-BN memristors for hardware security.

Inkjet printing electronics is a growing market that reached 7.8 billion USD in 2020 and that is expected to grow to ∼23 billion USD by 2026, driven by applications like displays, photovoltaics, lighting, and radiofrequency identification. Incorporating two-dimensional (2D) materials into this technology could further enhance the properties of the existing devices and/or circuits, as well as enable the development of new concept applications. Along these lines, here we report an easy and cheap process to synthesize inks made of multilayer hexagonal boron nitride (h-BN)-an insulating 2D layered material-by the liquid-phase exfoliation method and use them to fabricate memristors. The devices exhibit multiple stochastic phenomena that are very attractive for use as entropy sources in electronic circuits for data encryption (physical unclonable functions [PUFs], true random number generators [TRNGs]), such as: (i) a very disperse initial resistance and dielectric breakdown voltage, (ii) volatile unipolar and non-volatile bipolar resistive switching (RS) with a high cycle-to-cycle variability of the state resistances, and (iii) random telegraph noise (RTN) current fluctuations. The clue for the observation of these stochastic phenomena resides on the unpredictable nature of the device structure derived from the inkjet printing process (i.e., thickness fluctuations, random flake orientations), which allows fabricating electronic devices with different electronic properties. The easy-to-make and cheap memristors here developed are ideal to encrypt the information produced by multiple types of objects and/or products, and the versatility of the inkjet printing method, which allows effortless deposition on any substrate, makes our devices especially attractive for flexible and wearable devices within the internet-of-things.

A Quantum Random Number Generator with Light Source Monitoring Function

A Quantum Random Number Generator with Light Source Monitoring Function

True Random Number Generator Based on the Variability of the High Resistance State of RRAMs

True Random Number Generator Based on the Variability of the High Resistance State of RRAMs

Random Number Generator

Illustration plays an important role during education: The Galton board is a suitable tool for illustrating random processes and explaining probability distributions. We have created this tool in a virtual version, which facilitates data collection for statistical processing of experimental data and also enables the study of non-symmetrical distributions. The random processes on the device are simulated, which requires a random number generator. Since there were some doubts about the software-generated pseudo-random numbers, we created a true random number generator based on the input noise of microcontrollers.

Hardware implementation of a true random number generator integrating a hexagonal boron nitride memristor with a commercial microcontroller.

The development of the internet-of-things requires cheap, light, small and reliable true random number generator (TRNG) circuits to encrypt the data-generated by objects or humans-before transmitting them. However, all current solutions consume too much power and require a relatively large battery, hindering the integration of TRNG circuits on most objects. Here we fabricated a TRNG circuit by exploiting stable random telegraph noise (RTN) current signals produced by memristors made of two-dimensional (2D) multi-layered hexagonal boron nitride (h-BN) grown by chemical vapor deposition and coupled with inkjet-printed Ag electrodes. When biased at small constant voltages (≤70 mV), the Ag/h-BN/Ag memristors exhibit RTN signals with very low power consumption (∼5.25 nW) and a relatively high current on/off ratio (∼2) for long periods (>1 hour). We constructed TRNG circuits connecting an h-BN memristor to a small, light and cheap commercial microcontroller, producing a highly-stochastic, high-throughput signal (up to 7.8 Mbit s-1) even if the RTN at the input gets interrupted for long times up to 20 s, and if the stochasticity of the RTN signal is reduced. Our study presents the first full hardware implementation of 2D-material-based TRNGs, enabled by the unique stability and figures of merit of the RTN signals in h-BN based memristors.

“Password Authentication Key Exchange Protocol using Fish Tank Image based True Random Number Generator”

Abstract: We employ a straightforward configuration of a fish tank as the changeable environment, recording its photos over time, in order to limit the computational complexity. To create the initial seed, the image data is then submitted to a reduction method and hash function. In order to get true random numbers, we suggest a method for economically removing the true seed from the image data and applying it to a pseudo-random generator, in this case, a Linear Congruential Generator (LCG). The need for information security is increasing across a range of industries, and security concerns are receiving more and more attention as a result of the Internet's explosive growth in recent years. Any future value cannot be accurately anticipated based on the current set of values and random numbers are those that are a part of a sequence in which values are uniformly distributed over a defined set. A safe session key can be provided to a pair of users interacting over an unstable channel using password-based encrypted key exchange protocols, even if the top secret key or password they share is chosen at random from a tiny set of values. We offer two straightforward Bellovin and Merritt-based encrypted key exchange systems..