True Random Number Research Articles

A Single-Inverter-Based True Random Number Generator with On-Chip Clock-Tuning-Based Entropy Calibration Circuit

A Single-Inverter-Based True Random Number Generator with On-Chip Clock-Tuning-Based Entropy Calibration Circuit

Reduction of Operating Current by Harnessing the Field‐ and Damping‐Like Torque Ratios in Nonmagnet–Ferromagnet Heterojunctions

With the growing demand for high‐speed electronic devices with low energy consumption, spin–orbit torque (SOT) has become a significant focus. SOT can switch the magnetization direction in a material system with broken inversion symmetry, such as a normal metal (NM)/ferromagnet (FM) heterojunction. The SOT consists of two mutually orthogonal vector components along with the injected current direction: the transverse damping‐like torque (DLT) and the longitudinal field‐like torque (FLT). Numerous studies have mainly centered on the DLT for the SOT switching mechanism. However, DLT and FLT are essential to enhance SOT efficiency because FLT boosts the magnetization precession motion. Herein, heterojunctions consisting of NM 1 (Ta, W, or Pt)/NM 2 (Nb)/FM (CoFeB) are devised to manipulate the FLT‐to‐DLT ratio (η) through the change in Nb thickness. Furthermore, experimental confirmation exists for reducing threshold current as η increases. The SOT devices with substantial η generate random numbers. The National Institute of Standards and Technology Special Publication 800‐90B test verifies randomness and confirms that the SOT devices are beneficial sources for true random number generators (TRNGs). These findings indicate the crucial role of FLT in the SOT switching process and underscore its significance in developing SOT‐based TRNG devices.

Integrating Lorenz Hyperchaotic Encryption with Ring Oscillator Physically Unclonable Functions (RO-PUFs) for High-Throughput Internet of Things (IoT) Applications

With the combined call for increased network throughput and security comes the need for high-bandwidth, unconditionally secure systems. Through the combination of true random number generators (TRNGs) for unique seed values, and four-dimensional Lorenz hyperchaotic systems implemented on a Stratix 10 Intel FPGA, we are able to implement 60 MB/s encryption/decryption schemes with 0% data loss on an unconditionally secure system with the NIST standard using less than 400 mW. Further, the TRNG implementation allows for unique encryption outputs for similar images while still enabling proper decryption. Histogram and adjacent pixel analysis on sample images demonstrate that without the key, it is not possible to extract the plain text from the encrypted image. This encryption scheme was implemented via PCIe for testing and analysis.

High-efficiency TRNG Design Based on Multi-bit Dual-ring Oscillator

Unpredictable true random numbers are required in security technology fields such as information encryption, key generation, mask generation for anti-side-channel analysis, algorithm initialization, and so on. At present, the true random number generator (TRNG) is not enough to provide fast random bits by low-speed bits generation. Therefore, it is necessary to design a faster TRNG. This work presents an ultra-compact TRNG with high throughput based on a novel extendable dual-ring oscillator (DRO). Owing to multiple bits output per cycle in DRO can be used to obtain the original random sequence, the proposed DRO achieves a maximum resource utilization to build a more efficient TRNG, compared with the conventional TRNG system based on ring oscillator (RO), which only has a single output and needs to build multiple groups of ring oscillators. TRNG based on the 2-bit DRO and its 8-bit derivative structure has been verified on Xilinx Artix-7 and Kintex-7 FPGA under the automatic layout and routing and has achieved a throughput of 550 Mbps and 1,100 Mbps, respectively. Moreover, in terms of throughput performance over operating frequency, hardware consumption, and entropy, the proposed scheme has obvious advantages. Finally, the generated sequences show good randomness in the test of NIST SP800-22 and Dieharder test suite and pass the entropy estimation test kit NIST SP800-90B and AIS-31.

A High-Speed True Random Number Generator Based on Unified Selector-RRAM

A High-Speed True Random Number Generator Based on Unified Selector-RRAM

True Random Number Generator Based on RRAM-Bias Current Starved Ring Oscillator

True Random Number Generator Based on RRAM-Bias Current Starved Ring Oscillator

Design and Implementation of an On-Line Quality Control System for Latch-Based True Random Number Generator

Design and Implementation of an On-Line Quality Control System for Latch-Based True Random Number Generator

Design of True Random Number Generator Based on Multi-Ring Convergence Oscillator Using Short Pulse Enhanced Randomness

Design of True Random Number Generator Based on Multi-Ring Convergence Oscillator Using Short Pulse Enhanced Randomness

A high-speed true random number generator based on Ag/SiNx/n-Si memristor

A high-speed true random number generator based on Ag/SiNx/n-Si memristor

Effect of external magnetic fields on practical quantum random number generator

Quantum random number generator (QRNG) based on the inherent randomness of fundamental quantum processes can provide provable true random numbers which play an important role in many fields. However, the security of practical QRNGs is linked to the performance of realistic devices. In particular, devices based on the Faraday effect in a QRNG system may be affected by external magnetic fields, which will inevitably open a loophole that an eavesdropper can exploit to steal the information of generated random numbers. In this work, the effects of external magnetic fields on the security of practical QRNGs are analyzed. Taking the quantum phase fluctuation based QRNG with unbalanced Michelson interferometer as an example, we experimentally demonstrate the rotation angle of the Faraday rotation mirror (FRM) is influenced by external magnetic fields. Then, we develop a theoretical model between the rotation angle deviation of FRM and conditional min-entropy. Simulation results show that the imperfect FRM leads to a reduction in the variance of measured signal and extractable randomness. Furthermore, the impacts of practical sampling device on the extractable randomness are analyzed in the presence of imperfect FRM, which indicates suitable parameters of the sampling device can improve the security of practical QRNGs. Potential countermeasures are also proposed. Our work reveals that external magnetic fields should be carefully considered in the application of practical QRNGs.

A High Throughput STR-based TRNG by Jitter Precise Quantization Superposing

With the rapid development of integrated circuits and the continuous progress of computing capability, higher demands have been placed on the security and speed of data encryption in security systems. As a basic hardware security primitive, the true random number generator (TRNG) plays an important role in the encryption system, which requires higher throughput and randomness with lower hardware overhead. However, the throughput of TRNG is related to the entropy source’s quality and the randomness extraction methodology. To quantify the randomness of the entropy source with higher efficiency and quality, we utilize the independent jitter of the self-timed ring (STR) to generate original entropy and propose a high throughput jitter-based TRNG which can extract random information at the pulse of oscillation signal by jitter precise quantization superposing and random oscillation sampling. The proposed TRNG has been implemented on Artix-7 and Virtex-6 FPGAs. The generated true random number successfully passes the NIST SP800-22 and NIST SP800-90B tests while also exhibiting a minimum entropy greater than 0.9947. The most prominent superiority of our proposed TRNG is that it achieves a high throughput of 330 Mbps with an ultra-low hardware overhead of only 35 LUTs and 12 DFFs.

A lightweight true random number generator based on multi‐stage sampling the current starve based ring oscillator

AbstractIn this letter, a novel true random number generator (TRNG) with high energy‐efficient and throughput is proposed for cryptographic systems. The current starve based ring oscillator (CSRO) is biased in the subthrehold region as an entropy source. An individual ring oscillator (RO) is sampled using multiple sampling points of the CSRO working in the sub‐threshold region to obtain a multi‐channel sequence output, thereby fully exploiting the randomness of the entropy source. The proposed TRNG is implemented using a standard 40nm CMOS technology and the simulation results show that it provides high‐quality and 20.66 Mbps random sequences while only consuming 11.46 μW at 1.1 V, 25°C. In addition, the proposed TRNG passes the NIST SP 800‐22 and the NIST SP 800‐90B tests without post‐processing and outperforms the state‐of‐the‐art in terms of energy consumption per bit of the output bitstream, reaching 0.555pJ/bit.

A 3.3-Mbit/s true random number generator based on resistive random access memory

A 3.3-Mbit/s true random number generator based on resistive random access memory

In-situ electro-responsive through-space coupling enabling foldamers as volatile memory elements

Voltage-gated processing units are fundamental components for non-von Neumann architectures like memristor and electric synapses, on which nanoscale molecular electronics have possessed great potentials. Here, tailored foldamers with furan‒benzene stacking (f-Fu) and thiophene‒benzene stacking (f-Th) are designed to decipher electro-responsive through-space interaction, which achieve volatile memory behaviors via quantum interference switching in single-molecule junctions. f-Fu exhibits volatile turn-on feature while f-Th performs stochastic turn-off feature with low voltages as 0.2 V. The weakened orbital through-space mixing induced by electro-polarization dominates stacking malposition and quantum interference switching. f-Fu possesses higher switching probability and faster responsive time, while f-Th suffers incomplete switching and longer responsive time. High switching ratios of up to 91 for f-Fu is realized by electrochemical gating. These findings provide evidence and interpretation of the electro-responsiveness of non-covalent interaction at single-molecule level and offer design strategies of molecular non-von Neumann architectures like true random number generator.

Analyses of unpredictable properties of a wind-driven triboelectric random number generator

Wind-driven triboelectric nanogenerators (W-TENGs) are a promising candidate for an energy harvester because wind itself possesses unexhausted, ubiquitous, and clean properties. W-TENG has also been used as a random number generator (RNG) due to the inherent chaotic properties of wind that is also an entropy source. Thus, a W-TENG which simultaneously generates both power and true random numbers with a two-in-one structure, is a wind-driven RNG (W-RNG) like the Janus. However, a root cause of W-RNG unpredictability has not been elucidated. In this work, the unpredictability, which is essential and critical for an RNG, is statistically and mathematically analyzed by auto-correlation, cross-correlation, joint entropy, and mutual information. Even though the overall shape of the total output analog signals from the W-RNG looks like a sinusoidal wave that is not obviously unpredictable, discretized digital signals from the continuous analog output become unpredictable. Furthermore, partial adoption of 4-bit data from 8-bit raw data, with the aid of analog-to-digital converter hardware, further boosts the unpredictability. The W-RNG, which functions as a W-TENG, can contribute to self-powering and self-securing outdoor electrical systems, such as drones, by harvesting energy and generating true random numbers.

True random number generator based on spin–orbit torque magnetic tunnel junctions

True random number generators (TRNGs) play a pivotal role in solving NP-hard problems, neural network computing, and hardware accelerators for algorithms, such as the simulated annealing. In this work, we focus on TRNG based on high-barrier magnetic tunnel junctions (HB-MTJs) with identical stack structure and cell geometry, but employing different spin–orbit torque (SOT) switching schemes. We conducted a comparative study of their switching probability as a function of pulse amplitude and width of the applied voltage. Through experimental and theoretical investigations, we have observed that the Y-type SOT-MTJs exhibit the gentlest dependence of the switching probability on the external voltage. This characteristic indicates superior tunability in randomness and enhanced robustness against external disturbances when Y-type SOT-MTJs are employed as TRNGs. Furthermore, the random numbers generated by these Y-type SOT-MTJs, following XOR pretreatment, have passed the National Institute of Standards and Technology SP800-22 test. This comprehensive study demonstrates the high performance and immense potential of Y-type SOT-MTJs for the TRNG implementations.

MTJ-based random number generation and its application in SNN handwritten digits recognition

Spiking Neural Networks (SNNs) that require synapse weight initialization using random numbers have been widely used in the neural morphological system. However, the random numbers generated by traditional digital circuits have certain repeatability, and the entire computing architecture has issues such as high resource consumption and low integration. In this letter, a hardware system for true random number generation is realized through integrating a magnetic tunnel junction, a memory cell of MRAM (magnetic random access memory) chips, with an interface circuit and using the same mechanism as writing data in spin transfer torque MRAM. The generated true random numbers are evaluated using NIST SP800-22 standard and are used for synapse weight initialization in an SNN system. The recognition rate of the system initialized by the generated true random numbers is about 84% for an MNIST handwritten digit dataset, which is 2%–3% higher than that using a traditional linear feedback shift register. The reported work provides a new approach for better SNN performance.

Analysis and Construction of Nonlinear Correctors Used in True Random Number Generators

The problem of true random number generators (TRNGs) traces back to von Neumann’s 1951 work that aims to simulate an unbiased coin by using a biased coin with unknown probability. The core component in a TRNG is the corrector which is a post-processing function used to reduce or eliminate statistical weaknesses of physical random number generators. Note that an ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-resilient function is an ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-corrector. Hence, a natural question is how to construct an ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )- corrector which is not ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-resilient? In this paper, a framework concerning the construction of nonlinear ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-correctors with algebraic degree <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> +1 is proposed based on an equidistant linear code. We show that the derived correctors are ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> - 1)-resilient, but not ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-resilient. Given the importance of equidistant linear codes, we discuss how to get such a code with relatively flexible length, and how to get a pair of disjoint equidistant linear codes. In addition, the parameters comparison with linear correctors is given. It is shown that our method achieves the same correction order compared to the optimal linear method. As far as we know, the ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-correctors we constructed also possess the best-known correction order compared with the known nonlinear ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n,m</i> ) resilient functions. The algebraic degrees and nonlinearities of the constructed correctors are also analyzed. Through a pair of disjoint equidistant linear codes, the nonlinearity of the nonlinear ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-correctors can be improved. The results show that our ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, m, t</i> )-correctors also possess the best algebraic degree and nonlinearity for fixed ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n,m</i> ).

A True Random Number Generator Based on Semiconductor-Vacancies Junction Entropy Source and Square Transform Method

A True Random Number Generator Based on Semiconductor-Vacancies Junction Entropy Source and Square Transform Method

A 2.5 pJ/bit PVT-Tolerant True Random Number Generator Based on Native-NMOS-Regulated Ring Oscillator

In this brief, an energy-efficient true random number generator (TRNG) is presented based on the jitter noise of a single ring oscillator (RO). By XORing two different oscillation stages of the RO, consecutive pulses can be generated due to the fixed intrinsic propagation delay and more importantly, the time-varying jitter-noise-caused variation to the above delay. By continuously quantizing the above pulses’ width using another high-frequency RO-based time-to-digital converter (TDC), the TDC’s least significant bits (LSBs) are dominated by the jitter noise, of which the magnitude can be largely increased through reducing the RO’s supply voltage with a native NMOS transistor. Based on a 40-nm standard CMOS process, the proposed TRNG design is fabricated and extensively characterized. By passing the widely-exploited test tools of National Institute of Standards and Technology (NIST) and autocorrelation function, the proposed TRNG’s randomness has been well validated. Moreover, the randomness evaluation is further extended to various process-voltage-temperature (PVT) conditions, and the measured Shannon entropy is always larger than 0.999995, showing excellent PVT tolerance. Finally, the proposed TRNG features a high energy efficiency of 2.5 pJ/bit at a throughput of 53 Mbps.