Entropy Source Research Articles

Halide perovskite memristors as flexible and reconfigurable physical unclonable functions

Physical Unclonable Functions (PUFs) address the inherent limitations of conventional hardware security solutions in edge-computing devices. Despite impressive demonstrations with silicon circuits and crossbars of oxide memristors, realizing efficient roots of trust for resource-constrained hardware remains a significant challenge. Hybrid organic electronic materials with a rich reservoir of exotic switching physics offer an attractive, inexpensive alternative to design efficient cryptographic hardware, but have not been investigated till date. Here, we report a breakthrough security primitive exploiting the switching physics of one dimensional halide perovskite memristors as excellent sources of entropy for secure key generation and device authentication. Measurements of a prototypical 1 kb propyl pyridinium lead iodide (PrPyr[PbI3]) weak memristor PUF with a differential write-back strategy reveals near ideal uniformity, uniqueness and reliability without additional area and power overheads. Cycle-to-cycle write variability enables reconfigurability, while in-memory computing empowers a strong recurrent PUF construction to thwart machine learning attacks.

Design of True Random Number Generator Using Fingerprint as an Entropy Source and Its Implementation in S-Box

This paper deals with the design of a true random number generator (TRNG) using the fingerprint as an entropy source and its implementation in substitution box (S-box) of Advanced Encryption Standard (AES). Considering fingerprint as a unique and random arrangement of minutiae, these minutiae points are used as the source of entropy. The proposed design utilizes fewer resources minimizing hardware redundancy and enhancing the level of randomness. This TRNG has been designed and validated using Artix-7 FPGA. The data rate, speed and latency have been obtained as 40 Mbps, 5 Mbps and 305 ns, respectively. The generated random bit stream had also been sampled and converted to a binary format in MATLAB and tested through the National Institute of Standards and Technology (NIST) 800.22 statistical suite for validation. The proposed TRNG design pass efficiency achieved is more than 95% for a sample size of 10 binary sequences.

Design and Analysis of Configurable Ring Oscillators for True Random Number Generation Based on Coherent Sampling

True Random Number Generators (TRNGs) are indispensable in modern cryptosystems. Unfortunately, to guarantee high entropy of the generated numbers, many TRNG designs require a complex implementation procedure, often involving manual placement and routing. In this work, we introduce, analyse, and compare three dynamic calibration mechanisms for the COherent Sampling ring Oscillator based TRNG: GateVar , WireVar , and LUTVar , enabling easy integration of the entropy source into complex systems. The TRNG setup procedure automatically selects a configuration that guarantees the security requirements. In the experiments, we show that two out of the three proposed mechanisms are capable of assuring correct TRNG operation even when an automatic placement is carried out and when the design is ported to another Field-Programmable Gate Array (FPGA) family. We generated random bits on both a Xilinx Spartan 7 and a Microsemi SmartFusion2 implementation that, without post processing, passed the AIS-31 statistical tests at a throughput of 4.65 Mbit/s and 1.47 Mbit/s, respectively.

Design and FPGA Implementation of a Pseudo-random Number Generator Based on a Hopfield Neural Network Under Electromagnetic Radiation

When implementing a pseudo-random number generator (PRNG) for neural network chaos-based systems on FPGAs, chaotic degradation caused by numerical accuracy constraints can have a dramatic impact on the performance of the PRNG. To suppress this degradation, a PRNG with a feedback controller based on a Hopfield neural network chaotic oscillator is proposed, in which a neuron is exposed to electromagnetic radiation. We choose the magnetic flux across the cell membrane of the neuron as a feedback condition of the feedback controller to disturb other neurons, thus avoiding periodicity. The proposed PRNG is modeled and simulated on Vivado 2018.3 software and implemented and synthesized by the FPGA device ZYNQ-XC7Z020 on Xilinx using Verilog HDL code. As the basic entropy source, the Hopfield neural network with one neuron exposed to electromagnetic radiation has been implemented on the FPGA using the high precision 32-bit Runge Kutta fourth-order method (RK4) algorithm from the IEEE 754-1985 floating point standard. The post-processing module consists of 32 registers and 15 XOR comparators. The binary data generated by the scheme was tested and analyzed using the NIST 800.22 statistical test suite. The results show that it has high security and randomness. Finally, an image encryption and decryption system based on PRNG is designed and implemented on FPGA. The feasibility of the system is proved by simulation and security analysis.

Design and implementation of true random number generators based on semiconductor superlattice chaos

True random number generator (TRNG) is of the fundamental guarantees of information security. However, the commercially-available all-electronic TRNGs, no matter whether the thermal-noise-based or the oscillator-based ones, can merely reach the speed of a few Mbit/s due to the very limited entropy source, which is unable to meet the requirements of ultra-high-speed and ultra-large capacity of information propagation or storage. This paper proposes the design and implementation of semiconductor superlattice random number generator (SSL-RNG) by employing semiconductor superlattice chaos as entropy source. We introduce the entropy estimation method to evaluate the raw data from the entropy harvester quantitatively, thus optimized the parameter design of the LFSR-Toeplitz extractor for post-processing. We have also integrated the entropy acquisition circuit into an embedded FPGA-based platform as a standalone design to trade off the performance and cost. The resulting hardware's output passes the NIST standard statistical test with a full entropy throughput above 300 Mbit/s.

Advanced Data Encryption ​using 2D Materials.

Advanced data encryption requires the use of true random number generators (TRNGs) to produce unpredictable sequences of bits. TRNG circuits with high degree of randomness and low power consumption may be fabricated by using the random telegraph noise (RTN) current signals produced by polarized metal/insulator/metal (MIM) devices as entropy source. However, the RTN signals produced by MIM devices made of traditional insulators, i.e., transition metal oxides like HfO2 and Al2 O3 , are not stable enough due to the formation and lateral expansion of defect clusters, resulting in undesired current fluctuations and the disappearance of the RTN effect. Here, the fabrication of highly stable TRNG circuits with low power consumption, high degree of randomness (even for a long string of 224 - 1 bits), and high throughput of 1 Mbit s-1 by using MIM devices made of multilayer hexagonal boron nitride (h-BN) is shown. Their application is also demonstrated to produce one-time passwords, which is ideal for the internet-of-everything. The superior stability of the h-BN-based TRNG is related to the presence of few-atoms-wide defects embedded within the layered and crystalline structure of the h-BN stack, which produces a confinement effect that avoids their lateral expansion and results in stable operation.

Quantum Entropy Model of an Integrated Quantum-Random-Number-Generator Chip

We present the physical model for the entropy source of a quantum random number generator chip based on the quantum fluctuations of the photon number emitted by light-emitting diodes. This model, combined with a characterization of the chip, estimates a quantum min-entropy of over 0.98 per bit without post-processing. Finally, we show with our model that the performances in terms of security are robust against fluctuations over time.

Sensor-Based Entropy Source Analysis and Validation for Use in IoT Environments

The IoT market has grown significantly in recent years, and it is estimated that it will continue to do so. For this reason, the need to identify new solutions to ensure security is vital for the future development in this field. Inadequate sources of entropy are one of the factors that negatively influence security. In this study, inspired by NIST’s latest entropy estimation recommendations, we proposed a methodology for analyzing and validating a sensor-based entropy source, highlighted by an innovative experiment design. Moreover, the proposed solution is analyzed in terms of resistance to multiple types of attacks. Following an analysis of the influence of sensor characteristics and settings on the entropy rate, we obtain a maximum entropy value of 0.63 per bit, and a throughput of 3.12 Kb/s, even when no motion is applied on the sensors. Our results show that a stable and resistant entropy source can be built based on the data obtained from the sensors. Our assessment of the proposed entropy source also achieves a higher complexity than previous studies, in terms of the variety of approached situations and the types of the performed experiments.

A CRP-Space-Extended RRAM PUF With In-Cell Zero-Overhead Salicide-Blocked Contact

In this brief, we present an ultracompact physical unclonable function (PUF) based on the resistive random access memory (RRAM) with the in-cell salicide-blocked (SAB) contact. Different from most previously reported RRAM PUFs with only the RRAM cell's high-resistance state (HRS) utilized as the static entropy, its low-resistance state (LRS) is enabled with the proposed SAB contact resistance as a novel entropy source. Concretely, by adding a photolithography mask of “SAB” that widely exists in standard CMOS process to the source/drain contact of the mainstream one-transistor-one-resistor (1T1R) RRAM cell's access transistor, an SAB contact featuring large resistance stochasticity can be formed with zero design overhead of silicon area. With the SAB contact resistance connected in series, both HRS and LRS can be well-exploited to generate much more challenge-response pairs (CRPs), leading to significantly extended CRP space. In addition, the proposed RRAM PUF with in-cell SAB contact is validated using 0.18- μm standard CMOS process plus postprocessing steps for RRAM devices, and the normalized bitcell area is reported to be 77 F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /bit. By varying the operating temperature from -50 °C to 150 °C, the worst case bit error rate (BER) is measured to be 0.13% at 150 °C. Moreover, the excellent randomness of the proposed implementation is verified by passing both the National Institute of Standards and Technology (NIST) test and the autocorrelation function (ACF) test.

True Bit Generation by Using Two Different Noise Sources

Chaos-based random bit generators (RBGs) are used in encryption and in chaotic communication systems applications, such as synchronization and secure communication. Chaotic maps and circuits that display chaotic behavior as entropy sources are used to implement the random number generators (RNGs). In this study, a hybrid true random bit generator is proposed using Chua and memristor structures that display chaotic behavior as entropy sources. Continuous Chua and memristor outputs were sampled from the proposed hybrid structure. The samples obtained were converted into bit sequences by using modular arithmetic. Finally, both bit sequences were given as input to a summation generator. The output of the summation generator produces the desired bit sequences. The NIST Test Suite and the Scale Index tests were used on the resulting bit sequences to indicate their randomness. Also, correlation, complexity and key sensitivity analyses were performed for analyzing the security of the generated numbers.

A true random number generator that utilizes thermal noise in a programmable system‐on‐chip (PSoC)

SummaryThis study presents four designs for a true random number generator (TRNG) for Cypress programmable system‐on‐chip (SoC) (PSoC) devices, whose entropy source is the thermal noise of resistors. The first design includes a ΔΣ analog‐to‐digital converter (ADC) with two external resistors of 6 MΩ, where the resolution was set to 16 bits. The second, third, and fourth designs adopt the internal resistors of a programmable gain amplifier (PGA) as a noise source. The second design adopts a single‐stage PGA (gain 50) with a ΔΣ ADC, while the third design adopts a two‐stage PGA (gain 50 × 50) with a ΔΣ ADC. The fourth design adopts a trans‐impedance amplifier (TIA) with a ΔΣ ADC. All four designs have passed the National Institute of Standards and Technology (NIST) test suite.

Effect of photon statistics on vacuum fluctuations based QRNG

The speed of quantum random number generators (QRNGs) is a major concern for practical applications. In this work, we introduce scattering as a method to enhance the randomness characteristics of the entropy source. This method allows optical bit extraction with a faster sampling rate without compromising the randomness quality compared to the coherent source based balanced homodyne detection. Scattering is a probabilistic phenomenon which increases the chaotic behaviour of coherent sources. It broadens the distribution of photon statistics and makes it super-Poissonian. We show that a signal with super-Poissonian distribution has better randomness compared to a Poissonian one, indicated by their autocorrelation characteristics and the randomness test results. The use of scattering mechanisms as an entropy source eases the miniaturization of QRNGs, it also makes them compatible and adaptable to existing technologies.

The influence of random number generation in dissipative particle dynamics simulations using a cryptographic hash function.

The tiny encryption algorithm (TEA) is widely used when performing dissipative particle dynamics (DPD) calculations in parallel, usually on distributed memory systems. In this research, we reduced the computational cost of the TEA hash function and investigated the influence of the quality of the random numbers generated on the results of DPD calculations. It has already been established that the randomness, or quality, of the random numbers depend on the number of processes from internal functions such as SHIFT, XOR and ADD, which are commonly referred to as "rounds". Surprisingly, if we choose seed numbers from high entropy sources, with a minimum number of rounds, the quality of the random numbers generated is sufficient to successfully perform accurate DPD simulations. Although it is well known that using a minimal number of rounds is insufficient for generating high-quality random numbers, the combination of selecting good seed numbers and the robustness of DPD simulations means that we can reduce the random number generation cost without reducing the accuracy of the simulation results.

Random Telegraph Noise in Metal‐Oxide Memristors for True Random Number Generators: A Materials Study

AbstractSome memristors with metal/insulator/metal (MIM) structure have exhibited random telegraph noise (RTN) current signals, which makes them ideal to build true random number generators (TRNG) for advanced data encryption. However, there is still no clear guide on how essential manufacturing parameters like materials selection, thicknesses, deposition methods, and device lateral size can influence the quality of the RTN signal. In this paper, an exhaustive statistical analysis on the quality of the RTN signals produced by different MIM‐like memristors is reported, and straightforward guidelines for the fabrication of memristors with enhanced RTN performance are presented, which are: i) Ni and Ti electrodes show better RTN than Au electrodes, ii) the 50 μm × 50 μm devices show better RTN than the 5 μm × 5 μm ones, iii) TiO2 shows better RTN than HfO2 and Al2O3, iv) sputtered‐oxides show better RTN than ALD‐oxides, and v) 10 nm thick oxides show better RTN than 5 nm thick oxides. The RTN signals recorded have been used as entropy sources in high‐throughput TRNG circuits, which have passed the randomness tests of the National Institute of Standards and Technology. The work can serve as a useful guide for materials scientists and electronic engineers when fabricating MIM‐like memristors for RTN applications.

Chaotic Time-Delay Signature Suppression and Entropy Growth Enhancement Using Frequency-Band Extractor.

By frequency-band extracting, we experimentally and theoretically investigate time-delay signature (TDS) suppression and entropy growth enhancement of a chaotic optical-feedback semiconductor laser under different injection currents and feedback strengths. The TDS and entropy growth are quantified by the peak value of autocorrelation function and the difference of permutation entropy at the feedback delay time. At the optimal extracting bandwidth, the measured TDS is suppressed up to 96% compared to the original chaos, and the entropy growth is higher than the noise-dominated threshold, indicating that the dynamical process is noisy. The effects of extracting bandwidth and radio frequencies on the TDS and entropy growth are also clarified experimentally and theoretically. The experimental results are in good agreements with the theoretical results. The skewness of the laser intensity distribution is effectively improved to 0.001 with the optimal extracting bandwidth. This technique provides a promising tool to extract randomness and prepare desired entropy sources for chaotic secure communication and random number generation.

Tunnel FET‐based ultra‐lightweight reconfigurable TRNG and PUF design for resource‐constrained internet of things

SummaryConventional complementary metal oxide semiconductor (CMOS)‐based dedicated true random number generator (TRNG) and physically unclonable function (PUF) designs have exhibited higher energy consumption and large area overhead with technology scaling. In contrast, this paper for the first time presents emerging tunnel field‐effect transistor (TFET)‐based ultra‐lightweight reconfigurable TRNG and PUF design. A unique methodology is proposed that considers p‐i‐n forward current characteristics to generate random keys for PUF and TRNG designs. Leveraging the p‐i‐n forward current of TFET, a ring oscillator (RO) is designed that exhibits variation in the operating frequency and acts as the main source of entropy for both PUF and TRNG. The TRNG in the proposed design is robust and passed all the National Institute of Standards and Technology (NIST) tests. Considering the variation in p‐i‐n forward current, the uniqueness of PUF is calculated as 47.5% and 46% at a supply voltage of 0.5 and 0.45 V, respectively. Moreover, PUF achieves high reliability of 82% and 88.7% with supply voltage and temperature variations, respectively. The proposed design is proved to be compact with relatively lower gate count and shows low energy consumption of 4.8 pJ/bit at 0.5‐V supply voltage. With these performance metrics, the proposed design is highly suitable for resource‐constrained internet of things (IoT).

Quantum random number generator with discarding-boundary-bin measurement and multi-interval sampling.

A quantum random number generator (QRNG) provides a reliable means for the generation of true random numbers. The inherent randomness of the vacuum fluctuations makes the quantum vacuum state a superior source of entropy. However, in practice, the raw sequences of QRNG are inevitably contaminated by classical technical noise, which compromises the security of the QRNG. Min-entropy conditioned on the classical noise is a useful method that can quantify the side-information independent randomness. To improve the extractable randomness from the raw sequences arising from the quantum vacuum-based QRNG, we propose and experimentally demonstrate two approaches, discarding-boundary-bin measurement and multi-interval sampling. The first one increases the conditional min-entropy at a low quantum-to-classical-noise ratio. The latter exploits parallel sampling using multiple analog-to-digital converters (ADCs) and effectively overcomes the finite resolution limit and uniform sampling of a single ADC. The maximum average conditional min-entropy can reach 9.2 per sample when combining these two approaches together in contrast to 6.93 with a single 8-bit ADC.

Effect of vortex and entropy sources in sound generation for compressible cavity flow

The present study reports the effect of different source terms on the near and far-field acoustic characteristics of compressible flow over a rectangular cavity using hybrid computational aeroacoustics methodology. We use a low dispersive and dissipative compressible fluid flow solver in conjunction with an acoustic perturbation equation solver based on the spectral/hp element method. The hybrid approach involves calculating the base fields and the acoustic sources from a fluid simulation in the first step. In the next step, the acoustic solver utilizes the variables to predict the acoustic propagation due to the given sources. The validation of the methodology against benchmark cases provides quite accurate results while compared against the existing literature. The study is then extended to assess the importance of the entropy source term for the flow over a rectangular cavity. The predictions of hybrid simulations with vortex and entropy source terms reproduce the perturbation pressure values very close to the existing direct numerical simulation results. Moreover, the results suggest that the use of just the vortex source terms over-predicts the perturbation pressure near the source region. Finally, we have carried out detailed simulations with all the source terms to investigate the noise sources for compressible flow over the cavity for different Mach number ranges (M=0.4,0.5,0.6,0.7,1.5). The obtained acoustic spectra and the sound directivity are in close agreement with the reference experiment.

Analog-digital hybrid chaos-based long-haul coherent optical secure communication.

We propose and numerically investigate a chaotic optical coherent secure communication scheme, which supports long-haul secure transmission for signals in advanced modulation formats. A hybrid optical chaos system is designed with coordination of digital and analog signals. The hybrid entropy source provides a broadband analog optical chaos signal, which could serve as the carrier to load quadrature amplitude modulation (QAM) data. Simultaneously, a digital binary signal generated from the entropy source is transmitted to establish long-haul chaotic synchronization. Coherent detection is utilized at the receiver, and a digital signal processing (DSP) algorithm is adopted to reduce transmission distortion. A 5 Gbaud 16QAM signal is encrypted by a phase chaos carrier with the effective bandwidth of 5.8 GHz. A bit error rate (BER) below forward error correction (FEC) can be achieved after transmitting over 1600 km based on digital-signal-induced chaos synchronization technology. Optimal launch power is investigated to minimize nonlinear effects of transmission links. System security is guaranteed by the high dynamical complexity of the chaotic source and the sensitive time delay as the secret key.

Efficient Post-Processing for Physical-Layer Secure Key Distribution in Fiber

Post-processing is an essential step towards the practical deployment of physical-layer secure key distribution (SKD) in classical fiber channels. However, the comparison and combination of different post-processing methods are not explored yet. Here, we fully evaluate the post-processing protocol and analyze various combinations of quantization and information reconciliation (IR), and present the efficient solutions associated with the key entropy source between the legal parties. In addition, the SHA3-256 hash function-based privacy amplification is exploited to further enhance the robust key secrecy and randomness. The results show that, the proposed protocol significantly increases the achievable key generation rate (KGR) up to 130-205% using the combination of multi-bit adaptive quantizer and IR with syndrome-decoding LDPC, compared with the previous post-processing using the same original key waveforms extracted from physical-layer SKD.