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Bi2O2Se-Based True Random Number Generator for Security Applications
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Bi2O2Se-Based True Random Number Generator for Security Applications
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  • Bo Liu*
    Bo Liu
    Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    *Email: [email protected]
    More by Bo Liu
  • Ying-Feng Chang
    Ying-Feng Chang
    Artificial Intelligence Research Center, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
  • Juzhe Li
    Juzhe Li
    Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    More by Juzhe Li
  • Xu Liu
    Xu Liu
    Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    More by Xu Liu
  • Le An Wang
    Le An Wang
    Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    More by Le An Wang
  • Dharmendra Verma
    Dharmendra Verma
    Department of Electronic Engineering, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
  • Hanyuan Liang
    Hanyuan Liang
    School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, Pennsylvania 16801, United States
  • Hui Zhu
    Hui Zhu
    Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
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  • Yudi Zhao
    Yudi Zhao
    School of Information and Communication Engineering, Beijing Information Science & Technology University, Beijing 100101, China
    More by Yudi Zhao
  • Lain-Jong Li
    Lain-Jong Li
    Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, 999077, Hong Kong
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  • Tuo-Hung Hou
    Tuo-Hung Hou
    Department of Electrical Engineering and Institute of Electronics, National Yang Ming Chiao Tung University, 300 Hsinchu, Taiwan
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  • Chao-Sung Lai*
    Chao-Sung Lai
    Artificial Intelligence Research Center, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
    Department of Electronic Engineering, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
    Department of Nephrology, Chang Gung Memorial Hospital, Guishan District, 33305, Linkou, Taiwan
    Department of Materials Engineering, Ming Chi University of Technology, Taishan District, 24301 New Taipei City, Taiwan
    *Email: [email protected]
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ACS Nano

Cite this: ACS Nano 2022, 16, 4, 6847–6857
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https://doi.org/10.1021/acsnano.2c01784
Published March 25, 2022

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Abstract

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The fast development of the Internet of things (IoT) promises to deliver convenience to human life. However, a huge amount of the data is constantly generated, transmitted, processed, and stored, posing significant security challenges. The currently available security protocols and encryption techniques are mostly based on software algorithms and pseudorandom number generators that are vulnerable to attacks. A true random number generator (TRNG) based on devices using stochastically physical phenomena has been proposed for auditory data encryption and trusted communication. In the current study, a Bi2O2Se-based memristive TRNG is demonstrated for security applications. Compared with traditional metal–insulator–metal based memristors, or other two-dimensional material-based memristors, the Bi2O2Se layer as electrode with non-van der Waals interface, high carrier mobility, air stability, extreme low thermal conductivity, as well as vertical surface resistive switching shows intrinsic stochasticity and complexity in a memristive true analogue/digital random number generation. Moreover, those analogue/digital random number generation processes are proved to be resilient for machine learning prediction.

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Copyright © 2022 The Authors. Published by American Chemical Society
The recent advancement of wireless communication techniques, such as WIFI, Bluetooth Low Energy, 4G-LTE, LoRaWAN, and 5G millimeter-wave communication, has brought continual prosperity to the development of the Internet of Things (IoT), which enables convenience in human daily life. Meanwhile, a huge amount of data has been continuously produced, transmitted, stored, and processed at the edge and in the cloud, which poses significant security challenges for these highly connected devices and systems. Most of the available security protocols and encryption techniques are purely based on software algorithms and pseudorandom number generators, thus presenting potential vulnerability for a determined attacker to bypass those by exploiting high computing power or intelligent algorithms. To provide reliable and trustworthy random keys, hardware-generated primitives may offer an opportunity to provide security due to their physical-level intrinsic stochasticity. Thus, implementing hardware-based primitives into software-based encryption algorithms could be more reliable for next-generation security applications. Among various hardware candidates, emerging memristive devices with the inherent variability of their electrical parameters could be an option for a true random number generator (TRNG). (1−10) The memristive devices are being studied for a wide range of applications, including storage, in-memory logic computing, and neuromorphic computing. (11) Toward practical applications, the intrinsic stochastic cycle-to-cycle (C2C) variability, such as the random telegraph noise (RTN) and nonuniform switching voltages, could be one of the primary concerns. (12) Interestingly, although most of the research works in this field continually endeavor to diminish these “detrimental” effects, these intrinsic stochastic effects turn out to be valuable for cryptographic research and applications. (13)
Recently, harnessing two-dimensional (2D) materials to demonstrate hardware security applications is a new endeavor in the nanoelectronic community. Their dangling-bond-free interfaces and excellent surface-to-volume ratios facilitate versatile and fantastic security applications: (14) hardware camouflaging based on reconfigurable polymorphic gates based on black phosphorus or 2D heterostructures for avoiding reverse engineering (RE); (15,16) ML attack resilient physical unclonable function based on graphene or tungsten diselenide (WSe2) field-effect transistors; (17,18) advanced encryption system based on RTN signal generation in hexagonal boron nitride (h-BN) memristive devices. (19) In the 2D family, bismuth oxyselenide (Bi2O2Se) is a two-dimensional (2D) layered semiconductor with moderate bandgap, ultrahigh carrier mobility, and excellent air stability as well as surface-resistive switching behavior and low thermal conductivity, which could be suitable for hardware security applications. (20) The bismuth oxyselenide exhibits extremely low in-plane electron-effective mass, as confirmed by theoretical predictions and angle-resolved photoemission spectroscopy mapping (m* = 0.14 ± 0.02m0, where m0 is the free-electron mass). (21) This value is much lower than other semiconductor materials, including traditional Si (0.26m0) as well as 2D MoS2 (0.4–0.6m0) or BP (0.15m0 for mx* and 1.18m0 for my*). (22) Experimentally, the Bi2O2Se exhibits Hall mobility of 18500–28900 cm2 V–1 s–1 at 1.9 K and field-effect mobility of 1500 cm2 V–1 s–1 with a large on–off current ratio and nearly ideal subthreshold swing of 65 mV dec–1 in a transistor. Moreover, Bi2O2Se is also a good candidate for memristor architecture: First, as a bottom electrode: realization in-memory logic computing by carefully tuning the back-gated voltages. (23) Second, as switching layer: as revealed by conductive atomic force microscope (CAFM) very recently, an electric field in the vertical direction not only triggers the formation of Se vacancies and hillocks on the Bi2O2Se surface but also generates out-of-plane resistive switching based on that. (24) Moreover, because of its embodied ferroelectric soft phonon modes, Bi2O2Se has a very low thermal conductivity of 1.1 W m–1 K–1 and a large Seebeck coefficient of 148 μV K–1 (the Seebeck coefficient could be derived from the thermoelectric figure of merit). (25) As for the application of TRNG, the Bi2O2Se-based memristor should provide inherent stochastics. In this consideration, its moderate bandgap, high carrier mobility, and air stability, especially the low thermal conductivity and the vertical surface resistive switching properties, provide opportunities: (24) First, compared with metal electrode, the low thermal conductivity of Bi2O2Se leads higher heat aggregation within the insulation layer, especially concentrated at the conductive filament regions. Thus, more heat aggregation within the insulation layer will induce higher thermal activated C2C variability; Second, the surface resistive switching properties of Bi2O2Se layer may cause one more variable during the filament switching and rupture within the dielectric layer. The superposition of Se vacancies generation, hillocks formation, and resistive switching of Bi2O2Se surface, with the filamentary switching and rupture within insulation layer will further lead higher inherently stochastic of the C2C variability and set voltage distribution in the memristive system.
In this study, we demonstrated a state-of-the-art Bi2O2Se-based true random number generator for security applications. The RTN signals and the randomly distributed set voltages of the Bi2O2Se-based memristor are utilized as two kinds of entropy sources for the TRNG in analogue mode or digital mode, respectively. As demonstrated in the current study, the analogue typed TRNG could be utilized to encrypt and decrypt auditory data. Moreover, the digital typed TRNG guarantees the safety of the transmission channel through the Diffie–Hellman Key Exchange protocol. (26) The random number generation are based on C2C variability. To verify the data independency from cycle to cycle, both the data of RTN signals and resistive switching were fed into a Long Short-Term Memory (LSTM) typed recurrent neural network (RNN). As demonstrated in the current study, the Bi2O2Se-based TRNG are resilient against ML prediction.

Results and Discussion

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Figure 1a illustrated the M–I–M memristive structure of Bi2O2Se-based TRNG. The Al, AlOx, and Bi2O2Se are served as the top electrode, dielectric, and bottom electrode, respectively. Pd serves as the contact to Bi2O2Se due to its favorable work-function alignment. (21) Native AlOx was chosen as the switching medium due to its damage-free deposition process and low standard Gibbs free energy (−1582.9 kJ/mol) of Al to form its corresponding metal oxides. (26) Usually, when native AlOx is utilized as a dielectric layer (e.g., a MoS2 based top-gated transistor (27)), a post-annealing process should be carried out to reduce the interfacial dangling bonds and border traps. In the current study, the inherent plenty defect density (approximately 1019/cm3) (27) is useful for the random number generation and the following security applications. More information on synthesis, transfer, and characterization methods of the Bi2O2Se layer and the fabrication details are described in the Methods. There are two random number generation modes in the current study: RTN mode (Figure 1b1) and switching probability mode (Figure 1c1). The RTN signal generation could be explained by electron trapping/detrapping near the ruptured filament, as shown in Figure 1b2. Considering only one existing trap, the trapping process leads to further depletion of the conduction path and causes the current transition tc to a lower level δ0. The detrapping transition process te leads to the release of the trapped electron and recovers the current to the original level δ1. The traces of RTN signals will appear in the form of Figure 1b3 when the capture time constant τc is smaller than the emission time constant τe, and they will appear in the form of Figure 1b4 if τc is larger than τe. As for the switching probability mode, taking the median voltage value of the set voltage distribution (Figure 1c2), when the set occurs before the median voltage value, it counts as “1”; otherwise, it appears as “0”, as shown in Figure 1c3 and c4. Figure 1d exhibits the lattice structure of the Bi2O2Se layer, which is in a tetragonal phase (I4/mmm, a = 3.891 Å, c = 12.21 Å, and Z = 2). The [Bi2O2]n2n+ layer is sandwiched between the negatively charged [Se]n2n layers. To preserve the inversion symmetry of the lattice, Se layers always terminate at the top and bottom surfaces of Bi2O2Se. (21) Moreover, the phonon vibration A1g peak of the Bi2O2Se layer was probed via the Raman spectrum, as exhibited in Figure 1e. The A1g mode involves the vibration of Bi and O atoms along the z-axis of the crystal and is located at 164 cm–1, which is consistent with the previous reports. (28) Subsequently, a typically bipolar resistive switching performance is demonstrated in Figure 1f, where 10 μA is set as the compliance current (CC) to prevent a permanently hard breakdown. A set voltage of 2.88 V turns on the memristor from a high resistant state (HRS) to a low resistant state (LRS) and a reset voltage of −1.75 V turn off the memristor from LRS back to HRS. Consistent with the lattice structure in Figure 1d, the cross-sectional view of high-resolution transmission electron microscopy (HRTEM) with energy-dispersive X-ray spectroscopy was carried out to verify the crystallinity and elementary composition, as shown in Figure 1g,h1,h2,h3.

Figure 1

Figure 1. Illustration of Bi2O2Se-based TRNG: (a) device structure of Bi2O2Se-based memristor; (b1) RTN mode of analog type TRNG; (b2) the illustration of a trap nearby the filament (in HRS); RTN signals considering only one defect (b3) where the emission time τe is larger than capture time τc and (b4) where the capture time τc is larger than emission time τe; δ0 and δ1 stand for the lower and higher current states; te and tc stand for the transition process during emission and capture respectively; (c1) set probability mode of digital type RTN; (c2) illustration of set voltage probability distribution, where the dashed black line indicates the median value to generate random digital numbers “0” and “1”; (c3) successful Set utilizing the median voltage value, consider as “1”, and (c4) the failure Set utilizing the median voltage value, consider as “0”; (d) lattice structure of Bi2O2Se; (e) Raman spectrum of the Bi2O2Se lattice with the A1g peak located at 164 cm–1; (f) typical set and reset operation for the Bi2O2Se-based memristor by using CC at 10 μA; the switching time period is approximately 5 s; (g) HRTEM image of Bi2O2Se in the cross-sectional view, with a scale bar of 5 nm; the lattice height is 0.6 nm, which is consistent with the lattice structure of (d); element distributions of the Bi2O2Se lattice, including (h1) Bi, (h2) O, and (h3) Se, utilizing energy-dispersive X-ray spectroscopy equipped within the TEM, with a scale bar of 25 nm.

To clearly clarify the generation mechanism of RTN signals, an illustrated figure based on a nonradiative multiphonon (NMP) model is shown in Figure 2a. The NMP mode accounts for the structural relaxation of the insulator defects following a charge capture or emission event. (29) In Figure 2a, the oxygen vacancy VO has two stable states, VO2+ and VO0, and a metastable state, VO+. (30) The thermally activated charge transition between these states, including electron trapping and detrapping, leads the generation of the RTN signals. For crystallized insulators such as SiO2 or HfO2, most of the oxygen vacancies or trapping sites are located at the strained bonds where the defect bands and the time constants of the trapping and detrapping are identical (as well as the lattice form of Al2O3). (31,32) It leads to narrow time constant distribution and bistable RTN signals, which are very suitable for digital typed bit stream generation. (19) As for the amorphous nature of the AlOx, the defect bands could be located at many positions (Figure 2a only shows one typed defect level). According to the previous study based on Trap Spectroscopy by Charge Injection and Sensing (TSCIS) detection, the defects energy depth of the amorphous AlOx exhibits much wider defect region comparing with the lattice form of Al2O3. (33) Moreover, the time constants of the trapping and detrapping in the amorphous oxides are also widely distributed (from nanoseconds to many years). Since the defect energy depth and the time constants are all widely distributed, the superposition of those trapping and detrapping leads an analogue typed random number generation in RTN mode.

Figure 2

Figure 2. RTN mode of Bi2O2Se-based TRNG. (a) Mechanism of the RTN generation: the electron trapping and detrapping between two stable defective states VO2+ and VO0, driven by reading voltages and thermal effects, the current states vary stochastically between energy states: E1 and E2, w1 and w2, q1 and q2 represent the minimum potential energy, vibration frequencies, and equilibrium position of the defective states of the states 1 and 2, respectively; q represents the local equilibrium position, and M stands for the effective mass of the defect; (b) HRS and LRS current retention of Bi2O2Se-based memristor; the inset shows the RTN effect of HRS; (c) RTN effect at different temperatures, ranging from 300 to 380 K; (d,e) capture and emission transition time of the RTN effect at different temperatures; (f) RTN effect in different VBG, ranging from 0 to −1.5 V; (g,h) capture and emission transition time of the RTN effect at different VBG, (i) calculated effective influenced area of the filament gap region of (f), ranging from 0 V to −1.5 V; the sampling rate is 5 Hz for the RTN detection.

A 0.1 V constant voltage stress (CVS) was applied on the Bi2O2Se-based memristor both on its LRS state and HRS state. Apparently, the HRS current exhibits much more fluctuation than the LRS current in Figure 2b. (34) To further explore its characterization, RTN signals were detected in HRS under different temperatures, ranging from 300 to 380 K, as shown in Figure 2c. From 300 to 320 K, the current magnitude was increased due to the enhanced charge density within the filament gap region to a higher trap assist tunneling (TAT) current. Consequently, without any operation, the RTN current amplitude was quickly dropped at the following temperature conditions from 340 to 380 K. Structural relaxation of the AlOx layer may occur under this temperature region. Similarly, the enhanced temperature also leads to fluctuation and degradation on the resistive switching process, where the set voltage increases to more than 10 V at the 380 K condition (Figure S1a–d). To further analysis those RTN signals, the capture and emission time constants have been extracted from MATLAB scripts. As shown in Figure 2d,e, both the capture and emission constants are thermally activated and become shorter at higher temperature, which is consistent with the NMP theory. Compared with changes in the ambient temperature, tuning VBG could be more controllable to generate RTN signals at different magnitudes. As shown in Figure 2f, RTN signals were detected under different VBG ranging from 0 to −1.5 V. Similarly, the trapping and detrapping time constants were extracted in the same approach, shown in Figure 2g,h. Unlike with temperature increases, the enhanced vertical electric field does not vary much for the trapping and detrapping time constants. The current magnitude of RTN is positively related to VBG, indicating the current conduction path in the filament gap region is more activated under higher electric field. These conductive areas of each VBG are shown in Figure 2i. More information and calculation details are provided in Supporting Information section I and Figure S2a,b. Moreover, the generation of those RTN signals requires ultralow power consumption, ranging from 1 to 10 nW, as shown in Figure S2c.
From the viewpoint of memory or other related in-memory computing applications, RTN variability belongs to the reliability issue, which reduces the memory-sensing margin and should be diminished. From then viewpoint of cryptology, the stochastic nature of the RTN signals could be utilized in TRNG as the entropy source for cryptologic applications. To implement TRNG into cryptology, the RTN-based TRNG could be simply classified into two categories: digital type and analogue type. The digital bitstream could be feasible to encrypt digital data, for example, as the key for the XOR gate encryption (35) or the one-time password (OTP) bitstreams. (19) For the analogue RTN signals, it is more feasible to encrypt and decrypt analogue data, for example, human voice. To better visualize the features of RTN signals under different VBG, a Time Lag Plot (TLP) has been carried out to present the stochastic fluctuation in a form of current–time (It) traces. (36)Figure 3a–f shows the TLP of the RTN signals under different VBG ranging from 0 to −1.5 V. In those 2D maps, the points at the left-bottom and top-right corners represent the low and high current levels (δ0 and δn, where n = 1, 2, 3...), respectively, and the points at the top-left and bottom-right corners represent the transition from low to high and high to low current levels, which were related to the charge emission transition process τe and charge capture transition process τc respectively; (37) the background color represents the concentration of the points distribution. As the VBG decreased, the RTN signals plots change from two or several discrete areas into one large and merged area. According to the recent artificial neural network-based TLP analysis and classification, the RTN signals with large VBG could be considered as a component of white noise. (38) To demonstrate the encryption and decryption analogue data utilizing those RTN signals, a simple symmetric-key algorithm combining five types of RTN signals was proposed as shown in Figure 3g,h, where a female voice of “Hi Bob. Happy new year!” and a male voice of “Hi Alice. Happy new year!” were successfully encrypted and decrypted. Supporting Information section II provides more information on the calculation details. Although the male and female voices have different auditory frequencies (as shown in Figure S3a,b), they have been successfully encrypted (human ears cannot distinguish any original words) and decrypted without any distortion. By utilizing the current proposed cryptological method with the five types RTN signals, both female and male voices can efficiently encrypted and decrypted. For comparison, a bit XOR method has been carried out to encrypt and decrypt the voice. After encryption, human ears could still distinguish the original voice because approximately 50% of the original data still remained after encryption.

Figure 3

Figure 3. Time lag plot analysis of RTN signals and utilizing them for audio signal encryption and decryption. TLP analysis of RTN0 (a), RTN0.25 (b), RTN0.5 (c), RTN0.75 (d), RTN1 (e), and RTN1.5 (f), where τe and τc indicate the transition of current states of electron emission and capture and δ0 and δn indicate the current states from 0 to n, where the n equals to 1, 2, 3...; (g) original, encrypted, and decrypted female audio signal of “Hi, Bob. Happy new year”; (h) original, encrypted and decrypted male voice of “Hi Alice. Happy new year”.

Although the proposed method successfully encrypts and decrypts human voices, it is still unsafe if an eavesdropper Eve intercepts a piece of the voice through an insecure transmission channel and tries to decode the content. Once Eve knows the algorithm of the symmetric key for encryption and decryption, the transmission between the two communicated parties, Bob and Alice, is exposed. Thus, a secure transmission protocol is also necessary to further protect information safety. The secure data transmission in the IoT system often require random keys generation with security protocols to establish trusted communication channels, for example, the applications of wearable sensor networks or other intelligent applications running at the edge. (39,40) Harnessing hardware-based primitives into those software-based cryptography algorithms could be a more reliable option. In this scenario, a TRNG-based Diffie–Hellman Key Exchange protocol was demonstrated in the current study, which could solve this potential communication security problem. To realize this protocol, we utilized the variation of the set voltage in the Bi2O2Se-based memristor to construct a digital true random bitstream. Additionally, a peripheral circuit design on a breadboard is shown in Figure S4 to extract and save the random digital numbers in sequence. The set voltage distribution of the Bi2O2Se-based memristor from 270 DC cycles is shown in Figure 4a. The random bitstream generation is feasible by utilizing the variation of the set voltage distribution, as shown in the Figure 1c1–c4. Thanks to its non-van der Waals (vdW) interface, low thermal conductivity, and surface resistive switching, the Bi2O2Se-based memristor exhibits a much wider set of voltage distribution than a graphene-based memristor in a similar Al/AlOx structure. (41) To verify the randomness of the bitstream, Hamming Weight and intra-Hamming Distance have been calculated, (42) as shown in Figure 4b,c. The Hamming weight is the number of non-zero symbol of a string, also equivalent of the Hamming distance with an all-zero string in the same length. As shown in Figure 4b, the distribution of Hamming weight is approximately 50% with wide variation, indicating the high randomness of the bit distributions within those keys. The intra-Hamming Distance (intra-HD) is a term in the field of physical unclonable function (PUF), which is to defined as the number of bit substitutions to change one key to another. Note that the term “intra” indicates the generation of those keys in the same TRNG device. Ideally, the intra-HD should be 50% to avoid any speculation of the correlation between the keys. The 270 DC cycles based random numbers have been divided into 9 digital keys, and each key contains 30 random bits. As shown in Figure 4c, the intra-HD of the current Bi2O2Se based TRNG is ideally narrowly distributed around 50%, indicating a true randomness without correlation. More information and calculation details of the Hamming Weight and Hamming Distance are demonstrated in Supporting Information section III. On the basis of these results, the random number generation based on switching probability mode of Bi2O2Se-based memristive TRNG is truly random, independent, and reliable for further cryptographic applications.

Figure 4

Figure 4. Set probability mode of Bi2O2Se-based TRNG: (a) set voltage distribution of Bi2O2Se-based memristor from 270 DC cycles; (b) Hamming weight of Bi2O2Se-based digital TRNG from nine digital keys, and each key contains 30 bits; (c) intra-Hamming distance (HD) of those digital keys; (d) illustration of TRNG-based Diffie–Hellman Key Exchange protocol, where Bob and Alice successfully realize key exchange through an insecure channel.

On the basis of the generated random digital keys, a TRNG based Diffie–Hellman Key Exchange protocol was demonstrated in Figure 4d. The Diffie–Hellman key exchange protocol was originally proposed by Diffie and Hellman in 1976 to jointly establish a shared private key by using public keys and random numbers under an insecure channel. The security of this algorithm is based on the difficulty of solving discrete logarithms. Supposing Eve tried to decode the shared private key, she needs to calculate either (Ba mod p) or (Ab mod p). Because she does not know the random integer number a or b, it is impossible for her to get the private key. But if Eve knows either a or b, or the algorithm for random number generation, she could decode this security system, which is a forward secrecy (FS) issue. The FS is a feature for assurance of the session keys that are not compromised even if the historical secrets used in the past session key exchange are compromised. To address this concern, the intrinsic stochasticity and independence of the Bi2O2Se-based TRNG could guarantee the security of the transmission protocol as well as the FS issue. A detailed calculation process of the TRNG-based D-H key exchange protocol is demonstrated in Supporting Information section IV.
The security of the proposed cryptography system is based on the discrete logarithms and the hardware random number generation. Although the auditory data has been efficiently encrypted and decrypted, and private keys have been successfully changed via a D–H protocol, the random number generation in RTN mode and in the switching probability mode are highly related to the memristive C2C variability. To avoid the threat of potential speculation at physical level, further study of the C2C variability of the Bi2O2Se TRNG is highly necessary. On the basis of the study of in situ characterization analysis on a memristive system, (43) it has become more and more clear that the C2C variability is closely related to the nonregular conduction path formation during set process and the variation of the filament gap distance after the rupture of the conduction filament during the reset process. As verified by the detection of photoelectron emission microscopy (PEEM) on a graphene/Al2O3/SrTiO3/Nb:SrTiO3 memristive system, (44) the location, shape, and surrounding oxygen vacancy gradient of the active filament will change from cycle to cycle. Moreover, during those processes, nonfully growth subfilaments will also compete with each other to form the new active filament in the following cycles. Although the study on this field provides direct observation of the C2C variability, a critical question based on the C2C variability toward cryptological applications is still remain elusive: Are the C2C variabilities independent or physically correlated? If the C2C variabilities are physically correlated, they are vulnerable to being predicted by physical models or other algorithms.
In this consern, a Long Short-Term Memory (LSTM) network has been utilized to analysis the C2C variability including the sequences of RTN and switching results. The LSTM is a type of recurrent neural network that allows the outputs at a previous time step to be conjunctively used as coinputs at a following time step. (45) The LSTM cell, based on its input gate, forget gate, activation gate, and output gate, can update the cell state, remove irrelevant information, and propagate useful information to the next cell via feedback optimization and pointwise multiplication from cycle to cycle. (46)Figure 5a exhibits the structure of the LSTM unit (Figure 5a2). The input and output physical features are extracted from 270 switching results. The feature extraction processes are shown in Figure 5a1,a3: HRS current, current before set, LRS current, reset voltage, reset current, voltage after reset, and current after reset were considered as input features, and the set voltage value was considered as output feature. The gradual reset and the abrupt reset are related to the thermal effect, and those four physical features related to reset process are necessary for ML analysis. (47) In contrast, the voltage before set is not that necessary because all of the set transitions are abrupt for the current study. Before being fed into the LSTM RNN for calculation, all of the current parameters were subjected to logarithm calculation for feature scaling. More information for the LSTM initialization and optimization can be found in the Methods. Additionally, the sequential RTN data under different VBG were also fed into the LSTM network for analysis. As a comparison between the testing data and the prediction data, the LSTM could only predict the variation trend for each data set but could not well fit all the RTN features, as shown in Figure 5b1–b6). The discrepancy between RTN signals and the prediction results could be attributed to the inherently regression algorithm of the ML and also guarantee the unpredictable of the true random number in analogue type.

Figure 5

Figure 5. Machine learning analysis of the switching curves and RTN curves: (a1) cycle i of the switching curve of Bi2O2Se based memristor, where eight physical parameters are extracted for further LSTM-based ML analysis, including HRS current, current before set, set voltage, LRS current, reset voltage and current, voltage, and current after reset; (a2) demonstration of the LSTM cell, where the sigmoid and tanh stand for activation functions; (a3) cycle i+1 of the switching curve of Bi2O2Se-based memristor; the RTN signals in different VBG voltages as well as their prediction curves utilizing the LSTM-RNN: (b1) RTN0; (b2) RTN0.25; (b3) RTN0.5; (b4) RTN 0.75; (b5) RTN 1; (b6) RTN 1.5, the numbers after RTN stand for the absolute value of VBG, ranging from 0 V to −1.5 V; SHAP value of the LSTM model for visualizing the impacts of the switching parameters to the set voltage (where the set voltage is chosen as the output): (c) mean of the SHAP value(d) SHAP value, where red/blue color directions stand for the higher/lower magnitudes of the extracted parameters, where the SHAP stands for SHapley Additive exPlanations.

Compared with the RTN signal prediction, the calculation results of switching probability by LSTM network could provide more fundamental insights. To better visualize the correlation and contribution of the input features onto the output feature, Shapley value plots were carried out. The Shaley value plot is originated from game theory and local explanations, which could concisely leverage all the features’ contribution onto the model’s prediction of ML. As shown in Figure 5c, based on the LSTM recurrent calculations, the current before the set and the HRS current were the most important features contributed to the set voltages, followed by reset voltage, voltage after reset, current after reset, and reset current, where the most irrelevant feature is the LRS current. These calculation results in the mean Sharpley value are consistent with materials analysis and physical modeling: (48) First, before sets occur, three typical conduction modes exist depending on the voltage application as well as carrier injection rate, including Ohmic conduction (IV, where the amount of injected carriers (nI) and free carriers in thermal equilibrium (n0, assuming T = 300 K) is smaller than the intrinsic defects or trap sites (nT) nI + n0 < nT), space-charge-limited-current conduction (IV, (2) where nI + n0 > nT), and trap-filled limited conduction(IV3, where nI > n0 and nIn0). On the basis of the calculations, the starting point of the set (HRS current) and the transition point (current before set) are highly correlated with the set voltages, which is followed by the resistive switching mechanisms. (49) Second, the set process is also highly related to the reset process in the previous cycle, where the reset process is a thermal activated process containing filament rupture (at unpredictable positions). During the reset, drift and diffusion current compete with each other, and the reset voltage, voltage after reset, current after reset, and reset current are inherently stochastic. (41) These four physical features are also highly related to set voltage because the reset process turn off the device by formation a filament gap and determine the starting point for the next cycle. Third, the LRS current is almost determined with the compliance current. Not surprisingly, it is the most irrelevant feature to the output. Following the analysis of the mean Sharpley value, the Shapley value figure is more interesting, as shown in Figure 5d. The Sharpley value not only presents the correlation but also the contribution between the input features and the output feature. In the Sharpley value figure, the red/blue dot means that the higher/lower the input feature, the higher/lower positive or negative contribution (positive or negative contribution dependent on its location of x axis) to the output feature. Interestingly, most of the features demonstrated synergetic distribution of red dots and blue dots in both the positive and negative x axis, which statically verify the inherently stochastic, unpredictability, and independence of the set voltage distribution of Bi2O2Se-based memristors from cycle to cycle.

Conclusion

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In brief summary, a state-of-the-art Bi2O2Se-based TRNG was demonstrated and applied to security applications. Thanks to the intrinsic low thermal conductivity and vertical surface resistive switching of Bi2O2Se, the inherent stochasticity and complexity of the analogue and binary TRNG are guaranteed. The amplitude-controllable RTN signals with low energy consumption were utilized as analogue-type TRNG to encrypt and decrypt human voice. The widely distributed set of voltages of the Bi2O2Se-based memristor were utilized to generate random bitstreams for realizing the TRNG-based Diffie-Hellman Key Exchange protocol. Moreover, as demonstrated in the LSTM network-based analysis and Shapley value visualization, the bimode random number generator is proved to be resilient against machine learning prediction.

Methods

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CVD Synthesis of Bi2O2Se on Mica

The 2D Bi2O2Se nanosheets were synthesized in a low-pressure CVD furnace equipped with a 3-in. diameter horizontal quartz tube and three temperature-controlled zones. Powders of Bi2O3 and Bi2Se3 as precursors were placed in the central zone and upstream of the chamber with a distance of 8 cm, respectively. Ar gas was used as the carrier gas to transport the vaporized precursor to the targeting growth location of mica with a distance of 12 cm downstream. The tube was sealed, evacuated, and flushed with pure Ar gas to provide an oxygen-free environment. Typical growth conditions are described below. The temperature of Bi2Se3 source was 500 °C. The system pressure was controlled at 100 Torr and the flow rate of the carrier gas was 200 sccm. The growth time ranged from 10 to 40 min. After the deposition was complete, the furnace was cooled naturally to room temperature and the quartz tube was refilled with Ar gas to reach atmospheric pressure.

Characterization of the Bi2O2Se Nanosheets

After the material synthesis and transfer, a RAMaker confocal Raman spectrum with 100× objective lens with 532 nm excitation laser was carried out to probe its lattice information, where the spot size was approximately 0.5 μm. A focused ion beam (FIB) in a dual beam microscope was employed to obtain the cross-sectional images of the Bi2O2Se. The following lattice detecting was obtained via a high-resolution transmission electron microscope (TEM, JEM-2100F, acceleration voltage 200 kV). (50)

Fabrication of the Bi2O2Se-Based Electronic Device

Initially, a poly(methyl methacrylate) (PMMA) and polydimethylsiloxane (PDMS) assisted transfer was carried out to detach the Bi2O2Se nanosheet from the mica substrate and assemble on the targeted SiO2/Si substrate. In each step, the sample was sequentially cleaned with acetone, isopropyl alcohol (IPA), and deionized (DI) water. After the transfer process, the Bi2O2Se sample defined the metal contacts (50 nm Pd) and top dielectric and electrode (7 nm naturally formed AlOx and 50 nm Al), utilizing LED lithography. The deposition was via thermal evaporator, and the deposition rate was confined within 1 Å at 10–6 Torr to ensure the film uniformity and quality. Electrical properties were all measured in an Agilent B1500 semiconductor device parameter analyzer.

Parameter Optimization for the LSTM Prediction Model

All of the parameters of the LSTM predicting model were optimized via using the grid search technique. The preliminary options for each parameter were as follows: (a) training batch size, 16 and 32; (b) dropout value, 0, 0.1, and 0.3; (c) learning rate of optimizer Adam, 0.01 and 0.03; (d) hidden layers for the LSTM model, 3, 4, 5, 6, 7, and 8; (e) cells of the LSTM hidden layer, 4, 8, 16, 32, 64, and 128. In addition, each combination handled 4-fold cross-validations and repeated five times to obtain the best results in this study. Finally, the optimized parameters of LSTM time step = 16 and time step = 32 were “training batch size, 16; dropout value, 0.3; learning rate, 0.03; number of hidden layers, 4; cells of the LSTM hidden layer, 128” and “training batch size, 16; dropout value, 0.1; learning rate, 0.03; number of hidden layers, 4; cells of the LSTM hidden layer, 128”, respectively.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.2c01784.

  • Section I: calculation of effective RTN affected area; Section II: the calculation details of encryption and decryption of auditory signals; Section III: Hamming Weight and Hamming Distance; Section IV: an example of Bi2O2Se based TRNG for D-H key exchange protocol; Figure S1, switching performances of Bi2O2Se based memristor under different temperature, ranging from 320 to 380 K; Figure S2, box plot of VBG dependent RTN current, effective influenced area and power consumption of Bi2O2Se based memristor; Figure S3, the female of male voice signals in amplitude and frequency domain; Figure S4, the peripheral circuit design of Bi2O2Se-based TRNG in a bread board (PDF)

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Author Information

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  • Corresponding Authors
    • Bo Liu - Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of ChinaOrcidhttps://orcid.org/0000-0002-8648-5816 Email: [email protected]
    • Chao-Sung Lai - Artificial Intelligence Research Center, Chang Gung University, Guishan District, 33302 Taoyuan, TaiwanDepartment of Electronic Engineering, Chang Gung University, Guishan District, 33302 Taoyuan, TaiwanDepartment of Nephrology, Chang Gung Memorial Hospital, Guishan District, 33305, Linkou, TaiwanDepartment of Materials Engineering, Ming Chi University of Technology, Taishan District, 24301 New Taipei City, TaiwanOrcidhttps://orcid.org/0000-0002-2069-7533 Email: [email protected]
  • Authors
    • Ying-Feng Chang - Artificial Intelligence Research Center, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
    • Juzhe Li - Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    • Xu Liu - Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    • Le An Wang - Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    • Dharmendra Verma - Department of Electronic Engineering, Chang Gung University, Guishan District, 33302 Taoyuan, Taiwan
    • Hanyuan Liang - School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, Pennsylvania 16801, United States
    • Hui Zhu - Faculty of Information Technology, College of Microelectronics, Beijing University of Technology, Beijing 100124, People’s Republic of China
    • Yudi Zhao - School of Information and Communication Engineering, Beijing Information Science & Technology University, Beijing 100101, China
    • Lain-Jong Li - Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, 999077, Hong KongOrcidhttps://orcid.org/0000-0002-4059-7783
    • Tuo-Hung Hou - Department of Electrical Engineering and Institute of Electronics, National Yang Ming Chiao Tung University, 300 Hsinchu, TaiwanOrcidhttps://orcid.org/0000-0002-9686-7076
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This study was supported by grants from the Ministry of Science and Technology, Taiwan (MOST 110-2119-M-492-002-MBK, MOST 110-2221-E-182-043-MY3, and MOST 109-2221-E-182-013-MY3), and the Chang Gung Memorial Hospital (CORPD2J0073). We appreciate the discussion with Prof. Chia-Ming Yang and Dr. Tsung-Cheng Chen and the voice recording by Li Yang (Alice).

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  • Abstract

    Figure 1

    Figure 1. Illustration of Bi2O2Se-based TRNG: (a) device structure of Bi2O2Se-based memristor; (b1) RTN mode of analog type TRNG; (b2) the illustration of a trap nearby the filament (in HRS); RTN signals considering only one defect (b3) where the emission time τe is larger than capture time τc and (b4) where the capture time τc is larger than emission time τe; δ0 and δ1 stand for the lower and higher current states; te and tc stand for the transition process during emission and capture respectively; (c1) set probability mode of digital type RTN; (c2) illustration of set voltage probability distribution, where the dashed black line indicates the median value to generate random digital numbers “0” and “1”; (c3) successful Set utilizing the median voltage value, consider as “1”, and (c4) the failure Set utilizing the median voltage value, consider as “0”; (d) lattice structure of Bi2O2Se; (e) Raman spectrum of the Bi2O2Se lattice with the A1g peak located at 164 cm–1; (f) typical set and reset operation for the Bi2O2Se-based memristor by using CC at 10 μA; the switching time period is approximately 5 s; (g) HRTEM image of Bi2O2Se in the cross-sectional view, with a scale bar of 5 nm; the lattice height is 0.6 nm, which is consistent with the lattice structure of (d); element distributions of the Bi2O2Se lattice, including (h1) Bi, (h2) O, and (h3) Se, utilizing energy-dispersive X-ray spectroscopy equipped within the TEM, with a scale bar of 25 nm.

    Figure 2

    Figure 2. RTN mode of Bi2O2Se-based TRNG. (a) Mechanism of the RTN generation: the electron trapping and detrapping between two stable defective states VO2+ and VO0, driven by reading voltages and thermal effects, the current states vary stochastically between energy states: E1 and E2, w1 and w2, q1 and q2 represent the minimum potential energy, vibration frequencies, and equilibrium position of the defective states of the states 1 and 2, respectively; q represents the local equilibrium position, and M stands for the effective mass of the defect; (b) HRS and LRS current retention of Bi2O2Se-based memristor; the inset shows the RTN effect of HRS; (c) RTN effect at different temperatures, ranging from 300 to 380 K; (d,e) capture and emission transition time of the RTN effect at different temperatures; (f) RTN effect in different VBG, ranging from 0 to −1.5 V; (g,h) capture and emission transition time of the RTN effect at different VBG, (i) calculated effective influenced area of the filament gap region of (f), ranging from 0 V to −1.5 V; the sampling rate is 5 Hz for the RTN detection.

    Figure 3

    Figure 3. Time lag plot analysis of RTN signals and utilizing them for audio signal encryption and decryption. TLP analysis of RTN0 (a), RTN0.25 (b), RTN0.5 (c), RTN0.75 (d), RTN1 (e), and RTN1.5 (f), where τe and τc indicate the transition of current states of electron emission and capture and δ0 and δn indicate the current states from 0 to n, where the n equals to 1, 2, 3...; (g) original, encrypted, and decrypted female audio signal of “Hi, Bob. Happy new year”; (h) original, encrypted and decrypted male voice of “Hi Alice. Happy new year”.

    Figure 4

    Figure 4. Set probability mode of Bi2O2Se-based TRNG: (a) set voltage distribution of Bi2O2Se-based memristor from 270 DC cycles; (b) Hamming weight of Bi2O2Se-based digital TRNG from nine digital keys, and each key contains 30 bits; (c) intra-Hamming distance (HD) of those digital keys; (d) illustration of TRNG-based Diffie–Hellman Key Exchange protocol, where Bob and Alice successfully realize key exchange through an insecure channel.

    Figure 5

    Figure 5. Machine learning analysis of the switching curves and RTN curves: (a1) cycle i of the switching curve of Bi2O2Se based memristor, where eight physical parameters are extracted for further LSTM-based ML analysis, including HRS current, current before set, set voltage, LRS current, reset voltage and current, voltage, and current after reset; (a2) demonstration of the LSTM cell, where the sigmoid and tanh stand for activation functions; (a3) cycle i+1 of the switching curve of Bi2O2Se-based memristor; the RTN signals in different VBG voltages as well as their prediction curves utilizing the LSTM-RNN: (b1) RTN0; (b2) RTN0.25; (b3) RTN0.5; (b4) RTN 0.75; (b5) RTN 1; (b6) RTN 1.5, the numbers after RTN stand for the absolute value of VBG, ranging from 0 V to −1.5 V; SHAP value of the LSTM model for visualizing the impacts of the switching parameters to the set voltage (where the set voltage is chosen as the output): (c) mean of the SHAP value(d) SHAP value, where red/blue color directions stand for the higher/lower magnitudes of the extracted parameters, where the SHAP stands for SHapley Additive exPlanations.

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  • Supporting Information

    Supporting Information


    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.2c01784.

    • Section I: calculation of effective RTN affected area; Section II: the calculation details of encryption and decryption of auditory signals; Section III: Hamming Weight and Hamming Distance; Section IV: an example of Bi2O2Se based TRNG for D-H key exchange protocol; Figure S1, switching performances of Bi2O2Se based memristor under different temperature, ranging from 320 to 380 K; Figure S2, box plot of VBG dependent RTN current, effective influenced area and power consumption of Bi2O2Se based memristor; Figure S3, the female of male voice signals in amplitude and frequency domain; Figure S4, the peripheral circuit design of Bi2O2Se-based TRNG in a bread board (PDF)


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