佐藤 井一

Chaos-based secure communication provides a hardware-oriented approach to security by leveraging the extreme sensitivity and unpredictability of nonlinear dynamical systems. When the parameters of a chaotic oscillator are coupled to a physical device exhibiting state- and rate-dependent resistance, the resulting dynamics become increasingly difficult to model or replicate numerically. Among candidate devices, memristors display nonlinear, state- and rate-dependent resistance with current–voltage (I–V) hysteresis pinched at—and crossing—the origin, reflecting true resistive-memory behavior. In contrast, SiO ₂ nanofilms—fully CMOS-compatible and fabrication-stable—exhibit quasi-memristive resistive dynamics: their I–V loops resemble those of memristors but do not cross the origin, indicating the absence of genuine resistive memory [1,2]. Unlike a memristor, which maintains its resistance state when the voltage crosses the I–V origin, an SiO ₂ nanofilm reverts to its high-resistance state. In systems with frequently alternating input voltages, SiO ₂ nanofilms undergo resistance changes more often than true memristors, producing richer perturbations to the chaotic trajectory. These contrasting device behaviors raise the question: how do a standard memristive model and a memory-free SiO ₂ quasi-memristive model perform as physical keys in chaos-based secure communication? Hardware implementation of chaos introduces additional considerations. In analog chaotic communication, channel noise from imperfect transmission readily disrupts synchronization. Conversely, purely digital implementations eliminate subtle analog fluctuations—such as thermal noise—that can enhance the unpredictability of chaotic dynamics through sensitivity to initial conditions. Hybrid architectures, combining digitally generated chaotic dynamics with analog physical keys, offer a balance between communication robustness and physically induced deviations that continuously perturb the chaotic trajectory in unpredictable ways. In this work, we use system-level simulations to compare two physical-key models—an HP-type TiO ₂ memristor and a quasi-memristive SiO ₂ nanofilm—within hybrid chaos-based encryption systems. We first verify reliable decryption with each device and then evaluate their encryption performance. To evaluate synchronization and encryption performance, the hybrid chaos-based communication system was implemented in MATLAB/Simulink. The core chaotic dynamics were realized in discrete time, while the physical key was modeled as an analog nonlinear device. Two key models were examined: an HP-type memristor representing TiO ₂ devices [3], and a quasi-memristive SiO ₂ nanofilm derived from our experimental characterization [2]. Figure 1 illustrates a hybrid communication system incorporating an SiO ₂ nanofilm as the analog physical key. A digitally implemented Lorenz chaotic oscillator generates the carrier waveform, which is modulated by the input data (Fig. 1A) and transmitted to the receiver (Fig. 1B). Two receivers are considered: one using a resistor approximately matching the SiO ₂ nanofilm’s resistance, and one employing the SiO ₂ nanofilm model. Each time-domain waveform in Fig. 1A–D shows a short excerpt of the data stream. The right-hand panels display the corresponding I–V characteristics of the key elements. The resistor exhibits a linear response, whereas the SiO ₂ nanofilm produces a broad, dynamically varying quasi-memristive loop whose width and shape evolve with the broadband spectral components of the chaotic waveform. These resistance fluctuations continuously deflect the chaotic trajectory, making synchronization more difficult for a mismatched receiver. As a result, the resistor-based receiver fails to recover the meaningful data (Fig. 1C), while the SiO ₂ -keyed receiver achieves complete decoding with 100% bit matching (Fig. 1D). When the SiO ₂ nanofilm is replaced with an HP-type TiO ₂ memristor model, the matched receiver also achieves 100% bit matching, demonstrating that both devices can serve as effective keys within the hybrid architecture. To evaluate encryption performance, we analyzed information entropy, adjacent-pixel correlation, the χ ² test of histogram uniformity, the number of pixel change rate (NPCR), and the unified average changing intensity (UACI). Even without a physical key, the Lorenz-based chaotic system already exhibits high performance in these metrics. Integrating the HP-type memristor produced negligible changes, confirming that its inclusion does not degrade cryptographic performance. Incorporating the SiO ₂ nanofilm preserved this high performance while slightly increasing information entropy toward the ideal randomness value and reducing the χ ² statistic, indicating enhanced resistance to histogram-based statistical attacks. These results provide a unified view of how true and quasi-memristive behaviors influence chaos-based hardware security and clarify the distinct roles each device can play in physical-key cryptographic systems. [1] T. Suzuki, K. Ando, T. Ichinohe, S. Sato, ECS Meet. Abstr . MA2024-02 , 4650 (2024). [2] S. Sato, K. Ando, T. Suzuki, R. Eguchi, T. Ichinohe, Jpn. J. Appl. Phys . 64 , 10SP02 (2025). [3] A. G. Alharbi, M. H. Chowdhury, Memristor Emulator Circuits (Springer, 2020). Figure 1 <p></p>

Chaos-based secure communication leverages the intrinsic sensitivity to initial conditions and the inherent unpredictability of chaotic dynamics, and its security can be further enhanced by incorporating a physical key into the system. Memristive devices have been explored as such hardware keys; however, their limited fabrication reproducibility has hindered their practical implementation. Recently, we experimentally demonstrated that SiO ₂ nanofilms exhibit a superficially memristor-like dynamic resistive behavior, and our numerical analysis further suggested that this property could serve as an effective physical key in chaotic encryption schemes [1,2]. Subsequent analyses, however, revealed a weakness: the analog implementation of the communication scheme suffered from insufficient tolerance to transmission noise. In this work, we first characterize the experimentally observed electrical response of SiO ₂ nanofilms and discuss possible mechanisms underlying their dynamic resistive behavior. We then introduce a digital chaos-based communication framework designed to improve noise robustness, in which the experimentally derived SiO ₂ nanofilm model is incorporated as a physical key. The performance of this hybrid system is evaluated through numerical simulations, including image encryption tests using standard security metrics. SiO ₂ nanofilms with thicknesses ranging from 4–50 nm were fabricated by thermal oxidation of low-resistivity n-type silicon substrates. Although nominally identical oxidation conditions were used, slight thickness variations were present; actual oxide thicknesses were confirmed via X-ray photoelectron spectroscopy, with depth profiling performed as needed. For electrical characterization, a gold top electrode was deposited on each nanofilm via magnetron sputtering. Gold wires were then attached to the top electrode and to the side of the substrate using silver or carbon paste to form reliable electrical contacts. The diameter of the top electrode was 6 mm. The digital chaos-based communication system, incorporating the experimentally derived SiO ₂ nanofilm model, was designed and numerically evaluated in MATLAB/Simulink. This framework allowed the analog dynamic-resistance behavior of the nanofilm to be embedded into a fully digital encryption scheme and assessed through system-level simulations. Under sinusoidal voltage excitation, SiO ₂ nanofilms with thicknesses of 5–20 nm exhibited pinched hysteresis loops in their current–voltage (I–V) characteristics. Although the overall shape resembled a memristive response, the curves did not cross the origin, indicating behavior distinct from standard memristor models. The hysteresis window narrowed with increasing frequency. These features were reproduced well by an equivalent circuit consisting of a series resistance–capacitance pair together with a diode-like nonlinear element. While the capacitance matched a parallel-plate model using the dielectric constant of bulk SiO ₂ , the effective resistance was far lower than expected from bulk resistivity, suggesting additional, non-bulk conduction pathways. Three possible conduction mechanisms may contribute to this behavior: (i) carrier trapping and delayed release at interface states, (ii) field-assisted migration of metallic species, and (iii) direct carrier transport through partially conductive paths formed by electrical stressing [3]. To evaluate the potential impact of the experimentally obtained SiO ₂ nanofilm characteristics on digital chaos-based secure communication, we incorporated the nanofilm’s equivalent-circuit model into a digitally realized Lorenz oscillator. In this configuration, the Rayleigh number of the Lorenz system was modulated by the SiO ₂ nanofilm, which served as a shared physical key between the transmitter and receiver; thus, correct decryption was achieved only when identical nanofilm characteristics were used on both sides. Reliable synchronization and perfect recovery of the transmitted bitstream (100% bit matching) were achieved when the update timestep of the digital chaotic oscillator was set to less than approximately 1% of the duration of a single input bit. To further assess encryption performance, bitmap images were encrypted and decrypted using systems with and without the SiO ₂ nanofilm model. Five standard image-security metrics were examined: information entropy, adjacent-pixel correlation, χ ² test of histogram uniformity, number of pixel change rate (NPCR), and unified average changing intensity (UACI). Among these metrics, incorporation of the nanofilm brought the information entropy closer to the ideal value and produced a clear improvement in the χ ² statistic, demonstrating enhanced robustness against histogram-based statistical attacks. Adjacent-pixel correlations, NPCR, and UACI were already effectively at their ideal values to within practical numerical precision in the Lorenz-based scheme, and the incorporation of the nanofilm introduced only negligible upward or downward shifts—importantly without any perceptible degradation. Additional results, including encrypted image examples and numerical values, as well as simulations using discrete chaotic maps such as the Hénon map, will be presented at the conference. [1] T. Suzuki et al., ECS Meet. Abstr . MA2024-02 , 4650 (2024). [2] S. Sato et al., Jpn. J. Appl. Phys . 64 , 10SP02 (2025). [3] H. Watanabe et al., J. Appl. Phys. 85 , 6704 (1999).

Abstract This study examined the potential of silicon dioxide (SiO₂) nanofilms as dynamic resistive elements in secure chaos-based communication. The nanofilms exhibited a pinched hysteresis in their current–voltage (I–V) characteristics, reminiscent of their memristive behavior. To describe this response, we implemented an equivalent circuit model incorporating a resistor–capacitor element and antiparallel diodes in MATLAB/Simulink and LTspice. We observed qualitative agreement with the experimental data. These nanofilms were then integrated into a Lorenz-based chaotic circuit to evaluate their feasibility as symmetric keys for secure communication. The simulation results confirmed that only the receivers equipped with identical SiO₂ nanofilms successfully decoded the transmitted signal, demonstrating the potential of this approach for secure wired communication.