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Abstract
In this paper, a low-complexity two-level chaotic encryption scheme is introduced and experimentally demonstrated to improve the physical layer security of a 450-nm laser underwater optical wireless communication (UOWC) system using discrete Fourier transform spread discrete multi-tone (DFT-S DMT) modulation. In the first encryption stage, the original bit stream is encrypted with a chaotic sequence based on a one-dimensional Logistic map. In the second encryption stage, the real and imaginary components of the DFT-S symbols are further encrypted with a pair of separate chaotic sequences, which are generated from a two-dimensional Logistic iterative chaotic map with infinite collapse (2D-LICM). The experimental results indicate that the encryption operation has no negative effect on the performance of the proposed UOWC system. For chaotic encryption, the DFT-S DMT gives a better performance than the DMT scheme under different water turbidities. 55-m/4.5-Gbps and 50-m/5-Gbps underwater transmissions are successfully demonstrated by the chaotic encrypted DFT-S DMT scheme. To the best of our knowledge, this is the first time to verify the feasibility of chaotic encryption in a high-speed UOWC system.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As the human activities in underwater environments, such as marine safety, scientific research, and marine military have increased, the demand for a secure, reliable, high-speed, and long-distance underwater wireless communication is urgently required. The most widely applied traditional underwater acoustic communication suffers from low bandwidth, severe multi-path fading, and large time latency, while the radio frequency (RF) communication suffers from severe attenuation in seawater, resulting in a limited transmission distance [1,2]. Underwater optical wireless communication (UOWC) featuring high bandwidth, low latency, and low power consumption is an attractive technology as a complement and even a competitive solution to enhance the capacity and connectivity of acoustic communication and RF communication based underwater wireless networks [3,4]. In the past years, UOWC systems using blue or green light sources, such as light emitting diodes (LEDs) and laser diodes (LDs), have been pursued by researchers [5–18] with a higher capacity and longer transmission span. Among these reported results, Chi et al. reported a 15.17-Gbps bit-loading discrete multi-tone (DMT) transmission through a 1.2-m underwater channel based on a self-designed common-anode GaN-based five-primary-color LED (RGBYC LED) [6]. Featuring much larger bandwidths compared with LEDs, LDs are able to support higher data rates as well as longer transmission ranges. Lin et al. demonstrated a 5-m/14.8-Gbps 16-quadrature amplitude modulation orthogonal frequency division multiplexing (16-QAM-OFDM) UOWC system [8]. The net data rate of 18.09 Gbps over a 5-m water channel with a single LD employing probabilistic shaping (PS) to approach the underwater channel Shannon capacity limit was experimentally demonstrated in [10]. Xu et al. experimentally achieved a 56-m/3.31-Gbps UOWC system employing Nyquist single carrier frequency domain equalization with noise prediction [11]. Recently, a 100-m UOWC transmission system with an attenuation length of 24 using optical combination and arrayed sensitive receivers was experimentally achieved in [12]. A 500-Mbps non-return-to-zero on-off keying (NRZ-OOK) UOWC system with the transmission distance up to 100 m was also reported [13]. In order to reduce the alignment difficulty, a wide-beam LD is widely applied in UOWC, as demonstrated in [14]. However, due to the open characteristic of underwater channel, as well as gradual diffusion of the beam propagation in long distance, the transmission link of UOWC is susceptible to malicious attacks and the security of UOWC turns into a critical and inevitable issue in practical applications [15–17], especially in underwater multiple user application [18]. Notably, the security vulnerability of UOWC was firstly revealed in [16], in which the authors numerically investigated the security weaknesses of UOWC using Monte Carlo simulation and experimentally demonstrated a 2.5-Gbps OFDM based UOWC system with potential eavesdropping, confirming that UOWC might suffer from serious security threat due to the scattering effect. Furthermore, the authors in [17] proved that a message communication in UOWC system could be eavesdropped without a sender’s or addressee’s awareness by using a diffraction grating, and evaluated how far from the addressee the message can be eavesdropped. Nevertheless, an effective solution to the security of UOWC was not involved in [16,17].
At present, the most probed security strategies are implemented in the application and media access layers, mainly using authentication and access control methods [19]. However, the header information and the control data of the encrypted signal transmitted transparently in the physical layer are not protected, which provides the adversary with opportunities to break the encryption at the physical layer [20]. Different from the upper layer encryption, the physical layer encryption (PLE) is operated at the bottom of the entire Open System Interconnection (OSI) model, and is performed only through digital signal processing (DSP), for instance, bit scrambling, constellation rotation, symbol scrambling, and sub-carrier scrambling [21]. Therefore, the PLE scheme has the potential advantages, such as diversification of DSP implementation methods and effective protection of transmitted data, which is greatly suitable for UOWC systems. Owing to high initial condition sensitivity, chaos-based PLE schemes have attracted considerable attentions and have emerged as a promising solution to transmit data confidentially [19,20,22–25]. Among these schemes, the authors proposed matrix block optimization for peak-to-average-power ratio (PAPR) reduction and security improvement in an OFDM-PON by employing a 4D hyperchaotic system based on 2-dimensional logistic adjusted sine map (2D-LASM) [22]. An encryption OFDM-PON system employing selected mapping (SLM) to reduce PAPR was demonstrated in [23]. A high-security chaos encryption using feedforward neural network-based XOR operator with dynamic probability was carried out to improve the key space [24]. In [25], a secure and private non-orthogonal multiple access (NOMA) based visible light communication (VLC) employing a two-level chaotic encryption scheme was demonstrated. All the reported schemes in [19–25] implement DSP to encrypt transmitted symbols, and without the correct key, the original data cannot be recovered from the ciphertext for an eavesdropper. On this basis, the PLE scheme based on chaos can improve the security of data transmission, which is also meaningful to the UOWC systems. However, a scheme of such a mechanism for a high-speed and long-distance UOWC system has not been studied yet.
In this paper, a low-complexity hybrid bit-level and subcarrier-level encryption scheme based on chaotic sequences is introduced and experimentally demonstrated in UOWC system using discrete Fourier transform spread (DFT-S DMT) modulation. DFT-S with low computational complexity can combat high frequency fading in a band-limited communication system, which can potentially improve the bit error rate (BER) performance in a long-reach UOWC system [26]. In the first stage, a chaotic sequence generated from a one-dimensional (1D) Logistic map is utilized to encrypt the original bit stream. In the second stage, in order to further enhance the security of the UOWC system, a pair of new chaotic sequences based on a two-dimensional Logistic iterative chaotic map with infinite collapse (2D-LICM), are correspondingly employed to encrypt the real and imaginary parts of the DFT-S symbols. As far as we know, this is the first time to demonstrate the feasibility of chaotic encryption in a high-speed UOWC system. Simulation analysis is carried out to show that the chaotic sequences are extraordinarily sensitive to initial states and have a good randomness. For chaotic encryption, the performance of the DFT-S DMT is superior to that of the DMT scheme under different water turbidities and the effectiveness of image encryption is also experimentally demonstrated. Furthermore, 55-m/4.5-Gbps and 50-m/5-Gbps underwater transmissions are successfully achieved by the chaotic encrypted DFT-S DMT scheme. With a tiny difference of 10−15 from the correct key, the transmitted data cannot be decrypted by an eavesdropper. The experimental results show that the encrypted operation has no effect on the performance of the proposed UOWC system and has good security.
2. Principles of chaos-based encryption system
2.1. Structure of the chaotic encryption scheme
The block diagram of the proposed chaotic encrypted DFT-S DMT system using two-level encryption operations is illustrated in Fig. 1. The original data (e.g., audio, image, and video source) is firstly converted into a bit stream and then the resulting bit stream is encrypted by a chaotic sequence based on a 1D Logistic map in the first stage. The Logistic map is defined as follows [27]:
where ${w_0} \in (0,\;1)$ is the initial value, $\beta \in (3.569945627,\;4]$ is the bifurcation control parameter, i denotes the i-th iteration, and ${w_i}$ stands for the output of the i-th iteration. A chaotic sequence ${{\textbf w}^{(0)}} = [{w_1},{w_2},\ldots ,{w_{{N_b}}}]$ is generated after ${N_b}$ iterations and its value is between 0 and 1, ${N_b}$ is the length of the bit sequence. To generate a chaotic integer sequence, a preprocessing is carried out:To further enhance the security of the transmitted system, a 2D-LICM map based on two chaotic maps, i.e., ${x_{n + 1}} = \alpha {x_n}(1\textrm{ - }{x_n})$ and ${x_{n + 1}} = \textrm{sin}(c/{x_n})$, is employed to generate a pair of new chaotic sequences in the second stage, which is defined as [28]:
Note that the chaotic integer sequence ${\textbf s}$ and the chaotic sequence matrixes c and d can be calculated offline and stored for lookup table in the practical implementation. Since 1D encryption process only introduces shift operations in the first stage and the 2D encryption process only simply multiplies +1 or -1 without any multiplications in the second stage, the proposed scheme can completely avoid any complex multiplications but only with some shift/addition/subtraction operations, which is beneficial for low-complexity hardware implementation.
2.2. Analysis of chaotic maps with chaotic sequence
To demonstrate a good security of the chaotic encryption system, the sensitivity to initial states and random characteristic are quantitatively analyzed. The bifurcation diagram of a 1D logistic map in the first stage is depicted in Fig. 2(a). It can be observed that the generated sequence $\{ w\}$ can get a sophisticated kinetic behavior and changes with $\beta$ dramatically. When $\beta$ falls into the domain of $3 < \beta \le 3.45$, sequence $\{ w\}$ has two values, which gets 50% opportunity to get the right value. When $\beta$ falls into the domain of $3.569945627 < \beta \le 4$, the behavior changing of $\{ w\}$ falls into chaos status. Due to the unpredictable nature of chaos, the Logistic map can iterate a unique sequence. Lyapunov exponents (LEs) and maximum Lyapunov exponent (MLE) are two significant indicators to assess the chaotic identity of a dynamic system [28]. Due to higher LEs and MLE among 2D-Logistic maps [28], a 2D-LICM map is employed in our second stage. Figure 2(b) depicts the attractors of a 2D-LICM map, which shows an unpredictable path of the chaotic sequences and randomness.
Fig. 2. (a) Bifurcation diagram of a 1D Logistic map; (b) Attractors of a 2D-LICM map; (c) Sensitivity of the generated sequence $\{ w\}$ to initial value ${w_0}$ (with a tiny difference of 10−15); (d) Sensitivity of the generated sequence $\{ w\}$ to initial parameter $\beta$ (with a tiny difference of 10−15).
The sensitivity of the chaotic system to initial values and parameters is the basis to the proposed scheme. For the sake of discussion, we only take the generated sequence $\{ w\}$ in the first stage as an example. As Fig. 2 (c) and (d) shows, with only a tiny difference of 10−15 for the initial value or parameter, the values of the chaotic sequences present different evolution with the change of iteration number, which illustrates that the chaotic system is highly sensitive to the initial state. The random characteristic of chaos sequence is also significant to ensure the security of the proposed system. Auto-correlation and cross-correlation functions are often utilized to verify the random characteristic of the chaotic sequence. The normalized auto-correlation functions ${R_{ac}}(\tau )$ and cross-correlation functions ${R_{cc}}(\tau )$ are respectively expressed as:
Fig. 3. Auto-correlation and cross-correlation of chaos sequence $\{ w\} $. (a) Auto-correlation ${R_{ac}}(\tau )$; (b) Cross-correlation ${R_{cc}}(\tau )$ for two slightly different initial values ${w_0} = 0.3$ and ${w_0} = 0.3 + {10^{ - 15}}$.
2.3. Analysis of chaotic maps with images
Image transmission is a typical application of data communication. Image encryption is a visualized way by transforming the original digital image into an unrecognizable and noise-like cipher-image. Only with the correct key, a cipher-image can be correctly decrypted. In the following, we will test the encryption scheme for image transmission to further show the random characteristic of the cryptosystem. A good encryption algorithm should have the ability to reduce the correlation between adjacent pixels. Mathematically, adjacent pixels correlation coefficient ${\rho _{uv}}$ can be calculated by [28]:
where u represents the pixel sequence of the image data, v is another pixel sequence, in which each pixel is the adjacent pixel of u along the horizontal, vertical or diagonal direction, $E[{\cdot} ]$ is the expectation operation, ${\mu _u}$, ${\mu _v}$ are the average values of u, v, and ${\sigma _u}$, ${\sigma _v}$ are the standard deviations of u, v, respectively. $|{{\rho_{uv}}} |\in [0,\;1]$ and a larger $|{{\rho_{uv}}} |$ value means a stronger correlation between two pixel sequences.The correlation pixels distributions of raccoon grayscale image in horizontal, vertical, and diagonal directions are shown in Fig. 4(a∼c), respectively. The plain image and encrypted image are also depicted in Fig. 4(d) as reference. The figures show that most of points are close to the diagonal line of axis in the three directions for the plain images, which means that strong correlation exists between adjacent pixels in a natural image, while the pixel points distribute uniformly on the whole space for the cipher image to achieve a high randomness. Table 1 shows quantitative ${\rho _{uv}}$ results for two kinds of images (e.g., raccoon grayscale image and fruit color image). Obviously, the correlation coefficient ${\rho _{uv}}$ in the plain image is much stronger than that in the cipher image, indicating that the proposed scheme can break adjacent pixels correlation dramatically, which is of extreme importance for the security of the cryptosystem.
Fig. 4. Correlation distributions of adjacent pixels and plain/encrypted grayscale images for raccoon. The first row represents the plain images and the second row represents the cipher images. (a) Horizontal direction. (b) Vertical direction. (c) Diagonal direction. (d1) Plain image. (d2) Encrypted image.
Table 1. Absolute values of the correlation coefficients for the plain and cipher images
2.4. Security analysis
A good encryption system should have a sufficiently large key space to have a high security. As depicted in Fig. 5, structure of the key for our proposed cryptosystem, which consists of six parts, can be expressed as $\{ \beta ,\;\alpha ,\;\kappa ,\;{w_0},\;{x_0},\;{y_0}\}$. If these variables are all MATLAB type “long”, according to IEEE floating point standard [30], the computational precision of the 64-bit double-precision number is approximately 10−15. Thus, the space of the key, including system parameters $\beta \textrm{ } \in (3.569945627,\;4]$, $\alpha \in (0.5,\;1.969)$, $\kappa \in (0.721,\;1.4)$, system initial values ${w_0} \in (0,\;1)$, and ${x_0},{y_0} \in (\textrm{ - }1,\;1)$, can be approximately calculated as $0.4301 \times {10^{15}} \times 1.469 \times {10^{15}} \times 0.6790 \times {10^{15}} \times 1 \times {10^{15}} \times {(2 \times {10^{15}})^2} \approx 1.7 \times {10^{90}}$. The key space comparisons of our proposed and other reported methods are exhibited in Table 2. Although the key space of our scheme is not the largest, our cryptosystem with lower computational complexity is more suitable for a power-sensitive UOWC system. Taking Tianhe-2 supercomputer computing speed of 3.386 TFlop/s as an example, it takes at least 1.59×1066 years to obtain the correct key of the cryptosystem, which provides enough security against brute-force attacks [31].
Table 2. Key space comparisons of the proposed system and other schemes
3. Experimental setup
Figure 6(a) illustrates the experimental setup of the proposed chaotic encrypted DFT-S DMT-based UOWC system. At the transmitter side, the encrypted DFT-S DMT signals are generated by the arbitrary waveform generator (AWG, Tektronix 7122C), the signal amplitude of which is adjusted by a 26 dB electrical amplifier (EA) and an adjustable electrical attenuator (ATT). The encrypted signals combined with a direct current (DC) bias at a current of 75 mA (with an output optical power of ∼16.18 mW) are injected to a 450-nm fiber-pigtailed single-mode LD (Thorlabs LP450-SF15), which is mounted on a TEC module (Thorlabs LDM9LP). To reflect the encrypted optical signals for different aquatic channel lengths (e.g., 5 m, 15 m,…, 65 m), a pair of mirrors are attached to the inner sides of a 5-m water tank, which is filled with more than 400 litres tap water. At the receiver side, the encrypted optical signals focused by a lens are fed into an avalanche photodiode module (Menlo Systems APD210, 3-dB bandwidth: 1 GHz) and recorded by a digital serial analyzer (DSA) (Tektronix, DSA72004C), and finally decrypted offline in MATLAB program. The photographs of the LD transmitter, a light propagation channel for 65-m UOWC, APD receiver, and the corresponding DSP are shown in the subplots of Fig. 6. The corresponding parameter settings of the UOWC system are listed in Table 3.
Fig. 6. (a) Experimental setup of the proposed chaotic encrypted DFT-S DMT-based UOWC system. (b) and (f) Sections of digital signal processing at the transmitter and receiver sides, respectively. (c) Transmitter side. (d) Light propagation in the water tank. (e) Receiver side. AWG: arbitrary waveform generator; EA: electrical amplifier; ATT: adjustable attenuator; LD: laser diode; TEC: thermo-electric cooler; M1(2): mirror 1(2); DSA: digital serial analyzer.
Table 3. Parameter settings in the UOWC experiment
4. Results and discussions
In order to find the optimal operating point for the proposed UOWC system, the RF power attenuation is optimized according to the average error vector magnitude (EVM) of the received signals. Figure 7(a) shows the corresponding EVM performance under a 5-m tap water channel. When the attenuation is 0 dB, the LD works in a nonlinear region and thus, the DMT and DFT-S DMT signals suffer from severe nonlinear distortion, resulting in large EVMs. As the signal amplitude decreases, the influence of nonlinear distortion decreases and the EVM performance improve. However, the EVM performance dramatically deteriorates due to the low signal-to-noise ratio (SNR) when the RF attenuation exceeds 3 dB. Clearly, the encrypted and unencrypted schemes in our experiment share the same optimal RF power attenuation of 3 dB to achieve optimum operating point. Afterwards, to demonstrate the achievable data rate of the proposed encrypted UOWC system, BER performance versus different data rates are experimentally investigated. The measured BERs of the transmitted signals received by legal or illegal users are depicted in Fig. 7(b). 7% hard-decision forward error correction (HD-FEC) limit of 3.8×10−3 is drawn by the dashed line as reference. The BER performances for both the encrypted and unencrypted schemes become worse as the data rate increases. For the same modulation (DMT or DFT-S DMT), the BERs of the encrypted schemes are basically the same as those of the unencrypted one, which implies that the encrypted operation has no negative effect on the performance of the proposed UOWC system. The encrypted DFT-S DMT can support a data rate of ∼5.4 Gbps at a BER limit of 3.8×10−3, indicating a capacity enhancement of ∼10.2% compared with the encrypted DMT scheme. However, for the encrypted schemes with wrong key (a tiny difference of 10−15 from the correct key), BERs of about 0.5 are observed, which verifies that the eavesdropper cannot extract any useful information from the transmitted signals. Thus, the proposed encryption scheme can transmit data securely in a high-speed UOWC system.
Fig. 7. (a) EVM versus RF attenuation with different modulation schemes. (b) BER versus data rate for legal and illegal transmissions. w/o: without encryption, w: with encryption. The curves labeled as “wrong key” are the results of an illegal communication.
The performance of the proposed system is also experimentally studied in different water turbidities, namely tap water, “clear ocean”, and “coastal ocean” [32]. Different water types are obtained by adding different doses of 1% diluted MaaloxR suspension, the corresponding attenuation coefficients “c” of tap water, “clear ocean” (dose: 4 ml), and “coastal ocean” (dose: 28 ml) are 0.062, 0.150, and 0.399, respectively. Figure 8 shows the BER performance as a function of received optical power (ROP) under different water types. Compared with encrypted DMT scheme, over 1.2 dB and 3.2 dB ROP sensitivity improvements can be achieved by the encrypted DFT-S DMT at a data rate of 4.5 Gbps and 5 Gbps, respectively, as shown in Fig. 8(a). With respect to the encrypted DMT, at the same BER, the encrypted DFT-S DMT scheme requires a lower ROP, which indicates that it can achieve a higher data rate or a longer distance. Note that the ROP sensitivity improvement at a data rate of 5.0 Gbps between the encrypted DFT-S DMT and DMT schemes is larger than that at a data rate of 4.5 Gbps, indicating the robustness of the encrypted DFT-S DMT scheme in a higher speed transmission. Figures 8(b) and (c) show the BER performance as a function of ROP at data rates of 4.5 Gbps and 5.0 Gbps in “clear ocean” and “coastal ocean” condition, respectively. It can be seen clearly that at the same BERs, the corresponding ROPs are almost the same for all transmission cases under three different water types. For chaotic encryption, the performance of the DFT-S DMT is always superior to that of the DMT scheme under different water turbidities, exhibiting the robustness of the proposed scheme. Note that due to the saturation effect of the detector, little BER variations are observed when ROP is larger than -8 dBm. The BERs of the encrypted system with the wrong key are approximately equal to the BER of random noise (i.e., BER of 0.5), which shows the great feasibility of the chaotic encryption system in different water environments.
Fig. 8. The measured BERs of received signals at data rates of 4.5 Gbps and 5.0 Gbps under different water types. (a) tap water; (b) “clear ocean”; (c) “coastal ocean”. w/o: without encryption, w: with encryption. The curves labeled as “wrong key” are the results of an illegal communication.
Since scattering and absorption increase with the transmission distance, it is imperative to investigate the performance of the proposed system in different water transmission distances. The ROPs under different water transmission distances are exhibited in Fig. 9. Meanwhile, the fitting curve using a first-order function is also presented. Absolute value of the slope for the fitting curve representing the water attenuation coefficient in the experiment is 0.35 dB/m. The relationship between BER performance and transmission distance is illustrated in Fig. 10. It is observable that the BERs of the encrypted schemes basically overlap with the schemes without encryption, which is consistent with previous results as shown in Fig. 7 and Fig. 8. Moreover, 55-m/4.5-Gbps and 50-m/5-Gbps data transmission are achieved by the proposed chaotic encrypted DFT-S DMT scheme. Note that the measured ROP at 50 m is about -6.67 dBm as shown in Fig. 9, which is much higher than the minimum ROP of -11.2 dBm at a data rate of 5.0 Gbps as shown in Fig. 8. Under the BER limit of 3.8×10−3, the achievable transmission distance of the UOWC cryptosystem is extended from 5 m (with DMT modulation) to 50 m (with DFT-S DMT modulation) at fixed data rate of 5 Gbps, which is mainly due to the fact that DFT-S DMT can combat high frequency fading in a band-limited communication system and potentially improve the performance of a long-distance UOWC system. The distance-data rate product of the proposed system reaches to 250 Gbps-m. Without the correct keys, no matter the encrypted DMT or DFT-S DMT schemes, the transmitted data cannot be decoded correctly for the enumerated transmission distances, which substantiates the validity of the proposed scheme in different water transmission distances.
Fig. 10. BER versus different transmission distances at a data rate of (a) 4.5 Gbps and (b) 5.0 Gbps.
Finally, the performance of image encryption in the proposed DFT-S DMT-based UOWC system is also investigated. The reconstructed 512×512 raccoon grayscale image and fruit color image with/without the correct key at different SNRs are shown in Fig. 11. At different SNRs, the reconstructed images for a legal receiver with the correct key, are clearly depicted in Fig. 11(a)-(c) and (e)-(g). With the decreases of SNR, the quality of the reconstructed image gradually becomes worse. On the contrary, as shown in Fig. 11(d) and (h) at a SNR of 21.3 dB and 21.6 dB, respectively, with only a tiny difference of 10−15 from the correct key, the transmitted images cannot be reconstructed in the proposed cryptosystem for an illegal receiver, which from an intuitive perspective, further indicates that the proposed encryption scheme can transmit data securely.
Fig. 11. Reconstructed images at the receiver side for the chaotic encrypted DFT-S DMT-based UOWC system with different SNRs. (a∼c) Reconstructed raccoon grayscale images with the correct key at a SNR of 21.3 dB, 16.3 dB, and 14.4 dB, respectively. (d) Reconstructed raccoon grayscale image with the wrong key at a SNR of 21.3 dB. (e∼g) Reconstructed fruit color images with the correct key at a SNR of 21.6 dB, 16.4 dB, and 14.0 dB, respectively. (h) Reconstructed fruit color image with the wrong key at a SNR of 21.6 dB.
5. Conclusion
In this paper, we have introduced and experimentally demonstrated a high-speed and long-distance DFT-S DMT-based UOWC system employing a hybrid bit-level and subcarrier-level chaotic encryption scheme for physical layer security enhancement. Simulation analysis has shown that the chaotic sequences have a good randomness and are extraordinarily sensitive to the initial states. The encryption operation has no negative effect on the performance of the proposed UOWC system. For chaotic encryption, the performance of the DFT-S DMT is always superior to that of the DMT scheme under different water turbidities, exhibiting the robustness of the DFT-S DMT scheme. 55-m/4.5-Gbps and 50-m/5-Gbps underwater transmissions have been successfully demonstrated by the proposed UOWC cryptosystem. With the wrong key (a tiny different of 10−15 from the correct key), the transmitted data cannot be decoded correctly by an eavesdropper, which verifies the feasibility of our method. The low-complexity encryption method is promising to secure data transmission in future high-speed UOWC systems.
Funding
National Key Research and Development Program of China (2018YFC1407503); National Natural Science Foundation of China (11621101, 62001415); Natural Science Foundation of Zhejiang Province (LQ21F050013); Ningbo Science and Technology Project (2018B10093); the funding of Ningbo Research Institute; Fundamental Research Funds for the Central Universities(Zhejiang University NGICS Platform).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. M. Stojanovic, “Recent advances in high-speed underwater acoustic communications,” IEEE J. Oceanic Eng. 21(2), 125–136 (1996). [CrossRef]
2. E. Jimenez, G. Quintana, P. Mena, P. Dorta, I. Perez-Alvarez, S. Zazo, M. Perez, and E. Quevedo, “Investigation on radio wave propagation in shallow seawater: Simulations and measurements,” in Proc. IEEE 3rd Underwater Commun. Netw. Conf. (UComms), Aug./Sep. 2016, 1–5.
3. J. Xu, “Underwater wireless optical communication: why, what, and how? [Invited],” Chin. Opt. Lett. 17(10), 100007 (2019). [CrossRef]
4. Z. Zeng, S. Fu, H. Zhang, Y. Dong, and J. Cheng, “A survey of underwater optical wireless communications,” IEEE Commun. Surv. Tut. 19(1), 204–238 (2017). [CrossRef]
5. P. Tian, X. Liu, S. Yi, Y. Huang, S. Zhang, X. Zhou, L. Hu, L. Zheng, and R. Liu, “High-speed underwater optical wireless communication using a blue GaN-based micro-LED,” Opt. Express 25(2), 1193–1201 (2017). [CrossRef]
6. Y. Zhou, X. Zhu, F. Hu, J. Shi, F. Wang, P. Zou, J. Liu, F. Jiang, and N. Chi, “Common-anode LED on a Si substrate for beyond 15 Gbit/s underwater visible light communication,” Photonics Res. 7(9), 1019–1029 (2019). [CrossRef]
7. W. Tsai, H. Lu, H. Wu, C. Wei, and Y. Huang, “A 30 Gb/s PAM4 underwater wireless laser transmission system with optical beam reducer/expander,” Sci. Rep. 9(1), 8605 (2019). [CrossRef]
8. Y. Huang, C. Tsai, Y. Chi, D. Huang, and G. Lin, “Filtered multicarrier OFDM encoding on blue laser diode for 14.8-Gbps seawater transmission,” J. Lightwave Technol. 36(9), 1739–1745 (2018). [CrossRef]
9. C. Fei, X. Hong, G. Zhang, J. Du, Y. Gong, J. Evans, and S. He, “16.6 Gbps data rate for underwater wireless optical transmission with single laser diode achieved with discrete multi-tone and post nonlinear equalization,” Opt. Express 26(26), 34060–34069 (2018). [CrossRef]
10. X. Hong, C. Fei, G. Zhang, J. Du, and S. He, “Discrete multi-tone transmission for underwater optical wireless communication system using probabilistic constellation shaping to approach channel capacity limit,” Opt. Lett. 44(3), 558–561 (2019). [CrossRef]
11. X. Chen, W. Lyu, Z. Zhang, J. Zhao, and J. Xu, “56-m/3.31-Gbps underwater wireless optical communication employing Nyquist single carrier frequency domain equalization with noise prediction,” Opt. Express 28(16), 23784–23795 (2020). [CrossRef]
12. M. Zhao, X. Li, X. Chen, Z. Tong, W. Lyu, Z. Zhang, and J. Xu, “Long-reach underwater wireless optical communication with relaxed link alignment enabled by optical combination and arrayed sensitive receivers,” Opt. Express 28(23), 34450–34460 (2020). [CrossRef]
13. J. Wang, C. Lu, S. Li, and Z. Xu, “100 m/500 Mbps underwater optical wireless communication using an NRZ-OOK modulated 520 nm laser diode,” Opt. Express 27(9), 12171–12181 (2019). [CrossRef]
14. X. Sun, M. Kong, O. Alkhazragi, K. Telegenov, M. Ouhssain, M. Sait, Y. Guo, B. H. Jones, J. S. Shamma, T. K. Ng, and B. S. Ooi, “Field demonstrations of wide-beam optical communications through water–air interface,” IEEE Access 8, 160480–160489 (2020). [CrossRef]
15. H. Li, Y. He, X. Cheng, H. Zhu, and L. Sun, “Security and privacy in localization for underwater sensor networks,” IEEE Commun. Mag. 53(11), 56–62 (2015). [CrossRef]
16. M. Kong, J. Wang, Y. Chen, T. Ali, R. Sarwar, Y. Qiu, S. Wang, J. Han, and J. Xu, “Security weaknesses of underwater wireless optical communication,” Opt. Express 25(18), 21509–21518 (2017). [CrossRef]
17. D. Shaboy, D. Ronckban, and A. Handelman, “Tapping underwater wireless optical communication in pure water and natural Dead-Sea ultra-high-salinity water by diffraction grating,” Opt. Express 26(23), 29700–29711 (2018). [CrossRef]
18. L. Zhang, Z. Wang, Z. Wei, C. Chen, G. Wei, H. Y. Fu, and Y. Dong, “Towards a 20 Gbps multi-user bubble turbulent NOMA UOWC system with green and blue polarization multiplexing,” Opt. Express 28(21), 31796–31807 (2020). [CrossRef]
19. H. Wei, C. Zhang, T. Wu, H. Huang, and K. Qiu, “Chaotic multilevel separated encryption for security enhancement of OFDM-PON,” IEEE Access 7, 124452–124460 (2019). [CrossRef]
20. C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018). [CrossRef]
21. J. Zhang, A. Marshall, R. Woods, and T. Q. Duong, “Design of an OFDM physical layer encryption scheme,” IEEE Trans. Veh. Technol. 66(3), 2114–2127 (2017). [CrossRef]
22. T. Wu, C. Zhang, H. Wei, and K. Qiu, “PAPR and security in OFDM-PON via optimum block dividing with dynamic key and 2D-LASM,” Opt. Express 27(20), 27946–27961 (2019). [CrossRef]
23. Y. Xiao, Z. Wang, J. Gao, R. Deng, Y. Liu, J. He, and L. Chen, “Time-frequency domain encryption with SLM scheme for physical-layer security in an OFDM-PON system,” J. Opt. Commun. Netw. 10(1), 46–51 (2018). [CrossRef]
24. S. Han, B. Liu, Y. Mao, J. Ren, X. Wu, X. Xu, L. Jiang, J. Zhang, and J. Zhao, “High-security multi-slot chaos encryption with dynamic probability for 16-CAP PON,” IEEE Photonics J. 12(3), 1–10 (2020). [CrossRef]
25. Y. B. Yang, C. Chen, W. Zhang, X. Deng, P. F. Du, H. L. Yang, W.-D. Zhong, and L. Y. Chen, “Secure and private NOMA VLC using OFDM with two-level chaotic encryption,” Opt. Express 26(26), 34031–34042 (2018). [CrossRef]
26. C. Fei, X. Hong, G. Zhang, J. Du, Y. Wang, and S. He, “Improving the performance of long reach UOWC with multiband DFT-Spread DMT,” IEEE Photonics Technol. Lett. 31(16), 1315–1318 (2019). [CrossRef]
27. L. Liu, S. Miao, H. Hu, and Y. Deng, “Pseudorandom bit generator based on non-stationary logistic maps,” IET Inf. Secur. 10(2), 87–94 (2016). [CrossRef]
28. C. Cao, K. Sun, and W. Liu, “A novel bit-level image encryption algorithms based 2D-LICM hyperchaotic map,” Signal Process. 143, 122–133 (2018). [CrossRef]
29. W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding-based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014). [CrossRef]
30. IEEE Standard for Binary Floating-Point Arithmetic, IEEE standard pp. 754–1985, Aug. 1985.
31. G. Álvarez and S. Li, “Some basic cryptographic requirements for chaos-based cryptosystems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 16(08), 2129–2151 (2006). [CrossRef]
32. F. Hanson and S. Radic, “High bandwidth underwater optical communication,” Appl. Opt. 47(2), 277–283 (2008). [CrossRef]
