Security-enhanced watermark embedding and transmission based on synchronized chaotic semiconductor lasers

In this paper, we propose and numerically demonstrate a chaotic watermarking encryption and secure transmission scheme based on two synchronized response lasers (RLs) subject to identical injection from a driving laser (DL). In this proposed system, the chaotic signal from DL can be optimized after passing through a phase modulator and a dispersion component, then the chaotic signal with large bandwidth and low time delay signature is obtained. Simultaneously injecting this chaotic signal into two identical RLs, high-quality chaos synchronization between two RLs can be realized. Both synchronized chaotic signals are, respectively, divided into two parts. One is used to generate shared keys required by the watermarking encryption, and the other is used as chaotic carrier to realize the secure message transmission. After introducing the synchronized optical chaos into the watermarking encryption algorithm, the normalized correlation of the extracted watermark without long-distance transmission is 0.9554 and can still maintain above 0.9 over 200 km transmission fiber. The message transmission and watermark extraction have good robustness to the fiber parameter mismatches, and excellent performances can be maintained even within 20% mismatches range. In our method, synchronized high-quality optical chaotic signals from two RLs are used to watermark embedding and transmission, and double encryption can be realized, which can open a new path for future high-speed and security-enhanced watermark embedding and transmission.


Introduction
With the development of communication technology, telemedicine has become a common means of remote diagnosis and treatment, which can further alleviate the structural imbalance of medical resources. During the whole telemedicine process, the medical staff can diagnose, evaluate and treat patients through the telemedicine platform. Meanwhile, medical images, patients' electronic medical records (EMR) and other private information need to be transmitted at both ends through the public network, which can bear huge risks tampering and stealing these privacy information.
As a security verification mechanism, watermarking technology is widely used in data transmission and distribution to provide additional protection during the existing message transmission process. Most of previous works focus on watermark embedding in the transformation domain of the carrier image based on discrete cosine transform (DCT) [1], discrete Fourier transform (DFT) [2], or discrete wavelet transform (DWT) [3], which can make the image have enough robustness to attacks like rotation and cropping. And different transform technologies are combined to realize the imperceptibility of the carrier image [4][5][6][7][8][9][10][11][12].
The security of watermarking embedding and extraction is another important issue. During the watermarking encryption process, a chaos mapping is necessary to further improve the security of watermarking due to the ergodicity, sensitive dependence on initial conditions and parameters, and complex dynamic and deterministic behavior of chaos system. In 2018, Wang et al. [13] proposed a memristive chaotic system and introduced the output chaos to the watermark embedding process by using DWT. In the same year, Thakur et al. [14] realized watermark embedding by non-sub-sampled contourlet transform (NSCT), redundant discrete wavelet transform (RDWT) and singular value decomposition (SVD), and 2-D logistic mapping based chaotic encryption is applied in carrier image. In 2020, Alshoura et al. [15] raised a new chaotic image watermarking scheme based on SVD and Integer wavelet transform (IWT) with logistic and sine maps. However, abovementioned methods need to exchange the key parameters of the chaotic map at both transmission terminals, which will undoubtedly increase the risks of the system. Moreover, compared with chaotic mapping, chaos generated by semiconductor laser subject to external perturbations has unique advantages including high complexity and large bandwidth. Therefore, the application of chaotic system based on semiconductor laser in digital watermarking algorithm has become a challenging topic.
In this paper, the bandwidth and time delay signatures of the chaotic output from the driving laser with optical feedback can be optimized using a phase modulator (PM) and a dispersion component (De), and then the chaos signal is simultaneously injected into two identical response lasers (RLs). Under suitable injection parameters, two synchronized chaos outputs can be obtained, which are used to generate the key parameters of the watermarking algorithm and as the chaotic carrier of message transmission. Consequently, chaotic watermarking embedding and transmission based on double encryption technology is realized. Moreover, the influence of transmission length and the mismatches of fiber parameters on the watermarking transmission and extraction was further investigated. Also, the security of the proposed watermarking embedding and transmission scheme is preliminarily discussed. In the proposed scheme, two synchronized high-quality optical chaotic outputs from RLs are used to image scrambling to realize secure watermark embedding. Also, the synchronized chaotic signals are used as chaos carrier in the watermark transmission, which is actually the chaotic secure communication and can guarantee the security of messages transmission [16,17]. Consequently, this system gives a double encryption guarantee for watermark embedding and transmission. Additionally, compared with chaos generated by electrical method or mathematic algorithm, optical chaos from SL subject to external perturbation possesses broad bandwidth and better randomness. After passing through PM and De, the chaotic signals from two RLs are further optimized, and excellent chaotic signals with over 39.6 GHz bandwidth and below 0.05 time delay signature (TDS) are achieved. Therefore, this proposed scheme can provide a new method for constructing future highspeed security-enhanced watermark embedding and transmission system.
The other Sections of this paper are organized as follows. In Sect. 2, the descriptions for the principle and theoretical model of the proposed watermark embedding and transmission system. Section 3 gives chaos and chaos synchronization characteristics of driving laser and two response lasers, and demonstrates the watermark embedding, transmission and extraction. Moreover, the influence of parameter mismatches on image transmission performance and security evaluation of this system are presented. Finally, we briefly summarizes this paper in Sect. 4.
2 Theoretical model Figure 1 shows the system configuration for securityenhanced watermark embedding and transmission based on two synchronized optical chaos from semiconductor laser. A DL is routed into chaos under suitable optical feedback. Then the chaotic output from the DL is divided into two beams after passing through a PM and a De. One is injected into response laser 1 (RL1) through fiber link 1 (F1), and the other is injected into response laser 2 (RL2) through fiber link 2 (F2). Under appropriate injection parameters, RL1 and RL2 can achieve excellent chaotic signals with low TDS and broad bandwidth, and high-quality chaos synchronization can be realized [18]. Based on chaos synchronization between two RLs, security-enhanced watermark embedding and transmission can be achieved due to physically enhanced security of SLsbased chaos secure communication scheme [19,20]. In the process of watermark encryption, the synchronized chaos signals from two RLs are, respectively, used as key generators to control the watermark embedding process. During the message transmission, chaos masking (CM) [21] is used to hide image message with embedded watermark in the chaotic carrier of RL1, which is injected into a photodetector 1 (PD1) through fiber link F3. Meanwhile, one part of the chaotic output of RL2, as a reference signal, is sent into PD2 for decoding message. Then, message can be recovered by comparing the difference between two outputs of PD1 and PD2 and filtering high-frequency components with a low-pass filter. Finally, watermark can be extracted from the carrier image through the adopted watermarking extraction method. Additionally, the message transmission can be bidirectional between two RLs [20].

Watermarking encryption and extraction
In this section, the watermark embedding and extraction process will be introduced in detail. The original medical image (OMI, carrier image) is embedded with an electronic medical record (EMR, watermarking image) to produce the embedded image (EI). Here, the classical symbol image ''T'' is used to represent EMR, the size of OMI and EMR are, respectively, 256*256 and 32*32. The embedding process is shown below (Fig. 2): (a) The outputs of RLs are, respectively, sampled at equal step to obtain two sequences of the same length M. Then create two new binary sequences with M-1 length through comparing the value between two adjacent sampling points. If the sampling value is greater than that of the previous point, the point value in new sequence is set as 1. Otherwise, it is 0. Finally, convert these two binary sequences to two corresponding decimal sequences with a series of decimal numbers between 0 and 255. (b) The Arnold scrambling function is used to scramble the pixel points of the carrier image, and then embed the watermark into the scrambled image. The mathematical model of Arnold scramble is shown below: x n y n ! mod N ð Þ DF-delay fiber; OC-optic circulator; PC-polarization controller; PD-photodetector; EDFA-erbium-doped optical fiber amplifier and the inverse Arnold scramble is shown: where (x n ; y n Þ and ðx nþ1 ; y nþ1 ), respectively, represent the positions of pixels in the gray image before and after transformation, a and b are the scrambling parameters, n is the times of Arnold scrambling transformations, N is the length or width of the image, mod(N) represents modular operation. The values of the parameters a, b, n are randomly selected from two decimal sequences generated in step (a), and their positions in two decimal sequences are the same during the encryption and decryption process [12].
(c) By DWT, the scrambled medical image is decomposed into four parts: LL, LH, HL and HH. LL is a low-frequency sub-band, and HL, LH, HH are three high-frequency sub-bands. After performing DCT, the four sidebands are, respectively, transformed into LL1, LH1, HL1 and HH1, and then divided into four 8*8 blocks. (d) Pick the center point of each 8*8 block of LL1, LH1, HL1 and HH1, and replace the original value with the average of the four points around the selected point. Next, divide EMR into four pieces, and then select appropriate parameters to embed them into the 8*8 block of LL1, LH1, HL1 and HH1, respectively. (e) Perform inverse DCT (IDCT) and inverse DWT (IDWT) on the DCT coefficients embedded with EMR, and then an inverse Arnold scrambling is adopted to obtain the carrier image with embedded EMR image.
At the receiving end, an inverse process of watermark embedding is used to extract the complete watermark image.

Security-enhanced watermark transmission
In this section, chaotic output from RL1 is used as carrier to hide the medical image with embedded watermark, which can be decrypted by the reference signals from RL2 in the receiving end.
The modified Lang-Kobayashi equation is used to investigate the dynamic characteristics of DL and RLs by considering the feedback term and the injection term, and can be expressed as [22]: where the subscripts DL, RL1, and RL2 stand for driving laser, response laser 1, and response laser 2, respectively. E is the complex amplitude of the optical field and N represents the carrier number. a is the linewidth enhancement factor, G DL;RL1;RL2 is the gain coefficient, s p is the photon lifetime, k d is the feedback parameter for DL, r RL1;RL2 is the injection coefficient, s d is the feedback delay, x is the angular frequency, q is the electronic charge, I is the bias current, g is the differential gain coefficient, e is the gain saturation factor, N 0 is the transparent carrier number, b is the spontaneous emission rate, n presents the Gaussian white noise. The phase modulation is implemented by a typical LiNiO 3 phase modulator, which is mathematically described as: where the V p is the half-wave voltage of PM, the driving signal V key is mathematically described as V Key t ð Þ ¼ A 0 cosð2pf 0 tÞ, where A 0 stands for the amplitude and f 0 is the frequency. The dispersion component De is a dispersion media such as dispersive fiber and the corresponding transfer function in the frequency domain can be described as [23]: where L is the length of the dispersive fiber, b 2 ¼ ÀDek 2 =2pc is the group velocity dispersion, De is the dispersion coefficient, k is the wavelength of the chaotic carrier and c is the velocity of light in vacuum.
Applying the inverse Fourier transformation to Eq. (6), we can obtain the pulse response in the time domain: The signal propagation in optical fiber channel could be described by the following nonlinear Schrödinger equation [24]: where Eðz; TÞ presents the slowly varying amplitude of the optical field, z is the propagation length, a is the fiber loss constant, b 2 is the second-order dispersion coefficient, c is the nonlinear Kerr factor. The bandwidth and TDS characteristics of the DL and RLs outputs are, respectively, evaluated by calculating the effective bandwidth (EBW) and autocorrelation function (ACF). EBW is defined as the span between the DC and the frequency where 80% energy is contained in the RF spectrum [25]. The ACF is defined as [26]: where I t ð Þ ¼ EðtÞ j j 2 denotes the intensity, Dt denotes the time shift and hi stands for the time average. When i and j are identical, the peak value r locating at the feedback delay time in ACF is used to evaluate the matching degree between the time series and its timeshifted replica. When i and j represent different lasers, C corresponds to the cross-correlation function (CCF) and represents the synchronization quality between two chaotic signals.

Results and discussion
During the simulations, the fourth-order Runge-Kutta algorithm is adopted to solve the rate equations, and the split-step Fourier method is used to solve the nonlinear Schrödinger equation. For simplicity, all the typical intrinsic parameters of DL and RLs are assumed to be identical and set as [27]: 3.1 Generation of chaos signals with broad bandwidth and low TDS Figure 3 shows Moreover, there is no subsidiary peak in the ACF curves and TDS of two chaotic signals are suppressed to a very low level, which indicates that the complexity of chaos signals is greatly improved due to increasing difficulty to extract the external cavity characteristics in this proposed system [28]. The performance optimization of original chaos signals mainly originates from the combination of the spectrum expansion effect of PM and the phase-tointensity conversion of dispersion component [27]. Furthermore, the influence of injection intensity and frequency detuning on chaotic outputs from RLs is investigated, where only RL1 is considered due to the symmetric system structure and identical laser parameters. Figure 4 shows EBW and TDS of chaotic carrier from RL1 in the parameter space of k in and Dx. From  Fig. 4a, one can see that, r RL1 is maintained at a low level (below 0.05) within a relatively large area, which means r RL1 is effectively suppressed in these areas. Figure 4b shows the variations of EBW of chaos output in the parameter space of k in and Dx. Under our simulation conditions, the bandwidth of chaos carrier exhibits an increasing trend with the increase in the injection strength and frequency detuning due to the nonlinear effects. Combined Fig. 4a with (b), we can achieve synchronized high-quality chaotic signals with low TDS and broadband bandwidth for two RLs through adjusting the injection strength and detuning frequency, which can provide an excellent chaos resource for future security-enhanced highspeed chaos communication.

Chaos synchronization
In order to investigate the synchronization properties between arbitrary two chaotic signals from DL and two RLs, Fig. 5 displays the cross-correlation coefficients between arbitrary two chaotic signals when the system configuration is symmetric and the length of fiber link F 1 (or F 2 ) is 25 km. During the simulations, Fig. 3 Temporal waveform (first column), RF spectrum (second column), and ACF (third column) of the DL (first row) and RLs (second and third row) the parameters of F 1 (or F 2 ) are chosen as [29]: a ¼ 0:2 dB/km, b 2 ¼ À0:1ps 2 /km, c ¼ 1:5 W À1 /km. When the injection strength is 60 ns À1 , zero-lag highquality chaos synchronization between two RLs is achieved and the maximal C RL1;RL2 is almost 1 at Dt ¼ 0 while that between DL and arbitrary RLs is only about 0.1, as shown in Fig. 5(a1)-(a3). Figure 5(b1)-(b3) further shows the variation of the correlation coefficients with the injection strength from DL to two RLs. From these diagrams, one can see that, for relatively small injection strength, the same seed induces two RLs to output almost identical chaos signals due to nonlinear effect in lasers and highquality chaos synchronization between two RLs can be realized. Then the synchronization quality can be deteriorated due to complex dynamical outputs with increasing injection strength. Further increasing the injection strength, the influence of the injection light on the RLs gradually plays a determined role, thus CC RL1;RL2 gradually increase and finally reach about 1. For all simulated injection strength, the synchronization coefficient between DL and arbitrary RL is very low. Under this case, it is very difficult to recover the transmitted messages through directing stealing the signals from DL by illegal user, which can guarantee the security of information transmission between two RLs at a certain extent [18][19][20].

Watermark embedding, transmission and extraction
Based on high-quality chaos synchronization of two RLs, the message encryption is performed by adopting chaos modulation method, which can be mathematically described as E mm ðtÞ j j¼ E RL1 ðtÞ j j½1 þ M m mðtÞ, where E mm ðtÞ denotes the modulated carrier, mðtÞ is  The crosscorrelations between arbitrary two chaos outputs from DL and two RLs the original message, M m is the modulation depth and 0.05 is selected to guarantee that the message is well hidden in the chaotic carrier [30,31]. The message is recovered by the direct subtraction decoding which is where LPF means that the recovered message is filtered by a low-pass five-order Butterworth filter. The communication performance is quantified by calculating the Q-factor of recovered message, which is defined as: where hI 1 i and hI 0 i stand for the average power of bits ''1'' and ''0,'' respectively. r 1 and r 0 are the corresponding standard deviations. A Q-factor value greater than 6 corresponds to a satisfactory BER about 10 -9 [29].
In order to evaluate the communication performance under different transmission distances, pseudorandom message is transmitted and Q-factor evolution for recovered message as a function of the fiber channel length and transmission rate is shown in Fig. 6. From this diagram, one can see that, for a certain transmission rate, Q-factor of the decoded message remains relatively high for a certain fiber length, and then gradually decreases with further increasing transmission length. For a certain transmission length, with the increase in the transmission rate, Q-factor also shows a decreasing trend on a whole. With increasing the transmission length and rate, both chaotic carrier and messages can be distorted to a certain extent due to the dispersion and nonlinear effects in the optical fiber. Therefore, the synchronization performance is deteriorated and messages extraction become more difficult. It is worth noting that the calculation errors can exist due to the limited computing ability of our computer and random noise during our simulations, but the overall evolution trend of Q-factor with the transmission length and rate can help us to effectively understand this basic communication performance in this proposed system.
To explore the watermark embedding, transmission and extraction performances, we use a sample ''T'' as watermark image to represent EMR, which is embedded into an OMI and transmitted into a terminal through the proposed chaos secure communication system, then the embedded watermark can be extracted. Here, 10 Gbit/s image messages are transmitted. Normalized correlation coefficient (NC) and peak signal-to-noise ratio (PSNR) are used to evaluate the quality of EMR and carrier image, respectively, which are defined as: where l 1 and l 2 denote the mean values of I 1 and I 2 , respectively. When the original and extracted watermark image closely resembles one another, NC & 1.
In addition, when PSNR is over 30 dB, it is difficult to distinguish the carrier image with and without embedded watermark. Figure 7 presents the results of watermark embedding, secure transmission and extraction in detail after transmitting over 150 km fiber channel. From these diagrams, one can see that the watermark can be embedded in the original medical image and hidden based on chaotic encryption method, as shown in Fig. 7c, d. Then, the carrier image can be successfully decrypted after transmitting over 150 km fiber channel, as shown in Fig. 7e, and PSNR can be maintained over 30 dB, which means that almost no information lost during the transmission. Moreover, Fig. 7f shows the extracted watermark, and NC between original and extracted watermark is 0.9554, which denotes the successful watermark embedding and extraction based on the synchronized chaos system. Further simulations For investigating the secure message transmission performance in detail, Fig. 8 shows the transmission results of encoded image for the case in Fig. 7, here only part of encoded messages are displayed. From these diagrams, one can see that the encoded messages can effectively hidden in chaotic carrier, as shown in Fig. 8b. After transmitting over 150 km fiber, the messages can be successfully recovered with some distortions and the corresponding eye diagram is wideopen and clear, as shown in Fig. 8c, d, which means the Q-factor of decoded messages is higher than the conventional communication requirement with Q-fac-torP6 [32,33]. These results means that the proposed system can realize secure message transmission. Figure 9 further shows the variations of the PSNR of medical images and NC value of EMR under different transmission lengths. From these diagrams, one can see that PSNR is almost over 40 dB after transmitting over 200 km fiber channel, then gradually decreases with increasing the transmission length, but maintains over 30 dB even for 300 km transmission length. Similarly, NC value of EMR first maintains at a relative high level and then gradually decreases with increasing the transmission length. These phenomena can be explained as that, the dispersion, nonlinear effects and noise in the long-distance fiber will distort the transmitted information, then the chaotic carrier cannot be completely removed in the decryption process. Therefore, with the increase in transmission length, the degree of signal distortion gradually increases. After exceeding a certain long transmission distance, EMR cannot be effectively extracted from the carrier image although some information can be still obtained from the image.

Parameter mismatch robustness of the transmitted images
It is well known that, in chaos synchronization system, the decoding quality is partly determined by the residual chaotic carrier, which also affects the performance of extracted watermark image. Normally, as for messages transmission and decoding in this proposed system, if F 3 owns the same characteristics as that of DF, the chaotic carrier can be completely eliminated during the process of message decoding. However, the parameters mismatch between F 3 and DF may exist in reality. Thus, it is necessary to analyze the impact of mismatched fiber parameters including chromatic dispersion, power attenuation, fiber nonlinear effect, and fiber length. Here, for simplicity, we fix the parameters of F 3 and, respectively, adjust one of these typical parameters such as b 2 ; a; c and the length of DF. The relative parameter mismatches could be defined similar as Figure 10 displays the NC and PSNR evolutions for 10 Gb/s message as a function of Da, Db 2 , Dc and DL d . One can observe that the PSNR and NC have similar evolution trend and relatively good robustness to the fiber parameter mismatches with ± 20%.
Compared with other parameters, the negative Da mismatch has greater effect on PSNR and NC. It should be noted that multiple parameter mismatches will coexist in real scenarios, which can induce more complex dynamical evolution of this proposed system and image transmission process will become more complex.

Security analysis of watermark embedding and extraction
A. Key space When the key space is larger than 2 100 , the proposed watermark embedding scheme is enough secure to resist the brute force attack [34,35]. The total key space includes the embedding position and the used  Fig. 9 The variations of the PSNR value of medical images with embedded EMR and the NC value of EMR with the transmission length chaotic sequence. Especially, the chaotic sequence generated from the disturbed semiconductor laser has highly randomness and is used to control the Arnold scrambling and hide the carrier image with embedded watermark, which can greatly extend the key space. Therefore, the system security can be effectively guaranteed even for some brute force attacks.

B. Key sensitivity
In order to evaluate the key sensitivity in our watermark embedding and extracting scheme. Two binary sequence X 1 and X 2 are, respectively, used as secret key at the receiving end. These two sequences are the same and generated according to step (a) of watermark embedding process, but the value of first point in X 2 is artificially changed from 1 to 0. Figure 11 shows the watermark extraction results based on these two sequences. From these diagrams, one can see that, the watermark image can be successfully extracted by using the key X 1 , while the extraction with X 2 is failure, which means that the watermark embedding and extracting scheme is sensitive to the secret keys and a tiny change can induce the failed watermark extraction. Therefore, synchronized chaos sequence generation from two RLs is a key issue in our proposed system.

Security analysis of watermark transmission
Secure communication based on chaotic carrier generated by semiconductor laser has attracted wide attention due to its high security in hardware encryption. The security mainly depends on the difficulty of transmitter parameter identification and the sensitivity of synchronization quality to parameter mismatches. That is, the whole set of structural parameters and operational parameters play a key role during the communication between the transmitter and receiver. Usually, different attract scenarios can exist in the real communication [36,37]. In order to further embody the security of chaotic secure communication. Here, we take the most serious attract situation, in which the eavesdropper has stolen the structural parameters of legal users (RLs), and an illegal user (additional SL) can obtain the same parameters as RLs. Then the intercepted signal from the public channel is amplified and injected into SL to achieve chaotic Fig. 10 PSNR and NC as a function of the power attenuation, chromatic dispersion, nonlinear Kerr factor and length mismatch Fig. 11 The result of key sensitivity. a Original image with watermark. b Extracted watermark with X 1 . c Extracted watermark with X 2 synchronization through injection-locking effect for illegal message extraction. Figure 12 shows the decryption result under this type of illegal attack scenario, where Fig. 12a, b represents the original image and watermark, and Fig. 12c, d represents the extracted carrier image and watermark. Obviously, we cannot obtain any effective information about the carrier image and watermark. In our proposed scheme, watermark embedding and transmission critically depend on chaos synchronization performance between transmitter and receiver. However, it is very difficult to achieve high-quality chaos synchronization between watermark transmitter (legal user) and illegal user due to simultaneous amplification of chaos carrier, carrier image with watermark and noise during message transmission and extraction [38]. Consequently, illegal user cannot recover the carrier image and extract the embedded watermark. It should be noted that, parameter mismatches between RL and SL can further deteriorate the synchronization performance between watermark transmitter (legal user) and illegal user even if the injection-locking synchronization scheme is adopted by eavesdropper [39], which will induce the failure to extract the watermark.

Conclusion
Based on a chaotic synchronization system consisted of two RLs subject to identical chaotic optical injection, we propose and numerically investigate a chaotic watermarking encryption and transmission system. The simulated results show that, the chaotic signal with large bandwidth and low TDS is obtained after using a phase modulator and a dispersion component, and high-quality chaos synchronization is achieved between two RLs. Then, the EMR can be successfully embedded in OMI and securely transmitted over 200 km fiber channel, and the PSNR of carrier image is over 40 dB and the NC of EMR is maintained above 0.9 at the receiver end. In this proposed system, synchronized high-quality optical chaos generated by two RLs are used to watermark embedding and transmission and it is not necessary to share the secret key in the public channel. Therefore, the proposed double encryption method of watermark can more effectively guarantee the message security and realize high-speed and security-enhanced watermark embedding and transmission, which can effectively guarantee the security of privacy information of patients during the diagnosis and treatment process and provide a new message management pattern for future intelligent medical system.