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Abstract
In order to tackle the security and privacy problems in optical networks, a novel mesh-based optical security network exploiting double masking (DM) scheme for multipoint confidential communication is proposed and studied theoretically. For each node in the network, a pair of mutually asynchronous vertical-cavity surface-emitting lasers (VCSELs) are required as transceivers, and the delay fiber (DF) is used to set different time delays as network node markers. In this security network, the encryption of the message is implemented on the transmitter of the source node by using the DM scheme, and the encrypted message is transmitted to the receiver of the destination node through the optical network for decryption. Each network node can output its individual chaotic signals separately with different time delay markers. By regulating different internal parameter mismatches, the synchronization characteristics of transceivers in a security network are numerically analyzed by using the cross correlation coefficient. Simulation results show that the chaos synchronization between transceivers enjoys fantastic robustness to mismatched parameters. Meanwhile, the tolerance of the DM scheme to the inherent parameter mismatch is excellent, so it is suitable for constructing secure networks in optical networks. Besides, based on the high quality synchronization with a correlation coefficient of 0.983, the communication performances of the longest path channel are investigated for a given metropolitan area network scale. Two pieces of 10 Gb/s messages can be effectively concealed in the chaos and decoded gratifyingly behind 100 km transmission, and the system has reliable security to resist illegal attacks. Finally, the network performance simulation is conducted for diverse configurations of the mesh-based optical networks. All the results confirmed the chaotic encryption scheme provides a novel way for any two legitimate nodes to establish security keys in optical networks.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cryptographic technology relies on transforming the original client message into garbled message transmission and is one of the crucial means to preserve information security. Driven by the proliferation of massive data and the expansion of various multimedia services, as well as the increasingly sophisticated network architecture, the security threats faced by optical networks are also getting increasingly complex [1–3]. Due to inherent loopholes, optical networks are vulnerable to eavesdropping, tampering and multiple attacks. Therefore, making optical networks function in a secure way has become an extra-urgent research subject. In other words, the information is threatened on a global scale in today’s era. Thus the security of private information must be guaranteed [4–7]. With the deeper insight into the optical network security field in recent years, the attacks and eavesdropping of optical networks are thought to happen mainly at the physical layer [8]. Therefore, the defects in the physical layer deserve extensive attention. Owing to the chaotic signals indicating some incredible characteristics in related respects concerning cost, security, transmission rate, and transmission distance [9–15], using a chaos-based security scheme to encrypt messages at the physical layer is a desirable solution.
Recently, researchers present several physical-layer encryption techniques based on chaos for optical networks [16–22]. In the two-dimensional chaos permutation technique, a Logistic mapped permutation matrix is used to permute the sequence on frequency and time domain [16]. In chaotic quadrature amplitude modulation (QAM) encryption technique, generate a pair of key sequences by Logistic mapping, which are utilized to code the real and imaginary parts of QAM symbols, respectively [17,18]. In the chaotic constellation transformation encryption technique, scramble the modulated symbols by using an advanced cat map [19]. In the hybrid time–frequency domain encryption technique, the scheme generates phase rotation sequences for frequency domain encryption and indexes sequences for time domain interleaving by using the Lozi map and Logistic map, respectively [20]. In compressive sensing chaotic encryption scheme, the length of multimedia data is shortened by compression sensing technology, and then the shortened data is transmitted with chaotic encryption, where the pseudo-random numbers are generated by 2-dimensional logistic-sine-coupled map (2D-LSCM) [21]. In physical layer key distribution scheme based on chaotic encryption and signal synchronization, keys are embedded into the synchronous header sequence (SHS) and then encrypted utilizing DNA coding, where the chaotic sequences are generated by 1-D logical chaotic map [22]. However, most of the above reports utilize digital chaotic schemes to improve network security on the basis of existing networks, and the encryption method is relatively simple, which is not enough for higher security requirements.
Compared with traditional electrical chaotic [23,24], the optical chaos generated by semiconductor laser has advantages of low delay, large bandwidth, complex dynamic behavior and excellent security performance. Hence, optical chaos has been applied in many scientific disciplines: physical random bit generation (RBG) [25], reservoir computing (RC) [26], optical image encryption [27], liquid level sensor [28], and specifically in optical security communication [29–32]. In [33], chaotic synchronization based on semiconductor lasers is used for long-distance communication in a commercial fiber channel. Nevertheless, previous works concentrated mostly on the point to point communication. Until recent years, some research reports began to apply the chaos synchronization of lasers in multipoint-to-multipoint communication. In 2019, Li et al. reported a chaotic communication scheme for simultaneous bidirectional transmission based on ring networks [34]. Any two SLs on the ring network can realize chaotic synchronization. However, the specific transmission path is not deployed, which is easy to cause the communication messy of different SLs, and the chaotic encryption scheme is relatively simple with low security performance. In 2019, Zhang et al. theoretically and numerically investigated the chaos synchronization of intercoupling semiconductor lasers (SLs) network [35]. However, only the SLs of the same cluster in the network have the chaotic synchronization properties, and the SLs of the different clusters are not synchronized. Thus, chaotic communication is implemented only on a few SLs of identical clusters. In 2021, Liu et al. systematically demonstrated chaos synchronization in asymmetric coupling semiconductor lasers (ACSLs) networks [36]. However, when faced with other complex optical network topologies, how to effectively control and improve the stability of cluster synchronization is still a challenge to be solved. Hence, the synchronization property of optical chaos applied to optical networks is always highly expected to improve optical networking flexibility further. In addition, as far as the author knows, there is little attention to secure communication in optical networks based on optical chaos, and the correlated theoretical development is rarely reported in the literature.
In this paper, we proposed a novel optical security network system based on bidirectional chaotic communication to enhance the security of information transmission in optical network, which has not been previously fulfilled to the best of our knowledge. Here, we use a pair of mutually asynchronous vertical-cavity surface-emitting lasers (VCSELs) as transceivers. The external disturbances generated by the master lasers are injected into the slave lasers, which make the transceivers enter a chaotic state and increase the complexity of nonlinear dynamic behavior. The delay fiber (DF) is used to set different time delays as network node markers. Using the chaotic double masking (DM) scheme, the message encryption is implemented on the transmitter of the source node, and the encrypted message is transmitted to the receiver of the destination node through the optical network. Compared to the traditional one driving laser and two response lasers-based communication scheme, the DM scheme has two different chaotic masking signals that can suppress time-delay signature(TDS) to some certain degree, for this, Liu et al. have numerically analyzed the TDS of the DM scheme by employing the self-correlation function(SF) and permutation entropy(PE) [24], where for the mixed signal, the characteristic peak of SF is much smaller than the individual chaotic signal, and the lowest valley of PE is much bigger than the individual chaotic signal. These results have indicated the ability of DM scheme to suppress TDS, leading to a very difficult challenge for eavesdroppers to crack both two masking signals. Next, the high-quality chaotic synchronization of the transceiver is used to decrypt the message to complete the communication process. It is worth mentioning that the alterable length of DF is a critical factor to distinguish different network nodes. Furthermore, we investigate the communication quality and network performance of the security network.
The rest of this article is exhibited as follows. The network topology, chaotic system theory and model are presented in Section 2. In Section 3, dynamic analysis of the chaos of the security network transceiver is realized, and the effects of parameter mismatch on the synchronization performance of the transceiver are also studied. The simulation results of communication performance and network performance are presented. In Section 4, concise results are shown in detail and provide suggestions for future research on optical security networks.
2. System model and methods
2.1 Mesh network configuration
Our optical mesh network shown in Fig. 1 has n$\times$n transceivers, optical routers and a number of fibers connected with each other according to the mesh topology to form a communication system. The n$\times$n nodes are all labeled as ($x$, $y$), where the upper left corner of the network is defined as the network origin, represented by the coordinate (1,1). The right horizontal direction of the x-axis and the down direction of the y-axis are considered as the positive direction of the x-axis and the y-axis. In a mesh network, the transceivers connect to the optical routers through electronic/optical (E/O) and optical/electronic (O/E) interfaces. The E/O interface converts an electrical signal into an optical signal, and the O/E interface converts an optical signal into an electrical signal. To solve the lack of effective light buffering technology, we employ the optical circuit switching (OCS) mechanism in the optical mesh network, which fully utilizes the superiority of division of labor cooperation between the optical layer and electrical layer. Figure 2 outlines the communication protocol for the optical network topology based on the OCS mechanism. First, the source node sends a path-setup packet to the destination node, which contains the address of the target node and routing-related control signaling. The path-setup packets will be routed in the electrical control layer trace a path determined by the dimensional order routing algorithm proposed below. The destination node replies the acknowledge character (ACK) packet and sends it to return to the source node to trace the reverse path when it receives the path-setup packet. After receiving the reply, the source node confirms that the optical communication link has been established and has completed the relevant state configuration of the optical router in the path. The message begins to be transmitted in the optical path from the source node to the destination node. Finally, when the message transmission is completed, the source node sends the path-teardown packet to the destination node, and the reserved path is released. In this paper, the analysis model at the router level is on account of the dimensional order routing algorithm. Different from other routing algorithms, the path selection of the dimensional order routing algorithm is independent of the network state, only related to the address of the initial node and destination node. It is widely applied in deterministic routing. The specific process of the algorithm is that the encrypted message walks first in the X dimension until the X coordinate values of the current are equal to the X coordinate values of destination routers. Then the encrypted message walks along the Y dimension until the Y coordinate values of the current are equal to the Y coordinate values of destination routers. Finally, the encrypted message arrives at the destination node. Any network node uniquely determines a path.
Fig. 2. Communication protocol for optical network routing. The optical path is indicated by the dashed line, and the electronic path is indicated by the solid lines.
2.2 Message encryption and decryption system
The schematic diagram of message encryption and decryption process with the transceivers consisting of two groups of mutually asynchronous VCSELs is shown in Fig. 3. Among them, responding VCSEL($i$, $j$, $1$)(R-VCSEL($i$, $j$,1)) and responding VCSEL($i$, $j$,2)(R-VCSEL($i$, $j$,2)) jointly constitute the transceiver of node ($i$, $j$), and responding VCSEL($m$, $n$,1)(R-VCSEL($m$, $n$,1)) and responding VCSEL($m$, $n$,2)(R-VCSEL($m$, $n$,2)) jointly constitute the transceiver of node ($m$, $n$). Particular attention is paid that Node($i$, $j$) and Node($m$, $n$) are any two different nodes. From the left side of the schematic, driving VCSEL1(D-VCSEL1) is subjected to its own optical feedback and delayed positive optoelectronic feedback to enhance the complexity of its dynamics. R-VCSEL($i$, $j$,1) and R-VCSEL($m$, $n$,1) receive only optical injection by the D-VCSEL1, and no other external interference exists. The output from D-VCSEL1 is segmented into three portions by a beam splitter (BS). The first portion is detected by a photoelectric detector which converts an optical signal into an electrical current. After being amplified adequately by an amplifier, the current is fed back to the D-VCSEL1 to constitute a positive optoelectronic feedback circulation. The second part is fed back to the D-VCSEL1 via a mirror (M) to form a feedback loop. Through an optical isolator (OI) and a neutral density filter (NDF), the third part is transmitted to another BS. The OI and NDF are used to ensure unidirectional coupling and adjust injection strength, respectively. Then, two optical chaotic laser beams divided by BS are transmitted through fiber and coupled to R-VCSEL($i$, $j$,1) and R-VCSEL($m$, $n$,1), respectively. From the right side of the schematic, driving VCSEL2(D-VCSEL2) receives optical injection from injection VCSEL(I-VCSEL) and its own optical feedback that unidirectionally couples to R-VCSEL($i$, $j$,2) and R-VCSEL($m$, $n$,2). The right side has a transmission process roughly similar to the left side. Unlike R-VCSEL($i$, $j$,1) and R-VCSEL($m$, $n$,1), the outputs of R-VCSEL(i,j,2) and R-VCSEL($m$, $n$,2) require to be transmitted into the adders via the DF. The function of DF is twofold. Namely, 1) to distinguish different network nodes by setting up different time delays. The nodes with communication requirements achieve the communication process by adjusting the same time delay to avoid causing confusion in the communication process, and 2) DF is the second barrier to ensure communication security. Even if the reconstruction of the receiver is achieved by attacker. However, if the time delay cannot be obtained, the information cannot be effectively stolen. Therefore, By changing the length of DF, it can effectively avoid the attacker from obtaining the key time delay information of reconstructing the chaotic communication system, and then improve the security of communication. It is necessary for R-VCSEL($i$, $j$,1) and R-VCSEL($m$, $n$,1) to have similar inner parameters. Similarly, R-VCSEL($i$, $j$,2) and R-VCSEL($m$, $n$,2) also possess a matching inner. The laser outputs of R-VCSEL($i$, $j$,1) and R-VCSEL($m$, $n$,1) are mixed with the laser outputs of R-VCSEL($i$, $j$,2) and R-VCSEL($m$, $n$,2) transmitted through DF; thus, the output of each network node is equal.
Fig. 3. The schematic diagram of packet encryption and decryption system setup. The optical path is indicated by the dashed line, and the electronic path is indicated by the solid lines. I-VCSEL: injection VCSEL; D-VCSEL1, 2: driving VCSEL1, 2; R-VCSEL($i$, $j$, $p$) ($p$ = 1 or 2): responding VCSEL($i$, $j$, $p$), R-VCSEL($m$, $n$, $q$) ($q$ = 1 or 2): responding VCSEL($m$, $n$, $q$); ON: optical network; BS: beam splitter; DF: delay fiber; F: fiber; A: amplifier; M: mirror; PD: photoelectric detector; OI: optical isolator.
Chaotic masking (CM) encryption scheme can be used to model the communication process, which performs chaotic synchronization between network nodes and the process of encryption (or decryption) of a message. The BS splits the output of the transceiver at Node ($i$, $j$) into two arms. One beam is mixed with the message (m1) to form a transmitted signal, which is transmitted by fiber and sent over the optical network to the receiver at Node($m$, $n$) (The specific transmission process in an optical network has been described in detail above). The transmitted signal is compared to another beam of chaotic light without carrying the message to recover the inverse transmission message (m2). Node($m$, $n$) has modulation and demodulation processes similar to Node($i$, $j$), and the decrypted messages are M1 and M2, respectively.
For such a proposed system, in virtue of the spin-flip model (SFM) [30], the rate equations for I-VCSEL, D-VCSEL1, D-VCSEL2, R-VCSEL($i$, $j$, $p$)($p$=1 and 2) and R-VCSEL($m$, $n$, $q$)($q$=1 and 2) can be represented as:
Table 1. External parameters of VCSELs
3. Numerical simulation and discussion
The rate Eqs. (1) – (10) of VCSELs are numerically settled by adopting the fourth-order Runge-Kutta method. During the calculation, the physical meanings and specific parameters of all the internal parameters of VCSELs are provided in Table 2. Meanwhile, the central frequency of each VCSEL is fastened at 194 THz (the corresponding central wavelength is 1543 nm), and the external disturbance delay times are all installed to be 4 ns. The DF behind the outputs of R-VCSEL($i$, $j$,2) and R-VCSEL($m$, $n$,2) are set to be 2 ns and the others are taken as $\varDelta \omega _{oi}=\varDelta \omega _1=\varDelta \omega _2=3\times 10^9$ rad/s, $\delta _{1}=\delta _{2}=30$ $ns^{-1}$, $\xi =0.06$, $\eta =12$ $ns^{-1}$, $\eta _{1}=\eta _{2}=27.5$ $ns^{-1}$. On the basis of the above analysis, the numerical simulation results are depicted employing a pair of network nodes(Node(1,1) and Node(2,1))(In the following result analysis are all take examples as Node (1,1) and Node (2,1) if there is no special instruction).
Table 2. Internal parameters of VCSELs
3.1 Results of chaotic dynamics and chaotic synchronization
In Fig. 4, the output of time series, power spectrum, and phase in all the lasers are plotted. The consequence demonstrates that by controlling the parameters of the semiconductor laser and using different external perturbations to produce chaos with desired attributes. It is worth noting that a good correspondence between the output waveforms of R-VCSEL(1,1,1) and R-VCSEL(2,1,1) (R-VCSEL(1,1,2) and R-VCSEL(2,1,2)) are simple be recognized among the time series, power spectrum, and phase portraits. Therefore, R-VCSEL(1,1,1) and R-VCSEL(2,1,1) (R-VCSEL(1,1,2) and R-VCSEL(2,1,2)) are deemed to have similar nonlinear dynamics variation properties. It indicates that the corresponding VCSELs can realize ideal synchronization, which cast a crucial role in chaotic communication. The dynamic characteristics of the transceiver output at Node (1,1) and Node (2,1) are presented in Fig. 5, consisting of time series, power spectra, and phase portraits. Similar output characteristics also indicate good synchronization between network nodes.
Fig. 4. Time series (first row), power spectrum (second row), and phase portraits (third row) of D-VCSEL1, D-VCSEL2, R-VCSEL(1,1,1), R-VCSEL(2,1,1), R-VCSEL(1,1,2), R-VCSEL(2,1,2)(From left to right).
Fig. 5. (a) time series, (b) power spectra, and (c) phase portraits, where the first row is for the Node(1,1) and the second row is for the Node(2,1).
In order to further assess the chaos synchronization performance between network nodes, we state the functions accomplished by the cross-correlation function(CF) [30], which is a simple and powerful tool to extract dynamical features from the time series.
Fig. 6. The cross correlation coefficient between coupling relationship VCSELs or between network nodes, (a) D-VCSEL1 and R-VCSEL(1,1,1), (b) D-VCSEL2 and R-VCSEL(1,1,2), (c) R-VCSEL(1,1,1) and R-VCSEL(2,1,1), (d) Node(1,1) and Node(2,1), (e) D-VCSEL1 and R-VCSEL(2,1,1), (f) D-VCSEL2 and R-VCSEL(2,1,2), (g) R-VCSEL(1,1,2) and R-VCSEL(2,1,2).
Moreover, to further evaluate the complexity of chaotic signals, an important quantitative index, spectral entropy (SE), is also adopted, in which Shannon Entropy and Discrete Fourier Transform (DFT) are used to calculate the complexity. Therefore, SE can be defined as follows [37]: the time series $\{x(n), n=0,1,2\cdots,N-1\}$ are firstly removing its current part, and then take the DFT of the sequence $x(n)$. Next, the relative power spectral density of $x(n)$ is calculated as:
where $\sum _{k=0}^{\frac {N}{2}-1}P(k)=1$. Finally, the SE combining the concept of the Shannon Entropy can be defined as:Therefore, the SE is used to compare the nonlinear motion complexity of D-VCSEL1 using only optical feedback, only delayed positive optoelectronic feedback and both optical feedback and delayed positive optoelectronicfeedback sche mes. Under the given parameters, the values of SE are 0.6059, 0.0499, 0.616, respectively. The SE of using optical feedback and delayed positive optoelectronic feedback scheme is bigger than using only optical feedback scheme or using only delayed positive optoelectronic feedback scheme, which means using optical feedback and delayed positive optoelectronic feedback scheme has better complexity.
3.2 Influence of parameter mismatches
In the above analysis, we find that the high chaotic synchronization characteristic between network nodes is based on the identical parameters between corresponding VCSELs. However, it should be noted that parameter mismatch is almost unavoidable in virtual requirements. Therefore, we change the internal parameters of a VCSEL(R-VCSEL(2,1,1) or R-VCSEL(2,1,2)) on Node(2,1) while keeping the parameters of the other three VCSELs unchanged. $\gamma _n$, $\gamma _s$, $\gamma _a$ and $\gamma _p$ are taken as examples to acquaint their effects. It’s important to note that only change one of four internal parameters at a time. The relative parameter mismatches could be defined as [30]:
Fig. 7. Influence of the transceiver parameter mismatch between Node (1,1) and Node (2,1) on the quality of the synchronization, where (a) only changes the parameter of R-VCSEL(2,1,1), (b) only changes the parameter of R-VCSEL(2,1,2).
Fig. 8. Influence of $\gamma _n$ ((a1) and (b1)), $\gamma _s$ ((a2) and (b2)), $\gamma _a$ ((a3) and (b3)) and $\gamma _p$ ((a4) and (b4)) mismatch on the quality of the synchronization, where the black hollow circle is the Max-C between R-VCSEL(1,1,1) and R-VCSEL(2,1,1). The red star represents the Max-C of the transceiver between Node(1,1) and Node(2,1). The blue triangle represents the Max-C between R-VCSEL(1,1,2) and R-VCSEL(2,1,2). The first line only changes the parameter of R-VCSEL(1,1,2) and the second line only changes the parameter of R-VCSEL(2,1,2).
3.3 Message transmission and analysis
The communication performances of the optical security network are checked by exchanging messages between nodes. In the network constructed in Section 2, CM encryption scheme is used to encode the message. The modulation depth is set as 2%, which is sufficient to guarantee that the messages are perfectly concealed in the chaotic carriers. And two non return-to-zeros (NRZs) messages with 10 Gb/s are encrypted by Node(1,1) and Node(2,1). Other parameters of SMF are given in Table 3. Figure 9 reveals the original messages (blue), the recovered messages (red), the transmitted signals (green) and the eye diagrams (black) of the recovered messages, where (a) is for the transmission message1 from Node(1,1) to Node(2,1), (b) is for the transmission message2 from Node(2,1) to Node(1,1). Apparently, as shown in Fig. 9, although the messages are slightly distorted, the node can still successfully exchange messages with another node. In the communication system, eye diagrams are typically used as a way to quantify the quality of message transmission. From the fourth column, we can see two clear and open eye diagrams, which means messages can be successfully decoded on the transmission fiber optical link between the nodes.
Fig. 9. Original messages (blue), recovered messages (red), chaotic carrier (green) and eye diagrams (black) of the recovered messages, where (a) from Node(1,1) to Node(2,1) and (b) from Node(2,1) to Node(1,1).
Table 3. Parameters of SMF
However, in the process of information transmission, it is inevitable to be accompanied by fiber transmission losses. Transmission losses are generally determined by transmission distance. The longer the transmission distance, the greater the transmission loss. In this paper, there are several longest transmission paths in an optical mesh network. We mainly analyze the optical path between Node(1,1) and Node(n,n). Here, the configuration studied is a large metropolitan area network with a longest path of 100 km, and the longest transmission path of encrypted signals is shown in Fig. 1 as the solid green line. For the long-distance optical chaos communication, fiber link dispersion will cause the distortion of decoded message, which will have an extremely adverse effect on the communication performance of network nodes. Therefore, dispersion compensation is crucial. In this optical network, we use the dispersion compensation fiber (DCF) technology, a DCF link with negative dispersion is connected to SMF. The parameters of DCF are shown in Table 4. the original messages (blue), the recovered messages (red), The transmitted signals (green) and the eye diagrams (black) of the recovered messages are displayed in Fig. 10. From the diagram, the encrypted messages were recovered satisfactorily after transmission. And in the fourth column, we can see two clear and open eye diagrams, which means messages can be successfully decoded on the longest transmission fiber optical link. Meanwhile, it also means that encrypted messages can be transmitted satisfactorily between any two nodes in the network.
Fig. 10. Original messages (blue), recovered messages (red), chaotic carrier (green) and eye diagrams (black) of the recovered messages, where (a) from Node(1,1) to Node(n,n) and (b) from Node(n,n) to Node(1,1).
Table 4. Parameters of DCF
Furthermore, we also analyze the safety performance of the scheme. We assume that an illegal attacker obtains all the matching internal parameters of a key device by brute force disassembly and establishes a complete set of receiver. The external parameters are used as the security key for the scheme(The complete external parameter information is given in Table 1 in the manuscript). We assume that the variable size of illegal attackers exhaustive attack is $10^{-15}$, then our scheme can obtain a key space of ($10^{15})^{12}=10^{180}$, close to $2^{598}$. The key space is larger than $2^{100}$, which is sufficient to resist exhaustive attacks, so the system has reliable security. We randomly selected four external parameters to give a small change $(\varDelta =10^{-15})$. The Q factors, BERs and eye diagrams of the received messages by an illegal attacker are shown in Table 5 and Fig. 11.
We can observe that the Q factors of the recovered messages are less than 4.5 and the BERs are greater than $5\times 10^{-6}$ for an illegal attacker with the wrong key, far below the standard of communication $(BER\leq 10^{-9}$ and $Q\geq 6)$. Moreover, the quality of eye diagrams deteriorates seriously. Therefore, illegal attackers cannot properly steal the encrypted information.
Fig. 11. The eye diagrams of the received messages by an illegal attacker. (a)$\delta _1+\varDelta t$, (b)$\tau _{of1}+\varDelta t$, (c) $\eta +\varDelta t$, (d) $\tau _{of2}+\varDelta t$.
Table 5. The Q-Factors and BERs of the received messages by an illegal attacker
3.4 Network performance and analysis
Taking the 4$\times$4 network as an example, the network performance of a security mesh-based optical network is analyzed by using two vital indexes, end-to-end (ETE) delay and network throughput. The average of ETE delay refers to the time intervals between the source node generating the message and the destination node receiving the message. The throughput is the percentage of messages successfully received by the destination node in the transmission process. Each node generates messages individually and follows a negative exponential distribution in time intervals. The simulation results of ETE delay and throughput are shown in Fig. 12 and Fig. 13, where the optical packet size is 64 bits, 256 bits, 1024 bits and 4096 bits, respectively. It can be clearly seen from Fig. 12 and Fig. 13 that the increase of packet size can promote the network throughput and have better delay performance. When the offered load is small, the delay increases slowly with the increase of the offered load, but when the offered load increases to the saturation point, the ETE delay increases sharply. This is because the offered load is small, the data competition in the network is small, and no congestion occurs. In contrast, as the offered load increases, the network congestion problem is becoming increasingly serious, resulting in a substantial increase in ETE delay. When message transfers of different packet sizes reach saturation point, the offered loads are 0.02, 0.08, 0.14 and 0.18, respectively. It can be seen from Fig. 13, in the case of a small offered load, throughput increases with the increase of offered load, but after increasing to a certain value, it basically remains unchanged, which is due to an upper limit on the amount of data that the network can receive per unit time.
4. Conclusion
In conclusion, a novel optical security network based on bidirectional chaotic communication is proposed. The performances of this network have been investigated systematically. In our scheme, high quality chaos synchronization between transceivers of any two nodes is kept under suitable parameters. Chaotic signals with similar bandwidth-enhanced outputs are used as carrier signals for messages. Meanwhile, we also studied the parameter mismatch of the R-VCSELs and investigated the synchronization performance by introducing the CF. The result shows that the DM scheme could effectively improve the influence of the parameter mismatch synchronization performance. Therefore, it is more applicable used in the optical security network constructed by us. Furthermore, the communication performances of the network are investigated. Take a pair of nodes as an example, two 10 Gb/s messages are transmitted bidirectionally within 10 km, and the message can be restored successfully in the network. By adopting DCF dispersion compensation scheme, satisfying communication requirements can be achieved in a large metropolitan area network with the longest path of 100 km. Finally, we discussed the two vital indexes, ETE delay and network throughput, to evaluate the network performance and showed the variation trends of ETE delay and throughput under different configurations. This paper only studies the communication quality and network performance of optical mesh security networks. The future will focus on the security of other optical network topologies and adopt more effective schemes to improve the security of message transmission in the optical network.
Funding
Fundamental Research Funds for the Central Universities (XDJK2018B012); China Postdoctoral Science Foundation (2016M590875); Natural Science Foundation of Chongqing (2016jcyjA0581).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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