Bipartite Synchronization of Multi-Agent Systems With Signed Graph Under Deception Attacks and Application in Speech Communication

This paper addresses the bipartite synchronization of multi-agent systems with time-varying delays and signed graph under deception attacks, where the systems contain both the self-structure delayed term and the coupling delayed term. The deception attacks are assumed to be randomly launched at each impulse instant. By using the gauge transformation, Lyapunov function method, Halanay differential inequality and linear matrix inequality techniques, several sufficient conditions are newly established to guarantee the achievement of bipartite synchronization, in which some special cases of multi-agent systems without delay or deception attacks are further considered. Two numerical examples are provided to illustrate the effectiveness of the proposed results. Finally, a new multi-agent speech communication system is constructed based on the bipartite synchronization of the multi-agent systems, where two agents for point-to-point communication can generate synchronous chaotic encryption/decryption key streams. The experimental results show that the proposed multi-agent speech communication system has the advantages of high security against some classical attacks.


I. INTRODUCTION
A multi-agent system [1], [2] refers to a computing system composed of multiple agents interacting with each other in a certain environment, in which any agent can interact to complete more complex work. In recent years, multiagent systems have become a research hotspot in the field of control and artificial intelligence. The cooperative control of multi-agent systems is a hot research topic in the field of control. The cooperative control of multi-agent systems includes consensus control, rendezvous control, coalescence control, and formation control. The latter three can be regarded as the generalization and special cases of consensus control. The collaborative control of multi-agent systems has achieved extensive research results in the past The associate editor coordinating the review of this manuscript and approving it for publication was Yichuan Jiang . 20 years. For example, information flow and formation coordination control of vehicles [3], distributed vehicle coordination control with local information exchange [4], cooperative control of multi-agent systems and its application in unmanned vehicles [5].
In a multi-agent system, some agents track a given target or agent, which is called leader-following consistency phenomenon. The agent that plays a leading role in a multiagent system is called the leader, and the rest of the agents that need to follow the leader are called followers [6]. Leaderfollowing consistency means that the agents in the system communicate and coordinate with each other, so that the state values of all follower agents change with time, and finally track the state value of the leader agent. Leaderfollower consistency, on the one hand, it can simplify the design and implementation of the control system, on the other hand, it can further save energy and control costs.
While in the leaderless-following system, there must be information transmission and reception between each agent, and the consistency of the system depends on the interaction between all agents. That is, only through the joint action of all agents can all state variables of the system be consistent. The leaderless-following consistency has higher requirements on the design and imple-mentation of the control system, and the control cost is relatively large, but the control effect is more precise than the leader-following system.
Multiple agents need to transmit information through the network. The traditional network model is generally an undirected graph or a directed graph. A node of the network represents a single agent, and the edges with positive weights between nodes represent the communication between two agents. The above-mentioned network model is an unsigned network. However, with the further development of network research, we find that traditional unsigned networks cannot accurately describe some oppositional relationships in real society. For example, in the medical field, there is a relationship of promotion and antagonism between drugs, and in the field of society, there is a relationship of trust and distrust in the communication between people. Therefore, in the multiagent systems [7], [9], [30], [31], there will also be a certain cooperation and opposition between agents. In view of the above situation, the concept of signed graph is introduced [8], [9], where the weight of the edge in the signed graph is no longer limited to be positive, but can also be negative. An edge with a positive weight represents a cooperative relationship between the two agents, while an edge with a negative weight represents an antagonistic relationship. Therefore, the research on multi-agent systems is no longer limited to unsigned networks, but gradually extended to the signed network. Synchronization is considered to be one of the most important phenomena in complex dynamic network theory, and has important applications in a variety of physical, biological and technological systems [10]. Thus, the research on synchronization of signed network has attracted extensive attention of researchers. Altafni first put forward the concept of bipartite synchronization of signed networks, that is, the states of nodes would eventually converge to two parts with the same and opposite modulus [11], [12], where the consistency problem of signed network was transformed into a classical consistency problem only under the condition of balanced network structure. At present, there are many control methods to realize the bipartite synchronization of multi-agent systems with signed graph, such as state feedback control [13], sliding mode control [14], distributed control [15], intermittent control [16] and so on. Among them, there are many researches on pinning control, which sets key nodes and designs controllers to achieve control effect. In [17] and [18], the pinning control strategy is adopted to realize the bipartite synchronization of multiagent systems with signed graph. So far, based on different signed network models, some achievements have been made in the research of bipartite synchronization, including bipartite synchronization of Lur'e Networks [19] and bipartite synchronization for signed networks of harmonic oscillator systems [20]. Especially in [20], the communication delay of the network is considered and the convergence of the network is analyzed. In addition, Meng [21] studied the problem of bipartite containment tracking of signed networks, and Hu and Yu [22] adopted a time-delay control method to study the consensus problem of multi-agent systems in the cooperation-competition network with inherent nonlinear dynamics. In [23], Parastesh and Rajagopal et al. studied the synchronization of networks with linear diffusive coupling and proposed that the stability of the synchronous solution depends only on the average coupling and not on the instantaneous coupling. In [24], a modified signed-susceptibleinfectious-susceptible epide-miological model was proposed to study the dynamics of epidemic spreading on signed networks.
The multi-agent systems with signed graph will be affected by the delay. On the one hand, there is a time delay in the multiple agent itself, and the calculation of the devices in the system needs to consume a certain time. On the other hand, due to the limited transmission speed, transmission congestion and transmission delay are also normal phenomena, which will lead to divergence and oscillation, and the network system will be unstable, further reducing the performance of network information transmission. Bipartite synchronization of signed networks under transmission delay has recently attracted great interest in [25] and [26]. In [25], the problem of bipartite consensus was studied for multi-agent systems with antagonistic interactions and communication delays. In [26], the problem of exponential bipartite synchronization was studied for delayed signed networks with multi-links by aperiodically intermittent control. In addition to the impact of time delay, there are also security risks in the data transmission process, and the network control process is vulnerable to malicious attacks. As a way of network attack, deception attack will have a bad impact on the information interaction on the network. Deception attack means that correct information such as the output signal of the controller and the measurement signal of the sensor are tampered by the attacker and the wrong information is transmitted to the network. In response to the above phenomenon, people have studied the bipartite synchronization of multi-agent systems under the deception attacks. In [27], the samplingbased leaderless consensus problem for nonlinear multiagent systems under deception attacks is studied by using the decoupled method. In [28], based on impulse control, the secure synchronization of multi-agent systems under deception attack is studied. In [29], the fault-tolerant secure consensus tracking problem of nonlinear multi-agent systems with deception attacks and uncertain parameter delays is investigated under the impulse control framework. To the best of our knowledge, there have been few available results on bipartite synchronization of multi-agent systems with signed graph and deception attack considering both the self-structure delayed term and the coupling delayed term, which motivates the research in this paper.
Although there has been some progress in the application of bipartite synchronization of multi-agent systems, it is less VOLUME 11, 2023 reported in the field of secure communication. At the same time, chaotic signal is a natural cryptography signal because of its own pseudo-random characteristics. In this paper, we try to make use of the multi-agent system composed of nodes with chaotic dynamics to generate chaotic key streams, which can be applied in the speech communication based on its bipartite synchronization.
The contributions of this paper are summarized as follows.
• Firstly, the influence of self-structure delay, transmission delay and deception attack are simultaneously considered in the multi-agent systems with signed graph.
• Secondly, several sufficient conditions are newly established to guarantee the achievement of bipartite synchronization, in which some special cases of multi-agent systems without delay or deception attacks are further considered, by using the gauge transformation, Lyapunov function method, Halanay differential inequality and linear matrix inequality techniques.
• Thirdly, based on the bipartite synchronization results of multi-agent systems, a new chaotic multi-agent speech secure communication system is constructed to verify the feasibility of the proposed theoretical method.
The rest of the paper is arranged as follows. In Section II, some preparations are given and the bipartite synchronization problem of signed networks under self-delay, transmission delay and deception attacks is proposed. Section III proposes the sufficient conditions for the bipartite synchronization of the signed network and gives the relevant proof process. Section 4 further demonstrates the theoretical results through two numerical simulations. The fifth section is the specific application of the theoretical results of this paper. A new chaotic voice secure communication system is constructed to verify the feasibility of the proposed theoretical method. Finally, in Section VI, the relevant conclusions of this paper are given.
Notations:I N represents an N * N identity matrix, and 0 means zero matrix. λ min (A) and λ max (A) denote the minimum and maximum eigenvalues of matrix A, respectively. ⊗ represents the Kronecker product of the matrix. E {x} is the expectation of the random variable x. Pr ob {. . .} represents the probability of an event occurring. A > 0 means that matrix A is a positive definite matrix.

II. PRELIMINARIES AND PROBLEM FORMULATION A. SIGNED GRAPH THEORY
A signed graph consisting of N nodes can be represented by a triple combination G = {N , ε, A}, where N = {1, 2, . . . , N } is the node set, ε ⊆ N ×N is the edge set, and A = a ij N ×N denotes the adjacency matrix of signed graph. a ij = 0(i = j) ⇔ (i, j) ∈ ε, that is, there exists a directed edge from node j to node i. It is assumed that signed graph G doesn't contain any self-loop (a ii = 0, i ∈ N ). When G is a directed graph, a ij > 0 indicates that the relationship from node j to node i is cooperative, while a ij < 0 means that there is a competitive relationship from node j to node i [19], [20], [30].
The Laplacian matrix L = (l ij ) N ×N in signed graph G is given as follows:

Remark 1:
It is worth mentioning that the Laplacian matrix L associated with a signed graph G is not necessarily a zerorow sum matrix. One can easily get that the i-th row sum of L is N j=1,j =i a ij − N j=1,j =i a ij . It is obvious that if there exists j ∈ {1, 2, · · · , N } that satisfies a ij < 0, then L is not a zero-row sum matrix due to N j=1 l ij = 0, which is quite different from the traditional Laplacian matrix in unsigned networks.
Definition 1 [8], [20]: A signed graph G is said to be structurally balanced, if the nodes of signed graph are divided into two cluster N 1 and N 2 , Otherwise it is structurally unbalanced.

B. PROBLEM FORMULATION
Consider the multi-agent system consisting of N agents, which is subject to time-varying delay and deception attacks, each agent can be regarded as a node: where denotes the time-varying delay. It is assumed that 0 < τ (t) < τ withτ > 0 being a constant. and β are the coupling strengths with α > 0 and β > 0. g ij represents the (i, j)-th entry of the adjacency matrix associated with the underlying signed graph G of system (2) Similarly to [32], it is assumed that deception attacks randomly launch at each impulse instant. ψ(x i (t)) ∈ R n x represents a deception attack signal. The Bernoulli distribution sequence ρ(t p ), p ∈ N + takes values 0 and 1 with probability Pr ob ρ(t p ) = 1 =ρ and Pr ob ρ(t p ) = 0 = 1 −ρ, whereρ is a constant and 0 <ρ < 1.
Remark 2: The non-delayed coupling term α N j=1 g ij (x i (t) − sign(g ij )x j (t)) and the delayed coupling term ) are simultaneously considered in system (2). In addition, the dynamic system itself also considers the influence of the time-varying delay τ (t). In addition, if the time-varying delay τ (t) is ignored, that is, A 2 = B 2 = 0 in (2), and β = 0 in (2), and the influence of deception attacks is not considered.
Remark 3: In [32], it is pointed out that a physical attack may cause x i (t) to change suddenly at t p . This phenomenon is mathematically described as impulsive disturbance in the system (2). In addition, it is assumed that deception attacks occur randomly at each impulse moment, and the Bernoulli distribution sequence is used to describe the random occurrence of deception attacks [27].
Applying the Laplacian matrix L, the multi-agent system can be rewritten as: (3) is an odd function and satisfies the following inequality: where ν m is a given constant and ν m > 0.
is an odd function, ψ(x i (t)) ∈ R n x satisfies the following inequality: where θ is a given constant and θ > 0.
Definition 2: Under Assumption 3, the multi-agent system with signed graph is considered to achieve bipartite synchronization if satisfy: lim According to assumptions 1 and 2, f m (x im (t)) and ψ(x i (t)) are odd functions, and the multi-agent system (3) becomes the following form: After applying the Kronecker product, the system (4) is further transformed into the following: where Remark 4 [18]: One has ω i = 1 for all i = 1, 2, . . . , N , the bipartite synchronization reduces to the traditional synchronization.
Remark 5: As in the work in [18], [19], and [20], by introducing gauge transformation, the bipartite synchronization problem of system (3) with adjacency matrix A = a ij N ×N is transformed into the synchronization problem of system (4) with adjacency matrix A = a ij N ×N . Correspondingly, the Laplacian matrix L = (l ij ) N ×N becomes the Laplacian matrix L = (l ij ) N ×N , the row sum of the former is not all zero, and the latter is a zero-row sum matrix.
Definition 3 [33]: (Average Impulse Interval). The average impulse sequence t p ∞ p=1 is regarded to not be less than T a , if there exist a positive integer N 0 and a positive number T a that satisfies the following conditions: where N (t 0 , t) represents the number of impulsive times in the time period t 0 to t. Lemma 1 [34]: If the signed graph contains a directed spanning tree, then Laplacian matrixL =l ij = (ω i l ij ω j ) N ×N has a single zero eigenvalue and the other N − 1 eigenvalues all lie in the right half-plane.
Lemma 2 [35]: If the signed graph contains a directed spanning tree, then the matrix W = (ω ij ) (N −1)×(N −1) has no zero eigenvalues and all of its eigenvalues have positive real parts.

III. MAIN RESULTS
In this section, several sufficient conditions for the multiagent system with signed graph in Section 2 is obtained to achieve bipartite synchronization. Set the following piecewise function σ : It is easy to see that Theorem 1: Under Assumption 1-4, the multi-agent system (2) can achieve bipartite synchronization, if for given scalars λ > ε > 0, γ > 1, there exist matrices P i > 0, i = 1, 2, scalars δ 1 > 0, δ 2 > 0 and r > 0, such that the following linear matrix inequalities hold: where a satisfies a − λ + εe aτ = 0. Proof: Consider the following Lyapunov function: From Assumption 1, one obtains: where ϒ = diag{υ 1 , υ 2 , . . . υ nx }. When t ∈ t p−1 , t p , the derivative of V (t) along the multi-agent system is expressed as: By introducing all δ 1 > 0, δ 2 > 0, inequalities (11) and (12) into equation (13), it follows that foṙ where According to (7), 1 < 0 and 2 < 0, it follows from (14) thatV By Lemma 3, one has: where a > 0 and a satisfies a − λ + εe aτ = 0. When t = t p , the mathematical expectation of V (t p ) is expanded as follows: According to Assumption 2, the following inequalities hold: Therefore, Then, from inequality (8), it can be known that So that, for t ∈ t p−1 , t p , where ϑ = sup s∈[−τ ,0] e(s) 2 . By Definition 3, the following inequality can be obtained for t ∈ t p−1 , t p , Then According to the inequality (9), one obtains: Combined with the condition of bipartite synchronization in Definition 2, the multi-agent system with signed graph can achieve bipartite synchronization, and the proof is complete.
Remark 6: Under Assumptions 1-2 of the node function and Assumptions 3-4 of the system topology, by constructing a Lyapunov function and applying Halanay differential inequality in Lemma 3, Theorem 1 provides a new bipartite synchronization criterion for multi-agent systems under timevarying delay and deception attacks. The criterion involves the Kronecker product.

IV. NUMERICAL SIMULATION
This section presents two numerical examples to demonstrate the validity of our results in Section 3, both of which employ a chaotic system to describe the dynamic behavior of isolated node in system (2). Example 1: Consider a multi-agent system with signed graph of seven nodes, whose topology is the same as in [37], shown in Figure 1. Each chaotic agent can be regarded as a node in the system. The dynamic behavior of each individual agent is described by (2) with: From the above topology, the entire system is divided into two clusters, N 1 = {1, 2, 3} and N 2 = {4, 5, 6, 7}. The structure of the system is balanced and contains a directed spanning tree.
Let λ=2, ε=1 andτ = 0.3, then a = 0.7483 is the root of the equation a − λ + εe aτ = 0. Set ψ(x i (t)) = [0.3x i1 (t), − 0.3 sin(x i2 (t)), 0.3 tanh(x i3 (t))] T , then ψ(z 1 ) − ψ(z 2 ) ≤ θ z 1 − z 2 , ∀z 1 , z 2 ∈ R 3 with θ=0.3. Meanwhile, let T a = 0.5 and γ = 1.35 such that a − ln γ T a > 0 can be hold. Then feasible results are then solved by using linear matrix inequality technology. In the simulation, the impulse interval is taken as 0.5s. Figure 2 depicts the trajectories of x i (i = 1, 2, . . . 7) and the deception attacks occurrence at impulse instants. It can be seen from the figure that, at the impulse instants when the deception attacks really occur, even though the system states will be affected to make a jump, the trajectory of the system states will still maintain bipartite synchronization. These simulation results demonstrate the effectiveness of the proposed bipartite synchronization approach. Example 2: Consider a multi-agent system with signed graph composed by nine nodes, whose topology is the same as in [19] and [38] and shown in Figure 3. Each chaotic agent can be regarded as a node, which is described by equation (2) with: It can be verified that It can be seen from the above topology diagram that the structure of the system is balanced and the signed graph contains a directed spanning tree. The system can be divided into two clusters, which are N 1 = {1, 2, 3, 8, 9} and N 2 = {4, 5, 6, 7}. Assume )] T and parameters θ,ρ are same as those in example 1.
Let λ = 1, ε = 0.5 andτ = 1, then a = 0.3149 is the root of the equation a − λ + εe aτ = 0. Meanwhile, in order to meet the condition a − ln γ T a > 0, it is set that T a = 1 and γ = 1.3610. Feasible results are then obtained by solving the linear matrix inequalities in Theorem 1. In the simulation, the impulse interval is taken as 1s, that is t p − t p−1 = 1s. Figure 4 shows the trajectories of x i (i = 1, 2, . . . 9), and the deception attacks occurrence at impulse instants are also depicted. It is clear that the trajectory of the system states will still keep bipartite synchronous, even if the system states will be affected to jump at the impulse instants with deception attacks. These simulation results further illustrate the effectiveness of the proposed bipartite synchronization approach.

V. APPLICATION TO SPEECH COMMUNICATION
Multi-agent systems usually need to keep necessary communication, such as speech, video, text chat and so on, but the security of communication must be guaranteed. Based on the synchronization results of Example 1 obtained in Section 4, a new chaotic speech secure communication system is constructed to verify the feasibility of the proposed theoretical method.

A. SPEECH SECURE COMMUNICATION
Usually, duplex speech communication can be performed between agents. For simplicity, the simplex communication in which the agent i sends the encrypted speech signals to the agent j is taken as an example for analysis. As shown in Figure 5, a typical speech secure communication system consists of two parts, the sender and receiver. The sender of agent i encrypts a section of speech signals to produce signals similar to white noise by using the chaotic signals which are generated by node i in the multi-agent system (2). Then   the encrypted speech signals, the discrete iteration start time (N l _k) and the number i of agent are combined into a data packet to send. Accordingly, after receiving the data packet, the receiver of agent j decomposes it into the corresponding speech signals to be decrypted, the discrete iteration start time (N l _k) and the number i of sender agent. The multiagent systems with signed digraph, time-varying delay and deception attacks can realize bipartite synchronization to recover the original speech signals under the guarantee of Theorem 1, in which the chaotic signals generated by node i are used for speech encryption, while signals generated by node j are used for speech decryption. Furthermore, if and only if the encryption and decryption keys are completely consistent, it can be ensured that the sender of agent i and the receiver of agent j can produce the same or opposite key streams to recover the original speech signals. For simplicity, it is assumed that the encryption keys and the decryption keys are agreed in advance by both the sender of agent i and the receiver of agent j. The sender and receiver can be attached to the agent. In addition, the channel used for speech communication is a separate channel, independent of the topology of the multi-agent system with signed graph.
The workflow of chaotic speech secure communication between agent i and agent j is described as follows.
Step 1: A section of original speech signals to be sent by agent i is prepared. There are two kinds of voice, one is to record directly and send in real time, and the other is to read data directly from the recording file. Without losing generality, a direct recording is performed with the frequency of 8000Hz, and the resulting original speech signal is expressed as m (t).
Step 2: Given the parameter matrices (A1, B1, A2, B2), iteration step size ( T ) and initial values ((x 11 (0) , x 12 (0) , Given the initial encryption value (C_temp), according to Algorithm 1, at the sending end of agent i, the original speech signal is encrypted by using the generated chaotic state sequences x in (n= 1, 2, 3) , that is, the encrypted speech signals are obtained.
Step 3: The encrypted speech signal C(t), the discrete iteration start time (N 1 _k, N 2 _k, N 3 _k) and the number i of agent sender are combined into a data packet for transmission. Immediately, agent i sends the data packet to agent j. For simplicity, the one-encryption and one-transmission mode is adopted here. However, it is recommended to use segmentencryption and segment-transmission mode for long time speech signals.
After receiving the data packet, the receiver of agent j decomposes it into the corresponding speech signal to be decryptedC (t), discrete iteration start time (N 1 _k,N 2 _k,N 3 _k) and the number i of agent sender, which is transmitted through the exclusive communication channel.
Remark 7. Algorithms 1 and 2 are suitable for the point-topoint speech communication between multiple agents, using the chaotic signals generated by the point-to-point communication agent itself. These algorithms adopt the parallel encryption/decryption methods, that is, the speech signals are divided into several segments and encrypted/decrypted at the same time, so the encryption/decryption speed is

Algorithm 2 Speech Decryption
Initialization: Set L ← length(C(t));N 1 _k ← 3000 + i;N 2 _k ← 3007 + i;N 3 _k ← 3011 + i; for s = 1 : L 3 tmp1 = 10 ∧ (9 + mod(floor (P_temp * 10 ∧ 15) , 8)); tmp2 = dec2bin (mod(floor (P_temp * 10 ∧ 15) , 8), 3); end end greatly improved. In addition, the chaotic key streams (X (p) /X (q) , Y (p) /Ȳ (q) and Z (p)/Z (q)) generated by the multi-agent system with signed digraph are random, which ensures the security of encryption/decryption to a certain extent. The most important is to decide what kind of calculation (1 out of 8) the algorithm performs to generate key streams and where to start extracting chaotic signal, and these operations are not only related to the former key streams VOLUME 11, 2023 but also dependent on the former cipher signals, so as to resist various attacks.

B. TEST RESULTS AND PERFORMANCE ANALYSIS
Taking Agent 1 sending encrypted speech signals to Agent 5 as an example, this section gives the system test results and performance analysis to prove the effectiveness of the speech secure communication based on the proposed bipartite synchronization method. In this test, the initial encryption/decryption values C_temp/P_temp are all assigned as 0.12345. A section of recording signals to be encrypted is the voice of ''speech encryption'', as shown in Figure 6(a). The encryption algorithm shown in Algorithm 1 is used to produce encrypted speech signals, as shown in Figure 6(b). It can be seen that the encrypted speech signals are noise without any trace of original information. For simplicity, here Agent 5 used in the speech communication are homogeneous, that is, the parameters of the dynamic system are consistent are consistent with the encryption keys which are agreed in advance, and the discrete iteration start time of decryption node N 1 _k= 3000,N 2 _k = 3007,N 3 _k = 3011 is also consistent with Agent 1. The speech signals recovered after decryption are shown in Figure 6(c), from which it is obvious that the recovered speech signals are the same as the original speech signals. That is to say, Agent 5 can perfectly hear the original speech, while the eavesdropper can only hear a burst of noise during transmission. The Comparison signals between encrypted and decrypted speech signals are depicted in Figure 6(d).
An ideal secure communication must have good performance and enough robustness to resist different types of security attacks. The security analysis presented in this paper includes spectrogram, histogram, key space, key sensitivity and real-time, which are detailed as follows.  is shown in Figure 6(a). Figure 7(c) and (d) show the spectrogram and histogram of the encrypted speech signals as shown in Figure 6(b). It can be seen that the spectrogram (energy distribution) and histogram (signal value distribution) of the encrypted speech signals are uniform distributed, which are completely different from those of original speech signals, and can well protect the speech information against statistical analysis. In addition, Figure 7(e) and (f) present the spectrogram and histogram of the recovered speech signals after decryption, which are the same as those of the original speech signals.

2) KEY SPACE ANALYSIS
In the proposed algorithm, the keys include the parameter matrices (A1, A2, B1, B2) of the multi-agent system with signed digraph shown in (2), the iteration step size T, and the encrypted initial value C_temp. It is worth noting that the initial values of multi-agent system with signed graph have no effect on the recovery of original speech signals at receiver. If the calculation accuracy of 64 bit double precision number is 10 −14 , its key space can up to 10 14×18 ×1000 × 10 14 = 10 266+3 = 10 269 , which is large enough and has sufficient security to resist exhaustive attacks.

3) KEY SENSITIVITY ANALYSIS
An effective encryption algorithm should be sensitive to the keys. On the one hand, even a small change in the encryption keys will lead to a huge difference between the encrypted speech signals. On the other hand, the small difference between the encryption and the decryption keys will fail to recover the original speech signals.
In order to test the sensitivity of encryption keys, only a single encryption key is slightly changed each time. During the test, encryption keys are slightly changed as follows, and C_temp=0.12345+ω, where ω = 0.00000000000001. The error speech signals are respectively shown in Figure 8, which are obtained by comparing the encrypted speech signals using slightly changed encryption keys with the former signals shown in Figure 6(b). It is obvious that ''a millimeter miss'' of the encryption key will lead to ''a thousand miles'' between encrypted speech signals. Therefore, the proposed Algorithm 1 is sensitive to the encryption keys. In order to test the sensitivity between encryption and decryption keys, a group of decryption keys is similarly selected with tiny modification to decrypt signals in Figure 6 It can be clearly reflected from Figure 9 that the decrypted speech signals are harsh noise without any useful information, and they are completely different from the original speech signals. Therefore, unless the eavesdropper obtains the same decryption keys as the encryption keys, it will be impossible to decrypt and recover the original speech signals or obtain any useful information.

4) REAL-TIME ANALYSIS
It is expected that speech signals can be encrypted and decrypted in real time to meet the real-time requirements of speech secure communication. Still chosen ''Speech Encryption'' (see Figure 6(a)) to test, the encryption time with Algorithm 1 is 0.203574s, and the decryption time with Algorithm 2 is about 0.210356s, which can basically meet the real-time requirements of speech communication.

VI. CONCLUSION
This paper addresses the bipartite synchronization problem of multi-agent systems with signed graph, where the effects of time-varying delay and deception attacks are taken into account. By using a gauge transformation to transform the bipartite synchronization problem of multi-agent systems with signed graph into the traditional synchronization of multi-agent systems with unsigned graph, choosing the appropriate Lyapunov function and applying the Halanay differential inequality, a sufficient condition, which guarantees the bipartite leaderless synchronization for multi-agent systems with unsigned graphs, is newly obtained. When the delayed node-state term or the delayed coupling term is not considered separately, several criteria are established. The effectiveness of the synchronization results is then demonstrated by two numerical examples. Finally, a new multiagent speech secure communication system is constructed to verify the feasibility of the proposed synchronization results in practical applications.