CN111385305A - Distributed image encryption/decryption method based on average consistency - Google Patents

Distributed image encryption/decryption method based on average consistency Download PDF

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CN111385305A
CN111385305A CN202010190078.XA CN202010190078A CN111385305A CN 111385305 A CN111385305 A CN 111385305A CN 202010190078 A CN202010190078 A CN 202010190078A CN 111385305 A CN111385305 A CN 111385305A
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CN111385305B (en
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陈飞
王武广
冯宠
黄伯敏
项林英
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Northeastern University Qinhuangdao Branch
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00Network architectures or network communication protocols for network security
    • H04L63/04Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention provides a distributed picture encryption/decryption method based on average consistency, and relates to the technical field of control and information. The invention makes use of the characteristic of average consistency of the algorithm to enable each agent to approach the average value of the initial state. When an encrypted picture appears on the network, a computer in which the picture appears is called an agent, and the agent through which the picture flows on the network can form a network with a specific structure. Assuming that the agents satisfy a certain topology, under the action of a distributed average consistency algorithm, the state values of the agents through which the photos flow are continuously updated, the updated state value is the average value of the agent and its neighbors, and after a period of time, the state value of the encrypted photos on each agent becomes the average value at the initial moment. The average value corresponds to the true value of the picture, so that the picture becomes clear, and the purpose of decrypting the picture is achieved.

Description

Distributed image encryption/decryption method based on average consistency
Technical Field
The invention relates to the technical field of control and information, in particular to a distributed picture encryption/decryption method based on average consistency.
Background
A multi-agent system is a collection of a plurality of agents coupled to each other, each agent having a certain autonomy and being able to communicate with other agents by sensing the surrounding environment. There are significant advantages to using multi-agent system technology in large systems. In recent years, distributed cooperative control of a multi-agent system has become a hotspot of research in the control field, theoretical achievements are more and more abundant, and main related problems include consistency, coordinated tracking, formation control, distributed optimization, distributed average tracking and the like. The distributed average consistency algorithm has unique advantages in signal processing, and attracts wide research interests of researchers from different fields. For example, the image encryption/decryption is realized by using a distributed algorithm, so that the method has a series of advantages of low cost, high reliability, high flexibility and the like, and has a wide application prospect.
The encryption/decryption algorithm of the current picture is based on a single agent to process the image, and the encryption/decryption steps are complex, the calculated amount is large, and the robustness is poor. Especially when the number of pictures processed is extremely large, far exceeding the processing capacity of a single agent, the use of centralized algorithms becomes cumbersome and may even result in the inability to encrypt/decrypt the pictures within a specified time. Compared with the traditional image encryption/decryption method, the method for encrypting/decrypting the image by using the distributed average consistency algorithm can avoid centralized large-amount calculation, and can realize the encryption/decryption of the image no matter how large the number of the images to be processed is. For an encrypted picture, a distributed average consistency algorithm is applied for calculation, and all agents can finally reach the average value of the initial state, but not only the state of one agent finally reaches the average value of the states. This has the advantage that the states of a plurality of agents can be averaged to the initial state, so that any agent can reach the state after image decryption, that is, the decrypted image can be realized on any agent, which cannot be realized by using a single agent.
In the above background, we propose a distributed picture encryption/decryption method based on an average consistency algorithm. The basic idea of the algorithm is as follows: and aiming at the encrypted image containing white noise obtained by each intelligent agent, carrying out certain iterative steps to ensure that the state value of each intelligent agent finally reaches the average value of the initial moment state of the intelligent agent, wherein the average value corresponds to the real value of the picture. If the number of the intelligent agents is increased, namely the number of the processed pictures is increased, the finally obtained decryption effect is better. The application difficulty of the distributed average consistency algorithm is as follows:
(1) a multi-agent system needs to make all agents consistent according to local information of each agent;
(2) the state update for each agent at the next time needs to be updated with the state of all its neighbors.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a distributed picture encryption/decryption method based on average consistency;
the technical scheme adopted by the invention is as follows: a distributed picture encryption/decryption method based on average consistency comprises the following steps:
step 1: constructing a network structure topological graph describing the multi-agent system, wherein each node represents one agent, and each edge represents information interaction among the agents;
the network structure topological graph is a non-directional time invariant graph, and when the number of nodes is n, the network structure topological graph is represented as follows: g ═ V, E; wherein the content of the first and second substances,
Figure BDA0002415549970000021
a collection of nodes is represented as a set of nodes,
Figure BDA0002415549970000022
representing a set of edges, i, j representing a node in a topology graph, NjRepresenting a set of node j neighbors; since the network fabric topology is an undirected graph,so if j ∈ NiWhen the condition is satisfied, i ∈ N can be obtainedjAnd if j ∈ NiIf so, the node j is called as a father node, and the node i is called as a child node;
step 2: determining an adjacency matrix of the constructed network topology, as shown in formula (1):
Figure BDA0002415549970000023
wherein the term a in the adjacency matrixijRepresenting the weight value of the edge between the nodes i and j, if the edges between the nodes i and j are connected, then there is aij>0; if no edge between nodes i, j is connected, then there is aij0; for undirected graphij=aji
And step 3: establishing a state equation of the multi-agent, as shown in formula (2):
Figure BDA0002415549970000024
wherein the content of the first and second substances,
Figure BDA0002415549970000025
in order to control the input of the electronic device,
Figure BDA0002415549970000026
the state of the ith agent;
Figure BDA0002415549970000027
an m-dimensional vector which is a real number domain, wherein m is an integer greater than or equal to 1;
and 4, step 4: obtaining the initial value information of the multi-agent, wherein the picture expression after encryption is shown as formula (3):
f(x,y)=f0(x,y)+n(x,y) (3)
where f (x, y) is a noisy picture representation, f0(x, y) is an original picture expression, n (x, y) is an expression of noise, and the noise follows a gaussian distribution;
step 4.1: sampling a target picture containing noise for multiple times;
step 4.2: grouping the sampled pictures, and dividing the pictures into n groups according to the number n of nodes, namely the number of the intelligent agents is n, and carrying out averaging processing on the pictures in each group;
step 4.3: taking the averaged information as initial value information of each agent;
and 5: the distributed algorithm is designed according to the adjacency matrix and the state equation as shown in formula (4):
Figure BDA0002415549970000028
substituting the formula (4) into the equation of state formula (2) of the agent yields:
Figure BDA0002415549970000031
consider a discrete time system as shown in equation (6):
Figure BDA0002415549970000032
wherein x isi(k) For the state of the ith agent at time k, ε is the step size and ε>0; let p beij=εaij,pijRepresentation represents x at time k +1iEach k time x in the value of (1)jOccupied weight, and defining
Figure BDA0002415549970000033
Equation (6) is written as:
Figure BDA0002415549970000034
step 6: updating the state of the ith agent with the state values of the ith agent and its neighbor agents, wherein the formula is expressed as:
Figure BDA0002415549970000035
wherein j ∈ Ni,j=1,...,n,NiRepresenting a set of node i neighbors; substituting the initial value information for operation;
and 7: and increasing the number of the sampling pictures, changing the number of the intelligent agents according to the number of the sampling pictures, and repeating the steps 1 to 6 until a preset picture decryption effect is achieved.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the distributed picture encryption/decryption method based on average consistency provided by the invention makes each intelligent agent approach to the average value of the initial state by utilizing the characteristic of the average consistency of the algorithm. When an encrypted picture appears on the network, a computer in which the picture appears is called an agent, and the agent through which the picture flows on the network can form a network with a specific structure. Assuming that the agents satisfy a certain topology, under the action of a distributed average consistency algorithm, the state values of the agents through which the photos flow are continuously updated, the updated state value is the average value of the agent and its neighbors, and after a period of time, the state value of the encrypted photos on each agent becomes the average value at the initial moment. The average value corresponds to the true value of the picture, so that the picture becomes clear, and the aim of decrypting the picture is fulfilled; has the following advantages:
(1) and the interference effect of the encryption noise in the picture is weakened by adopting a distributed average consistency algorithm, so that the aim of decrypting the picture is fulfilled.
(2) The requirement on the network structure is simple, and the practicability is strong.
(3) The decryption of the image is realized by utilizing a distributed algorithm, and the method has a series of advantages of small calculated amount, high reliability, high flexibility, low operation cost and the like.
Drawings
FIG. 1 is a flowchart illustrating a distributed image encryption/decryption method based on average consistency according to the present invention;
FIG. 2 is a diagram illustrating a multi-agent network architecture according to an embodiment of the present invention;
fig. 3 is a noise picture with picture μ ═ 0 and σ ═ 1 according to an embodiment of the present invention;
fig. 4 is a noise reduction image after 10 agents pass through a noise picture with picture μ being 0 and σ being 1 according to an embodiment of the present invention;
fig. 5 is a noise reduction image after 50 agents pass through a noise picture with picture μ being 0 and σ being 1 according to an embodiment of the present invention;
fig. 6 is a noise reduction image after the noise picture with picture μ ═ 0 and σ ═ 1 passes through 100 agents according to the embodiment of the present invention;
fig. 7 is a noise picture with picture μ ═ 0 and σ ═ 10 according to an embodiment of the present invention;
fig. 8 is a noise reduction image after 10 agents pass through a noise picture with picture μ ═ 0 and σ ═ 10 according to an embodiment of the present invention;
fig. 9 is a noise reduction image after 50 agents pass through a noise picture with picture μ being 0 and σ being 10 according to an embodiment of the present invention;
fig. 10 is a noise reduction image after a picture μ ═ 0 and a ═ 10 noise picture passes through 100 agents according to an embodiment of the present invention;
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The technical scheme adopted by the invention is a distributed picture encryption/decryption method based on average consistency, as shown in figure 1, comprising the following steps:
step 1: constructing a network structure topological graph describing the multi-agent system, wherein each node represents one agent, and each edge represents information interaction among the agents;
the network structure topological graph is a non-directional time invariant graph, and when the number of nodes is n, the network structure topological graph is represented as follows: g ═ V, E; wherein the content of the first and second substances,
Figure BDA0002415549970000041
a collection of nodes is represented as a set of nodes,
Figure BDA0002415549970000042
representing a set of edges, i, j representing a node in a topology graph, NjRepresenting the set of neighbor nodes of the node j, if j ∈ N is the case because the topological graph of the network structure is an undirected graphiWhen the condition is satisfied, i ∈ N can be obtainedjAnd if j ∈ NiIf so, the node j is called as a father node, and the node i is called as a child node;
the present embodiment considers a multi-agent system with a ring network structure and n-10, as shown in fig. 2.
Step 2: determining an adjacency matrix of the constructed network topology, as shown in formula (1):
Figure BDA0002415549970000043
wherein the term a in the adjacency matrixijRepresenting the weight value of the edge between the nodes i and j, if the edges between the nodes i and j are connected, then there is aij>0; if no edge between nodes i, j is connected, then there is aij0; for undirected graphij=aji
Since the weighted values in the topological graph in this embodiment are all 1, then aijWhen the number is 1, the nodes i and j are connected by edges;
and step 3: establishing a state equation of the multi-agent, as shown in formula (2):
Figure BDA0002415549970000051
wherein the content of the first and second substances,
Figure BDA0002415549970000052
in order to control the input of the electronic device,
Figure BDA0002415549970000053
the state of the ith agent;
Figure BDA0002415549970000054
an m-dimensional vector which is a real number domain, wherein m is an integer greater than or equal to 1;
and 4, step 4: obtaining the initial value information of the multi-agent, wherein the picture expression after encryption is shown as formula (3):
f(x,y)=f0(x,y)+n(x,y) (3)
where f (x, y) is a noisy picture representation, f0(x, y) is an original picture expression, n (x, y) is an expression of noise, and the noise follows a gaussian distribution;
step 4.1: sampling a target picture containing noise for multiple times;
step 4.2: grouping the sampled pictures, and dividing the pictures into n groups according to the number n of nodes, namely the number of the intelligent agents is n, and carrying out averaging processing on the pictures in each group;
step 4.3: taking the averaged information as initial value information of each agent;
and 5: the distributed algorithm is designed according to the adjacency matrix and the state equation as shown in formula (4):
Figure BDA0002415549970000055
substituting the formula (4) into the equation of state formula (2) of the agent yields:
Figure BDA0002415549970000056
consider a discrete time system as shown in equation (6):
Figure BDA0002415549970000057
wherein x isi(k) For the state of the ith agent at time k, ε is the step size and ε>0; let p beij=εaij,pijRepresentation represents x at time k +1iEach k time x in the value of (1)jOccupied weight while
Figure BDA0002415549970000058
Equation (6) is written as:
Figure BDA0002415549970000059
each agent updates the current state value to the average value of the current state value and all the neighbor states of the agent, and finally the state of each agent approaches to the average value of the initial state;
step 6: updating the state of the ith agent with the state values of the ith agent and its neighbor agents, wherein the formula is expressed as:
Figure BDA00024155499700000510
wherein j ∈ Ni,j=1,...,n,NiRepresenting a set of node i neighbors; substituting the initial value information for operation;
and 7: and increasing the number of the sampling pictures, changing the number of the intelligent agents according to the number of the sampling pictures, and repeating the steps 1 to 6 until a preset picture decryption effect is achieved.
Wherein, aij1 means that the nodes i and j are connected by edges; a isij0 means that no edge is connected between nodes i, j.
In the embodiment of the present invention, a distributed picture encryption/decryption method based on average consistency is used to encrypt/decrypt a picture in the embodiment, as shown in fig. 3-10, fig. 3 is a noise picture in which a picture μ is 0 and σ is 1 in the embodiment of the present invention; fig. 4 is a noise reduction image after 10 agents pass through a noise picture with picture μ being 0 and σ being 1 according to an embodiment of the present invention; fig. 5 is a noise reduction image after 50 agents pass through a noise picture with picture μ being 0 and σ being 1 according to an embodiment of the present invention; fig. 6 is a noise reduction image after the noise picture with picture μ ═ 0 and σ ═ 1 passes through 100 agents according to the embodiment of the present invention; fig. 7 is a noise picture with picture μ ═ 0 and σ ═ 10 according to an embodiment of the present invention; fig. 8 is a noise reduction image after 10 agents pass through a noise picture with picture μ ═ 0 and σ ═ 10 according to an embodiment of the present invention; fig. 9 is a noise reduction image after 50 agents pass through a noise picture with picture μ being 0 and σ being 10 according to an embodiment of the present invention; fig. 10 is a noise reduction image after a picture μ ═ 0 and a ═ 10 noise picture passes through 100 agents according to an embodiment of the present invention; where snr represents the value of the signal-to-noise ratio. It can be seen from the figure that as the number of agents increases, the signal-to-noise ratio of the picture is continuously increased, and the quality of the decrypted picture becomes better and better.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (2)

1. A distributed picture encryption/decryption method based on average consistency is characterized by comprising the following steps:
step 1: constructing a network structure topological graph describing the multi-agent system, wherein each node represents one agent, and each edge represents information interaction among the agents;
the network structure topological graph is a non-directional time invariant graph, and when the number of nodes is n, the network structure topological graph is represented as follows: g ═ V, E; wherein the content of the first and second substances,
Figure FDA0002415549960000011
a collection of nodes is represented as a set of nodes,
Figure FDA0002415549960000012
representing a set of edges, i, j representing a node in a topology graph, NjRepresenting the set of neighbor nodes of the node j, if j ∈ N is the case because the topological graph of the network structure is an undirected graphiWhen the condition is satisfied, i ∈ N can be obtainedjAnd if j ∈ NiIf so, the node j is called as a father node, and the node i is called as a child node;
step 2: determining an adjacency matrix of the constructed network topology, as shown in formula (1):
Figure FDA0002415549960000013
wherein the term a in the adjacency matrixijRepresenting the weight value of the edge between the nodes i and j, if the edges between the nodes i and j are connected, then there is aij>0; if no edge between nodes i, j is connected, then there is aij0; for undirected graphij=aji
And step 3: establishing a state equation of the multi-agent, as shown in formula (2):
Figure FDA0002415549960000014
wherein the content of the first and second substances,
Figure FDA0002415549960000015
in order to control the input of the electronic device,
Figure FDA0002415549960000016
the state of the ith agent;
Figure FDA0002415549960000017
an m-dimensional vector which is a real number domain, wherein m is an integer greater than or equal to 1;
and 4, step 4: obtaining the initial value information of the multi-agent, wherein the picture expression after encryption is shown as formula (3):
f(x,y)=f0(x,y)+n(x,y) (3)
where f (x, y) is a noisy picture representation, f0(x, y) is an original picture expression, n (x, y) is an expression of noise; and the noise follows Gaussian distribution;
and 5: the distributed algorithm is designed according to the adjacency matrix and the state equation as shown in formula (4):
Figure FDA0002415549960000018
substituting the formula (4) into the equation of state formula (2) of the agent yields:
Figure FDA0002415549960000019
consider a discrete time system as shown in equation (6):
Figure FDA00024155499600000110
wherein x isi(k) For the state of the ith agent at time k, ε is the step size and ε>0; let p beij=εaij,pijRepresentation represents x at time k +1iEach k time x in the value of (1)jOccupied weight while
Figure FDA0002415549960000021
Equation (6) is written as:
Figure FDA0002415549960000022
step 6: updating the state of the ith agent with the state values of the ith agent and its neighbor agents, wherein the formula is expressed as:
Figure FDA0002415549960000023
wherein j ∈ Ni,j=1,...,n,NiRepresenting a set of node i neighbors; substituting the initial value information for operation;
and 7: and increasing the number of the sampling pictures, changing the number of the intelligent agents according to the number of the sampling pictures, and repeating the steps 1 to 6 until a preset picture decryption effect is achieved.
2. The distributed picture encryption/decryption method based on average consistency according to claim 1, wherein the step 4 specifically comprises the following steps:
step 4.1: sampling a target picture containing noise for multiple times;
step 4.2: grouping the sampled pictures, and dividing the pictures into n groups according to the number n of nodes, namely the number of the intelligent agents is n, and carrying out averaging processing on the pictures in each group;
step 4.3: and taking the averaged information as initial value information of each agent.
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