CN113312635A - Multi-agent fault-tolerant consistency method and system based on state privacy protection - Google Patents

Multi-agent fault-tolerant consistency method and system based on state privacy protection Download PDF

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CN113312635A
CN113312635A CN202110416322.4A CN202110416322A CN113312635A CN 113312635 A CN113312635 A CN 113312635A CN 202110416322 A CN202110416322 A CN 202110416322A CN 113312635 A CN113312635 A CN 113312635A
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CN113312635B (en
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汪京
侯健
张明悦
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Zhejiang University of Technology ZJUT
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Abstract

The invention discloses a multi-agent fault-tolerant consistency method based on state privacy protection, wherein the related multi-agent fault-tolerant consistency method based on state privacy protection comprises the following steps: s1, constructing a multi-agent fault-tolerant consistency system model; s2, processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm; and S3, performing interactive iterative processing on all processed intelligent agents to enable the state values of all good intelligent agents to be consistent. The invention provides a method for protecting the privacy of each state value of an agent in a Q consistency algorithm by using a homomorphic encryption algorithm, and the privacy of the agent is protected by encrypting each state value of the agent at each time, so that a neighbor agent cannot acquire the state value of the agent. Meanwhile, while privacy is protected, wrong agents can be identified through continuous interactive iteration, and finally the state values of all good agents are consistent.

Description

Multi-agent fault-tolerant consistency method and system based on state privacy protection
Technical Field
The invention relates to the technical field of multi-agent control, in particular to a multi-agent fault-tolerant consistency method and system based on state privacy protection.
Background
In recent years, with the continuous development of multi-agent technology, the multi-agent technology has been widely applied to many fields such as traffic control, smart grid, production and manufacturing, unmanned aerial vehicle control and the like. As a basis for the multi-agent coordination control problem, the consistency problem is mainly a problem of how to design an algorithm based on limited information exchange between individuals in a multi-agent system so that the states of all agents reach the same state.
In the multi-agent consistency system, not all agents update the state of the agents according to a given algorithm, wherein system errors comprise internal factors and external factors, the internal factors such as the agents are damaged to cause the individuals to be incapable of working normally, and the external factors such as the agents are controlled by enemies to become malicious nodes. Therefore, under the condition that abnormal nodes exist in the intelligent agent network, how to enable all normal nodes to still reach the same state is very important.
In the present data explosion era, it is very important to protect the privacy of individual information, and the privacy protection of information becomes a hot spot of current research. In the field of multi-agents, privacy protection is gradually used in the research of multi-agent consistency, but the method of using privacy protection in the problem of multi-agent fault-tolerant consistency is not many. Especially when there are malicious nodes in the agent, it is necessary to consider privacy in the fault-tolerant consistency algorithm.
Disclosure of Invention
The invention aims to provide a multi-agent fault-tolerant consistency method and system based on state privacy protection, aiming at the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a multi-agent fault-tolerant consistency method based on state privacy protection comprises the following steps:
s1, constructing a multi-agent fault-tolerant consistency system model;
s2, processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and S3, performing interactive iterative processing on all processed intelligent agents to enable the state values of all good intelligent agents to be consistent.
Further, in step S1, a multi-agent fault-tolerant consistency system model is constructed, wherein the topology of the multi-agent is represented as: g (V, E), V ═ {1,2, …, n } represents a set of agents,
Figure RE-GDA0003193860810000021
representing the connection relationships between agents.
Further, the processing, by the agent in step S2 through the homomorphic encryption algorithm, specifically is: the agent generates a pair of keys through a homomorphic encryption algorithm, wherein the keys comprise a public key and a private key.
Further, the step S3 specifically includes:
s31, the intelligent agent i encrypts the state value of the intelligent agent i through the public key of the intelligent agent i to obtain a first encryption result, and the intelligent agent i sends the first encryption result and the public key of the intelligent agent i to the adjacent intelligent agent j of the intelligent agent i;
s32, the neighbor agent j encrypts the state value of the neighbor agent j by using the public key sent by the agent i to obtain a second encryption result;
s33, calculating the difference value between the first encryption result and the second encryption result, and attaching the calculated difference value to a random number betajThe exponential power of the intelligent agent i to obtain a third encryption result, and sending the obtained third encryption result back to the intelligent agent i;
s34, the intelligent agent i carries out decryption operation on the third encryption result by using a private key of the intelligent agent i to obtain a first decryption result;
s35, the agent i updates the state value of the agent i by using the first decryption result and the weight of the agent j to obtain an updated state value;
s36. mixing betajBy replacement with
Figure RE-GDA0003193860810000022
And repeatedly executing steps S31 to S34, the agent i obtains a second decryption result;
s37, calculating an incentive value of the agent j through the first decryption result and the second decryption result, and calculating comprehensive trust degree according to the acquired incentive value;
s38, updating the weight of the agent i to each neighbor agent j through all the comprehensive trust degrees obtained through calculation to obtain the updated weight;
s39, the intelligent agent i updates the state value of the intelligent agent i by using the updated weight;
s40, repeating the steps S31 to S39 to enable the state values of all good agents to be consistent.
Further, the updated state value obtained in step S35 is represented as:
Figure RE-GDA0003193860810000031
wherein, x'iRepresenting the updated state value of the agent i; x is the number ofiRepresenting a state value of the agent i at the last moment; alpha is alphaijRepresents the weight of agent i to agent j; x is the number ofjRepresents a state value at a time previous to agent j; omegaiRepresenting random noise; beta is aj(xj-xi) Representing the first decryption result.
Further, in step S37, the reward value of agent j is calculated as:
Figure RE-GDA0003193860810000032
wherein r isijRepresenting a prize value;
Figure RE-GDA0003193860810000033
representing the second decryption result.
Further, in step S37, the comprehensive confidence level is calculated according to the obtained bonus value, and is represented as:
Qij'＝Qij+η(rij-Qij)
wherein Q isij' represents the updated comprehensive trust degree of the node i to the node j; qijRepresenting the comprehensive trust degree of the node i to the node j; η represents the step size.
Further, the updated weight obtained in step S38 is represented as:
Figure RE-GDA0003193860810000034
wherein, alpha'ijIndicating the weight of agent i to agent j after the update.
Further, in step S39, agent i updates its state value with the updated weight, which is expressed as:
Figure RE-GDA0003193860810000035
wherein, x "iIndicating the state value of agent i after the second update.
Correspondingly, a multi-agent fault-tolerant consistency system based on state privacy protection is further provided, and comprises:
the building module is used for building a multi-agent fault-tolerant consistency system model;
the processing module is used for processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and the iteration module is used for carrying out interactive iteration processing on all processed intelligent agents so as to enable the state values of all good intelligent agents to be consistent.
Compared with the prior art, the invention provides a homomorphic encryption algorithm to carry out privacy protection on the state value of each agent in the Q consistency algorithm, and the neighbor agents can not obtain the state values of the agents by encrypting the state values of the agents at each moment, so that the privacy of the agents is protected. Meanwhile, while privacy is protected, wrong agents can be identified through continuous interactive iteration, and finally the state values of all good agents are consistent.
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FIG. 1 is a flowchart of a multi-agent fault-tolerant consistency method based on state privacy protection according to an embodiment;
FIG. 2 is a flow chart of a homomorphic encryption algorithm provided in accordance with one embodiment;
FIG. 3 is a flowchart of an update iteration of any good agent provided in the first embodiment;
fig. 4 is a schematic diagram of the topology of the intelligent agent provided in the second embodiment;
fig. 5 is a state update diagram of all agents provided in the second embodiment over time.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
The invention aims to provide a multi-agent fault-tolerant consistency method and system based on state privacy protection, aiming at the defects of the prior art.
Example one
The embodiment provides a multi-agent fault-tolerant consistency method based on state privacy protection, as shown in fig. 1, including the steps of:
s1, constructing a multi-agent fault-tolerant consistency system model;
s2, processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and S3, performing interactive iterative processing on all processed intelligent agents to enable the state values of all good intelligent agents to be consistent.
The method for multi-agent fault-tolerant consistency based on state privacy protection provided by the embodiment aims to ensure that each node does not directly transmit own state in the process of achieving fault-tolerant consistency of a multi-agent system, and the state value is encrypted by using a homomorphic encryption principle, so that the privacy protection of the node state is realized. The strategy is realized by applying a homomorphic encryption-based scheme to the Q-consistency method.
In the method, each agent scores each moment of the neighbor agent and updates the Q value immediately by comparing the difference value between the agent and the neighbor agent, calculates the weight of each neighbor agent according to the Q value, updates the state value of the agent according to the weight, and reflects the wrong agent. Because the requirement of the existing general technology on network topology is high, the number of error nodes in the neighbor agent is required to be less than half of the number of the whole neighbors, and the method of the embodiment has no such limitation.
A multi-agent fault-tolerant consistency method based on state privacy protection is mainly characterized in that a homomorphic encryption technology is adopted in a Q consistency method to carry out privacy protection on states, and meanwhile, calculation of a reward function in the Q consistency method and updating of states of agents are not affected after the states of the agents are encrypted. Finally, the state values of the good agents are consistent, and the wrong agents are identified.
In step S1, a multi-agent fault-tolerant consistency system model is constructed.
A multi-agent topology is represented by a directed graph G (V, E), where V ═ 1,2, …, n represents a set of agents,
Figure RE-GDA0003193860810000051
representing the connection relationships between agents.
In this embodiment, if agent i can receive information from agent j, agent j is said to be a neighbor of agent i, and the neighbor set of agent i is denoted as NiWhere { j | (j, i) ∈ E }, the state information at time k of agent i is represented as xi(k)。
There are several erroneous agents in agent set V, and the types of erroneous agents include random state values, constant state values, and types with a probability of error.
In step S2, the agents in the constructed system model are processed by a homomorphic encryption algorithm.
Agent i generates a pair of keys (k) by a homomorphic encryption algorithmpi,ksi) Wherein k ispiIs a public key, ksiIs the private key, E (x, k) denotes the encryption algorithm and D (x, k) denotes the decryption algorithm.
The Paillier algorithm is a common homomorphic encryption algorithm, and comprises the following parts:
generating a secret key:
(1) first, two large prime numbers p and q are selected
(2) And n ═ p × q, g ═ n +1
(3) Let λ ═ lcm (p-1, q-1), where lcm (·) is the least common multiple of the two parameters
(4) Let mu be (L (g)λmodn2))-1Wherein
Figure RE-GDA0003193860810000061
(5) In this case, the public key is (n, g) and the private key is (λ, μ)
And (3) encryption process:
as for the plaintext m, there is a clear text m,
Figure RE-GDA0003193860810000062
selecting random number r < n, and encrypting by c-gmrn(modn2)
And (3) decryption process:
the decryption process for the ciphertext c is
Figure RE-GDA0003193860810000063
In step S3, interactive iterative processing is performed on all processed agents, so that the state values of all good agents are consistent.
In the present embodiment, steps S31-S34 are to protect the state privacy during the process of transferring the state value by a homomorphic encryption method between agents, i.e. the schematic diagram shown in fig. 2; steps S35-S40 are the process of any agent update iteration, i.e., the schematic shown in FIG. 3.
The method specifically comprises the following steps:
s31, the intelligent agent i sends the state value x of the intelligent agent iiBy means of its own public key kpiEncrypting to obtain a first encryption result E (x)i,kpi) Agent i encrypts the first encryption result E (x)i,kpi) And its own public key kpiSending the information to the own neighbor agent j;
s32, using the public key k sent by the agent i, the neighbor agent jpiEncrypt its own state value xjObtaining a second encryption result E (x)j,kpi)；
S33, calculating a first encryption result E (x)i,kpi) And a second encryption result E (x)j,kpi) Difference between them, and applying the calculated difference to a random number betajTo the power of the exponent to obtain a third encryption result
Figure RE-GDA0003193860810000064
At this time, the third encryption result is represented as E (β) according to the homomorphic encryption propertyj(xj-xi),kpi) The third encryption result E (beta) is obtainedj(xj-xi),kpi) Sending back to agent i;
s34. the agent i encrypts the third encryption result E (beta)j(xj-xi),kpi) Using its own private key ksiCarrying out decryption operation to obtain a first decryption result betaj(xj-xi) (ii) a Wherein the decryption operation is denoted as D (E (beta)j(xj-xi),kpi),ksi)；
S35, using the first decryption result beta by the agent ij(xj-xi) And weight α to agent jijUpdating the state value of the self to obtain an updated state value x'iExpressed as:
Figure RE-GDA0003193860810000065
wherein, x'iRepresenting an agent iThe state value after the first time of updating; x is the number ofiA value representing a time of day on agent i; alpha is alphaijRepresents the weight of agent i to agent j; x is the number ofjRepresents a state value at a time previous to agent j; omegaiRepresenting random noise; beta is aj(xj-xi) Representing the first decryption result.
S36. mixing betajBy replacement with
Figure RE-GDA0003193860810000071
And repeatedly executing steps S31-S34, the agent i obtains the second decryption result
Figure RE-GDA0003193860810000072
S37, a first decryption result beta is obtainedj(xj-xi) And a second decryption result
Figure RE-GDA0003193860810000073
Calculating a reward value r for agent jijCalculating the comprehensive trust degree according to the obtained reward value;
calculating a reward value r for agent jijExpressed as:
Figure RE-GDA0003193860810000074
wherein r isijRepresenting a prize value;
Figure RE-GDA0003193860810000075
representing the second decryption result.
According to the obtained reward value rijCalculating the comprehensive trust degree, which is expressed as:
Q'ij＝Qij+η(rij-Qij)
wherein Q isij' represents the updated comprehensive trust degree of the node i to the node j; qijRepresenting the comprehensive trust degree of the node i to the node j; η represents the step size.
S38, updating the weight of the agent i to each neighbor agent j through the calculated Q to obtain an updated weight, wherein the updated weight is represented as:
Figure RE-GDA0003193860810000076
wherein, alpha'ijIndicating the weight of agent i to agent j after the update.
S39, using updated weight alpha 'by agent i'ijUpdating its own state value, wherein if agent i is the wrong agent, the own state value is updated according to the type of the error;
agent i uses updated weight α'ijTo update its state value, expressed as:
Figure RE-GDA0003193860810000077
wherein, x "iRepresenting the state value of the agent i after the second update; n is a radical ofjRepresenting a neighbor set for node j.
In the embodiment, the error node updates its own state according to its own error type, such as random update, and maintains an initial value. The system can gradually reduce the weight of the good node to the wrong node according to the algorithm, thereby slowly neglecting the influence of the wrong node, and only updating the state in the good node to realize the state consistency.
S40, repeating the steps S31 to S39 to enable the state values of all good agents to be consistent.
According to the method, the state value of each intelligent agent in the Q consistency algorithm is subjected to privacy protection by using a homomorphic encryption algorithm, and the state value of each neighbor intelligent agent cannot be acquired by encrypting the state value of each intelligent agent at each moment, so that the privacy of each neighbor intelligent agent is protected. Meanwhile, while privacy is protected, wrong agents can be identified through continuous interactive iteration, and finally the state values of all good agents are consistent.
Correspondingly, a multi-agent fault-tolerant consistency system based on state privacy protection is further provided, and comprises:
the building module is used for building a multi-agent fault-tolerant consistency system model;
the processing module is used for processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and the iteration module is used for carrying out interactive iteration processing on all processed intelligent agents so as to enable the state values of all good intelligent agents to be consistent.
Example two
The difference between the multi-agent fault-tolerant consistency method based on state privacy protection provided by the embodiment and the first embodiment is that:
this embodiment will be described by taking 9 agents as an example.
FIG. 4 illustrates a multi-agent fault-tolerant coherent system topology. The system has 9 agents, wherein nodes 0, 1,2 and 3 are wrong agents, the rest are good agents, the types of the wrong agents include random errors and constant errors, and the arc tail of the directed edge is used for representing the neighbor nodes of the arc head.
The agent in fig. 4 is processed through steps S1-S3, and the processing manner is similar to that of the embodiment, which is not repeated herein.
Fig. 5 shows the results of an experiment performed according to the topology of fig. 4, wherein the horizontal axis is a time series and the vertical axis is the state value of each agent. The state values of each agent are recorded at each time. It can be seen that the state values of all good agents slowly tend to agree over time.
The results of the experiment were evaluated as follows:
1. convergence property
As shown in FIG. 5, the state values of all good agents converge to be consistent gradually, because random noise ω is added when the agent updates its state valueiSo that the state value of the last node will cause less disturbance.
2. Applicability of the invention
In the prior art, there is usually a conditional limit that the number of wrong agents in neighbor nodes of good agents cannot exceed half of the total number of neighbors. However, as shown in fig. 4, the number of the error agents in the neighbor nodes of agents No. 4, 7, and 8 is greater than or equal to half of the number of the neighbor nodes. However, according to the algorithm, the nodes can better identify the wrong intelligent agent and enable the states of the good intelligent agent to be consistent.
3. Safety feature
The algorithm shows that the state value of the intelligent agent and the state value of the neighbor are not directly transmitted when the intelligent agent and the neighbor exchange information, but the state value of the intelligent agent and the neighbor exchange information is encrypted through a public key and transmitted. The private key is only obtained by the intelligent agent, so that other intelligent agents cannot obtain the real state value of the intelligent agent. Secondly, because the decryption information obtained by the self contains two unknowns, the specific state value of the neighbor node cannot be deduced; in addition, the reward value of the neighbor node of the intelligent agent can be calculated according to two continuous information transmissions, so that the state of the intelligent agent can be updated.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (10)

1. A multi-agent fault-tolerant consistency method based on state privacy protection is characterized by comprising the following steps:
s1, constructing a multi-agent fault-tolerant consistency system model;
s2, processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and S3, performing interactive iterative processing on all processed intelligent agents to enable the state values of all good intelligent agents to be consistent.
2. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 1, wherein the multi-agent fault-tolerant consistency system model is constructed in step S1, wherein the topology of the multi-agent is represented as: g (V, E), V ═ {1,2, …, n } represents a set of agents,
Figure FDA0003026020360000011
representing the connection relationships between agents.
3. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 2, wherein the processing of the agent in step S2 by the homomorphic encryption algorithm is specifically: the agent generates a pair of keys through a homomorphic encryption algorithm, wherein the keys comprise a public key and a private key.
4. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 3, wherein the step S3 specifically comprises:
s31, the intelligent agent i encrypts the state value of the intelligent agent i through the public key of the intelligent agent i to obtain a first encryption result, and the intelligent agent i sends the first encryption result and the public key of the intelligent agent i to the adjacent intelligent agent j of the intelligent agent i;
s32, the neighbor agent j encrypts the state value of the neighbor agent j by using the public key sent by the agent i to obtain a second encryption result;
s33, calculating the difference value between the first encryption result and the second encryption result, and attaching the calculated difference value to a random number betajThe exponential power of the intelligent agent i to obtain a third encryption result, and sending the obtained third encryption result back to the intelligent agent i;
s34, the intelligent agent i carries out decryption operation on the third encryption result by using a private key of the intelligent agent i to obtain a first decryption result;
s35, the agent i updates the state value of the agent i by using the first decryption result and the weight of the agent j to obtain an updated state value;
s36. mixing betajBy replacement with
Figure FDA0003026020360000012
And repeatedly executing steps S31 to S34, the agent i obtains a second decryption result;
s37, calculating an incentive value of the agent j through the first decryption result and the second decryption result, and calculating comprehensive trust degree according to the acquired incentive value;
s38, updating the weight of the agent i to each neighbor agent j through all the comprehensive trust degrees obtained through calculation to obtain the updated weight;
s39, the intelligent agent i updates the state value of the intelligent agent i by using the updated weight;
s40, repeating the steps S31 to S39 to enable the state values of all good agents to be consistent.
5. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 4, wherein the updated state value obtained in step S35 is represented as:
Figure FDA0003026020360000021
wherein, x'iRepresenting the updated state value of the agent i; x is the number ofiRepresenting a state value of the agent i at the last moment; alpha is alphaijRepresents the weight of agent i to agent j; x is the number ofjRepresents a state value at a time previous to agent j; omegaiRepresenting random noise; beta is aj(xj-xi) Representing the first decryption result.
6. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 5, wherein the reward value of agent j is calculated in step S37 and is represented as:
Figure FDA0003026020360000022
wherein r isijRepresenting a prize value;
Figure FDA0003026020360000023
representing the second decryption result.
7. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 6, wherein the step S37 is to calculate the comprehensive trust degree according to the obtained reward value, which is expressed as:
Qij'＝Qij+η(rij-Qij)
wherein Q isij' represents the updated comprehensive trust degree of the node i to the node j; qijRepresenting the comprehensive trust degree of the node i to the node j; η represents the step size.
8. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 7, wherein the updated weights obtained in step S38 are expressed as:
Figure FDA0003026020360000024
wherein, alpha'ijIndicating the weight of agent i to agent j after the update.
9. The multi-agent fault-tolerant consistency method based on state privacy protection as claimed in claim 8, wherein the agent i updates its state value with the updated weight in step S39, which is expressed as:
Figure FDA0003026020360000031
wherein, x "iIndicating the state value of agent i after the second update.
10. A multi-agent fault-tolerant consistency system based on state privacy protection, comprising:
the building module is used for building a multi-agent fault-tolerant consistency system model;
the processing module is used for processing the intelligent agent in the constructed system model through a homomorphic encryption algorithm;
and the iteration module is used for carrying out interactive iteration processing on all processed intelligent agents so as to enable the state values of all good intelligent agents to be consistent.
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