Gaussian mixture distribution homomorphic encryption fusion method based on key information packaging

Abstract

The invention particularly relates to a Gaussian mixture distribution homomorphic encryption fusion method based on key information packaging. The method comprises the following steps: establishing a state equation of target motion and a sensor measurement model; predicting and updating a target state by using a Gaussian mixture probability hypothesis density filter to obtain posterior probability density distribution of each sensor node, and performing pruning and merging processing to obtain a target posterior estimation Gaussian set; converting a mean value and a covariance in the posteriori estimation Gaussian set of each sensor node into an information vector and a precision matrix; uniformly quantizing the information vector and the precision matrix, and encrypting quantized data through a Paillier homomorphic encryption method; and transmitting the encrypted data to a fusion center for geometric mean fusion, and carrying out decryption and inverse quantization on the encrypted data by the fusion center to obtain a state estimation result of the target. According to the method, under the condition that the original fusion precision is not lost, the leakage risk of key information in the fusion process is further reduced.

Description

Technical Field

[0001] This invention relates to the field of multi-sensor information fusion, specifically to a Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation. Background Technology

[0002] With the rapid development of multi-sensor networking systems, information fusion technology is increasingly being applied to state estimation problems. Arithmetic mean (AA) and geometric mean (GA) are two typical methods that have attracted great attention from researchers at home and abroad. Among them, GA fusion has the advantages of high computational efficiency, strong recovery of sensors (such as false alarms), and fault tolerance for arbitrary degree of inter-node correlation. This fusion algorithm has shown remarkable performance in the design of single-sensor and multi-sensor estimators.

[0003] Existing research often focuses on fusing key information acquired by sensor nodes, such as the position estimate and covariance estimate of the tracked target. This information needs to be transmitted via inter-sensor communication networks before fusion. In reality, exposed channels are frequently subject to eavesdropping attacks, a preliminary step in spoofing and denial-of-service attacks. Attackers can easily eavesdrop on critical data packets transmitted over these channels, leading to the leakage of significant amounts of sensitive information and subsequent, more targeted network attacks. Therefore, to protect the privacy and security of multi-sensor network data and prevent more destructive malicious attacks at the source, the Gaussian mixture probability distribution mean fusion method urgently needs further optimization to address the high risk of critical information leakage.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] To address the issue of easy leakage of critical information during sensor fusion, this invention provides a Gaussian mixture distribution homomorphic encryption fusion method based on critical information encapsulation.

[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to a first aspect of the present invention, a Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation is provided, the method comprising: Establish the state equation of the target motion and the sensor measurement model; The target state is predicted and updated using a Gaussian mixture probability hypothesis density filter to obtain the posterior probability density distribution of each sensor node. The target posterior estimation Gaussian set is then obtained through pruning and merging. The mean and covariance of the posterior estimates of each sensor node in the Gaussian set are transformed into an information vector and a precision matrix. The information vector and precision matrix are uniformly quantized, and the quantized data is encrypted using the Paillier homomorphic encryption method. The encrypted data is transmitted to the fusion center for geometric mean fusion. The fusion center decrypts and dequantizes the encrypted data to obtain the state estimation result of the target.

[0008] In some exemplary embodiments, the state equation of the target motion and the sensor measurement model are expressed as follows:

[0009]

[0010] In the state equation, It is a state transition matrix, which represents the transformation of the target state from the previous time step to the current time step; This represents systematic error; in the measurement equation, It is a measurement vector used to update the system state value; Characterization measurement transformation matrix; For measurement errors, both systematic errors and measurement errors are assumed to be independent Gaussian white noise. In some exemplary embodiments, the step of using a Gaussian mixture probability hypothesis density filter to predict and update the target state, and obtaining the posterior probability density distribution of each sensor node, specifically involves: The posterior density function in the Gaussian mixture probability hypothesis density filter is estimated by recursion using the mean, weights, and covariance of the Gaussian mixture. The intensity function is given by the form of a weighted sum of intensity functions.

[0011] In the formula, For a set of sensor network nodes, , representing the first The node of the first The weights of the Gaussian components, , express Follow the mean The covariance is Gaussian distribution; Regarding the first Each node, in The one-step prediction probability density distribution at time t is expressed as:

[0012] In the formula, The intensity function predictions representing surviving targets, derived targets, and newly formed targets are all in Gaussian mixture form; exist The posterior probability density distribution at time t consists of undetected terms and detected terms:

[0013] In the formula, , Let be the probability of the sensor detecting the target, assuming that all sensor nodes are the same.

[0014] In some exemplary embodiments, the step of obtaining the target posterior estimation Gaussian set through pruning and merging processes specifically involves: .

[0015] In some exemplary embodiments, the formula used to transform the mean and covariance of the posterior estimate Gaussian set of each sensor node into an information vector and a precision matrix is ​​as follows:

[0016] in, For the precision matrix, For information vectors, For the average transmission value, For covariance. In some exemplary embodiments, the encryption of the quantized data using the Paillier homomorphic encryption method specifically involves: The precision matrix is ​​calculated according to the predefined quantization strategy. and information vector Obtain by uniform quantization The gateway generates and broadcasts the key for this moment to each node. Nodes 1 and 2 according to Paillier homomorphic encryption was applied to the quantized information set to obtain:

[0017] In the formula, Indicates to To perform Paillier homomorphic encryption, encrypting a matrix means encrypting each element of the matrix individually. In some exemplary embodiments, transmitting the encrypted data to the fusion center for geometric mean fusion specifically involves:

[0018] .

[0019] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation as described in the first aspect.

[0020] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation described in the first aspect above.

[0021] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation as described in the first aspect by executing the executable instructions.

[0022] The Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation provided in the embodiments of the present invention transforms the fusion object through information encapsulation and transmits the homomorphically encrypted information, satisfying semantic security. Furthermore, by changing the information transmission type, it confuses eavesdroppers' inherent understanding of the fused transmission information, further reducing the risk of leakage of key information during the fusion process without sacrificing the original fusion accuracy. This method is applicable to information fusion between multiple sensors and better meets the current development needs of related fields. It should be understood that the above general description and the following detailed description are merely exemplary and explanatory and do not limit the present invention. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0024] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0025] Figure 2 This is a simulation scenario of an embodiment of the method of the present invention.

[0026] Figure 3These are simulation tracking results from embodiments of the method of this invention.

[0027] Figure 4 These are the simulation accuracy results of the embodiments of the method of the present invention. Detailed Implementation

[0028] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0029] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0030] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation. Based on a Gaussian mixture filter-based GA fusion algorithm, this method aims to transform the mean and covariance of the original fusion object into an information vector and a precision matrix, respectively, through information encapsulation, followed by homomorphic encryption before information transmission and fusion. This further reduces the risk of key information leakage during the fusion process without sacrificing the original fusion accuracy. (Reference) Figure 1 As shown, the specific steps may include: Step 1: Establish the state equation for the target motion: (1) The sensor measurement model is modeled as follows: (2) In the formula, It is a state transition matrix, which represents the transformation of the target state from the previous time step to the current time step; This represents systematic error (noise). In the measurement equation, It is a measurement vector used to update the system state value; Characterization measurement transformation matrix; The measurement error (noise) is assumed to be independent Gaussian noise.

[0031] Step 2: Perform filtering estimation using a Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter. In this embodiment, GM-PHD filtering is used for target state prediction and updating. The posterior density function in this filter is estimated by recursion using the mean, weights, and covariance of the Gaussian mixture. The intensity function is given in the form of a weighted sum of intensity functions. (3) In the formula, For a set of sensor network nodes, , representing the first The node of the first The weights of the Gaussian components, , express Follow the mean The covariance is The Gaussian distribution.

[0032] The system in The one-step prediction probability density distribution at time t is expressed as: (4) In the formula, The intensity function predictions representing surviving targets, derived targets, and newly formed targets are all in Gaussian mixture form. (5) (6) (7) In the formula, This indicates the probability of the target surviving.

[0033] The system in The posterior probability density distribution at time t consists of undetected terms and detected terms: (8) In the formula, , Let be the probability of the sensor detecting the target, assuming that all sensor nodes are the same.

[0034] The posterior probability density distributions of each sensor node are pruned and merged to obtain... The Gaussian set of the posterior estimate of the target at time: (9) Step 3: Use homomorphic encryption GA fusion based on key information encapsulation to fuse the information from each sensor node, and transmit it to the gateway for decryption. Taking two sensor nodes as an example, the GA fusion result is: (10) In the formula, (11) (12) (13) (14) In order to avoid directly transmitting the mean during the fusion process Covariance Key information, such as [specific information], is transformed into other forms through information encapsulation for transmission. This method utilizes the characteristics of GA fusion under GM-PHD filters to convert it into a precision matrix. and information vector ,Right now (15) exist At any given time, the precision matrix is ​​adjusted according to the pre-defined quantization strategy. and information vector Obtain by uniform quantization The gateway generates and broadcasts the key for this moment to each node. Nodes 1 and 2 according to Paillier homomorphic encryption is applied to the quantized information set to obtain (16) In the formula, Indicates to Performing Paillier homomorphic encryption on a matrix means encrypting each element of the matrix individually. Because Paillier homomorphic encryption is correct for both homomorphic addition and homomorphic scalar multiplication, the fusion of information encapsulation and the homomorphically encrypted GA is transformed into... (17) (18) The decryption formula is as follows: (19) (20) In the formula, Indicates to Perform the decryption operation. For inverse quantification strategy, where Since equal-weighted parameters do not involve critical information, they can be transmitted directly. The parameters can be calculated using the original formula after decoding the original mean and covariance; therefore, there are no parameters that cannot be calculated or obtained. Thus, the gateway can ultimately obtain the sensor network's state estimate of the target at the current moment. (twenty one) This method is an extension of the Paillier homomorphic encryption method, and therefore satisfies the standard security definition of encryption schemes: semantic security, that is, indistinguishability under Chosen Plaintext Attack (IND-CPA), which means that the ciphertext will not reveal any information about the plaintext, and the scheme can be reduced to the decision composite residue hypothesis.

[0035] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0036] Example 1 Step 1: Set up the simulation scene.

[0037] The simulation scene is set to a two-dimensional Cartesian coordinate system, and the detection area is... The target motion model is a constant acceleration (CA) motion model, as shown below: (twenty two) In the formula, Indicates the sampling time interval. , respectively indicating that the target is in Position, velocity, acceleration and axial direction Position, velocity, and acceleration along the axis, in units of , Indicates process noise. Its power spectral intensity (twenty three) (twenty four) sensor nodes The measurement model is (25) In the formula, , respectively representing the target in Axial position measurement and Position measurement in the axial direction, in units of , Indicates measurement noise (26) In the formula, sensor nodes The standard deviation of measurement noise.

[0038] In this simulation scenario, the specific parameter settings are as follows. , The number of sensor nodes is 2, corresponding to Therefore (27) (28) The total detection time is Twelve tracking targets are set, and their status information and tracking start and end times are shown below: Table 1. Initial parameters and start and end times of the target

[0039] Step 2: Determine the state estimate of the GM-PHD filter.

[0040] Set the target survival probability Sensor node detection probability clutter density (That is, an average of 30 clutter echoes per scan), pruning threshold Merge threshold Maximum number of Gaussian terms .

[0041] The initial intensity function is (29) In the formula, the number of Gaussian components weight The state and error covariance matrices are (30) The predicted newborn target intensity function is (31) In the formula, (32) The sensor node uses the GM-PHD filtering method to estimate the target state, obtaining the Gaussian set of the local state estimate of the target at the current time. (33) Step 3: Multi-sensor fusion parameter estimation.

[0042] Step 3-1: Information Encapsulation and Homomorphic Encryption pass Obtain the local state estimate set of the target after object transformation: (34) A uniform quantization strategy is used to prepare data before homomorphic encryption. Each element in Using the same quantization strategy ,Right now (35) In the formula, This is a set of quantization thresholds, specifically taking the values... Therefore, the quantification level .

[0043] Paillier homomorphic encryption is used to further encapsulate the information, specifically for the quantized information set. Each element in Encrypt separately to obtain The weight information is transmitted together to the fusion center for encrypted fusion according to equations (17), (18), and (13).

[0044] Step 3-2: Decryption and Inverse Quantization The fusion center transmits the fusion result to the gateway. Based on the generated private key, the gateway decrypts and inverses the quantization according to equations (19) and (20) to obtain the sensor network's state estimation result of the target at the current moment: (36) Step 4: Performance index comparison.

[0045] To demonstrate the superiority of the proposed method, existing target tracking and information fusion methods are selected for comparison, including single-sensor GM-PHD filtering results (Single-GM-PHD) and GA fusion results after dual-sensor GM-PHD filtering (GA-GM-PHD). In the field of multi-target tracking, evaluating the performance of algorithms requires considering not only the target's state error but also the cardinality estimation error of the set. Therefore, this method uses the Optimal Sub-PattenAssignment (OSPA) distance as a comparison metric, defined on two sets, given the set... and ,and , can be obtained The OSPA distance of order is: (37) In the formula, the cutoff distance is taken. This determines the importance of the target base estimation accuracy relative to the position estimation accuracy, and the order. This determines the sensitivity of the metric to statistical outliers. Indicates the cutoff metric. express The set of all permutations of .

[0046] To reduce the uncertainty of the simulation results, the number of Monte Carlo experiments was set to 100.

[0047] Table 2 Average performance of different methods

[0048] The performance comparison of this method with other methods is evident in the simulation. This method shows a significant performance improvement over Single-GM-PHD, and its target tracking performance is comparable to that of GA-GM-PHD without information encapsulation and encryption. This is because this method incurs losses during data quantization, and the presence of noise may lead to more accurate results after recovering the quantized data. However, the Paillier homomorphic encryption method used in this method satisfies semantic security and confuses eavesdroppers' preconceived notions about the fused transmission information by changing the information transmission type, thus significantly improving security performance. Therefore, the simulation results demonstrate the effectiveness of this method in sensor information fusion.

[0049] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments.

[0050] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0051] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0052] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0053] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation, characterized in that, The method includes: Establish the state equation of the target motion and the sensor measurement model; The target state is predicted and updated using a Gaussian mixture probability hypothesis density filter to obtain the posterior probability density distribution of each sensor node. The target posterior estimation Gaussian set is then obtained through pruning and merging. The mean and covariance of the posterior estimates of each sensor node in the Gaussian set are transformed into an information vector and a precision matrix. The information vector and precision matrix are uniformly quantized, and the quantized data is encrypted using the Paillier homomorphic encryption method. The encrypted data is transmitted to the fusion center for geometric mean fusion. The fusion center decrypts and dequantizes the encrypted data to obtain the state estimation result of the target.

2. The method according to claim 1, characterized in that, The state equation for the target motion and the sensor measurement model are expressed as follows: In the state equation, It is a state transition matrix, which represents the transformation of the target state from the previous time step to the current time step; This represents systematic error; in the measurement equation, It is a measurement vector used to update the system state value; Characterization measurement transformation matrix; For measurement errors, both systematic errors and measurement errors are assumed to be independent Gaussian white noise.

3. The method according to claim 2, characterized in that, The method of using a Gaussian mixture probability hypothesis density filter to predict and update the target state, and obtaining the posterior probability density distribution of each sensor node, is as follows: The posterior density function in the Gaussian mixture probability hypothesis density filter is estimated by recursion using the mean, weights, and covariance of the Gaussian mixture. The intensity function is given by the form of a weighted sum of intensity functions. In the formula, For a set of sensor network nodes, , representing the first The node of the first The weights of the Gaussian components, , express Follow the mean The covariance is Gaussian distribution; Regarding the first Each node, in The one-step prediction probability density distribution at time t is expressed as: In the formula, The intensity function predictions representing surviving targets, derived targets, and newly formed targets are all in Gaussian mixture form; exist The posterior probability density distribution at time t consists of undetected terms and detected terms. composition: In the formula, , Let be the probability of the sensor detecting the target, assuming that all sensor nodes are the same.

4. The method according to claim 3, characterized in that, The process of obtaining the target posterior estimate Gaussian set through pruning and merging is as follows: 。 5. The method according to claim 4, characterized in that, The formula used to transform the mean and covariance of the posterior estimate Gaussian set of each sensor node into an information vector and a precision matrix is ​​as follows: in, For the precision matrix, For information vectors, For the average transmission value, For covariance.

6. The method according to claim 5, characterized in that, The encryption of the quantized data using the Paillier homomorphic encryption method specifically involves: The precision matrix is ​​calculated according to the predefined quantization strategy. and information vector Obtain by uniform quantization The gateway generates and broadcasts the key for this moment to each node. Nodes 1 and 2 according to Paillier homomorphic encryption was applied to the quantized information set to obtain: In the formula, Indicates to To perform Paillier homomorphic encryption, encrypting a matrix means encrypting each element of the matrix individually.

7. The method according to claim 6, characterized in that, The process of transmitting the encrypted data to the fusion center for geometric mean fusion is as follows: 。 8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the Gaussian mixture distribution homomorphic encryption fusion method based on key information encapsulation as described in any one of claims 1 to 7 by executing the executable instructions.

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