CN105631360A - Private data aggregating method based on multidimensional decomposition in sensor network - Google Patents

Abstract

The invention discloses a method for gathering private data based on multidimensional decomposition in a sensor network. In sensor networks, the general differential privacy method based on Laplacian noise mechanism may cause over-perturbation phenomenon due to large global sensitivity, thus destroying the utility of pooled data. The method proposed by the invention realizes differential privacy protection by decomposing a single data stream into exponentially weighted multi-dimensional data streams, and adding independent noise to each dimensional data stream according to the local sensitivity and privacy budget of each dimension. Compared with the pooling process under the general Laplacian noise mechanism, this method provides better data utility while ensuring the same degree of user privacy.

Description

Privacy data aggregation method based on multi-dimensional decomposition in sensor network

Technical field:

The invention belongs to the field of privacy protection, and in particular relates to a method for gathering private data based on multidimensional decomposition in a sensor network.

Background technique:

Various sensors in many new sensor networks (such as smart grids, participatory perception systems, etc.) collect time-series data related to users or the environment and transmit them to the server. High-level statistical analysis and data mining operations. On the one hand, the data aggregation operation reduces data redundancy and transmission volume, thereby reducing energy consumption and data delay time. On the other hand, the data aggregation operation only transmits key or purpose-related data to upper-layer nodes or servers, which also reduces the possibility of fine-grained data being leaked to a certain extent. Although fine-grained information cannot be directly accessed, detailed monitoring results may still be inferred from the results of changing real-time data aggregation. For example, residential electricity consumption information collected by smart meters in smart grids can be used to infer the opening and closing of equipment. Status, continuous calorie data collected by wearable sensors can reveal the user's physical condition. At present, there have been a lot of valuable research on the privacy protection problem of data aggregation process in sensor networks. Among them, the protection method based on differential privacy ensures that the aggregation results of two adjacent data sets are very similar, making it difficult for attackers to manipulate aggregation. The results infer a single data record, providing good data utility while maintaining user privacy. Generally, the differential privacy method based on the Laplacian noise mechanism may cause over-disturbance due to the large global sensitivity, thus destroying the utility of the data.

Invention content:

The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method for gathering private data based on multidimensional decomposition in a sensor network. This method can improve the utility of gathering data while ensuring the same level of user privacy as the general method. .

In order to achieve the above object, the present invention adopts following technical scheme to realize:

The privacy data aggregation method based on multi-dimensional decomposition in the sensor network first adds the noise generated by the multi-dimensional decomposition noise mechanism to the monitoring data generated in each time slot, and then uses the generated data for privacy data aggregation, which specifically includes the following steps:

Step1 initialization: Given the dimension base b and the global sensitivity g, calculate the number of dimensions d, and calculate the local sensitivity _si on each dimension, where i=1,2,...,d are the decomposed dimensions;

Step2 Data acquisition and decomposition: Obtain the monitoring data directly through the underlying hardware equipment, obtain the original monitoring value X _t corresponding to each time slot t, and decompose it into d-dimensional data

Step3 Data perturbation: According to the local sensitivities _si and privacy budget ε in each dimension, generate d noise components that obey the Laplace distribution and are independent of each other and add it to Noise results on

Step4 privacy aggregation: combine the d-dimensional aggregation results of the previous time slot and the d-dimensional noise result of the current slot Get the d-dimensional aggregation result of the current time slot

Step5 data synthesis and release: Noise the results of each dimension according to different dimension weights The aggregation result R _t of privacy protection is obtained through synthesis and released to the outside world.

The further improvement of the present invention is that the specific operation of Step1 is as follows: the dimension base b is a natural number greater than or equal to 2, the global sensitivity g is the maximum estimated value of the monitoring data, and the expression of the dimension number d is

The expression of local sensitivity s _i in each dimension is

Among them, the expression (2) indicates that the local sensitivity on the lower dimension i=1,2,...,d-1 is b-1, and the sensitivity on the highest dimension i=d is determined by the dimension base b, The global sensitivity g and the number of dimensions d are jointly determined.

A further improvement of the present invention is that the original monitoring value X _t in Step2 is:

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

in, is the i-th dimension component of the original monitoring value X _t , and b ^i-1 is the dimension weight of the i-th dimension.

The further improvement of the present invention is that the specific operation of Step3 is: generate d noise components that satisfy ε-differential privacy and are independent of each other Require Obey the probability density function as formula (4) Laplace distribution:

$\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ~</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

Among them, n is the noise variable, and the parameter λ is jointly determined by the local sensitivity _si and the privacy budget ε in the corresponding dimension, namely

Noise results in each dimension The expression is

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

in, is the i-th dimension component of the original monitoring value X _t , is the noise component in the corresponding dimension.

The further improvement of the present invention is that Step4 obtains the aggregation result of each dimension privacy protection for

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

in, is the aggregation result of the i-th dimension in the previous time slot, and the aggregation result of each dimension when time slot t=0 is 0.

The further improvement of the present invention is that the specific operation of Step5 is to noiseize the results of each dimension according to different dimension weights w _i After the synthesis, the aggregated result R _t released to the outside world is

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Among them, b ^i-1 represents the dimension weight w _i of the i-th dimension;

Restoring the privacy protection monitoring value Y _t from the published aggregation results is

_Yt = _{Rt - Rt-1} (16).

With respect to prior art, the present invention adopts following technical solution to realize:

The privacy data aggregation method based on multi-dimensional decomposition in the sensor network described in the present invention decomposes a single data stream into multi-dimensional data streams with exponential weights, and adds Independent noise achieves differential privacy protection. Compared with the pooling process under the general Laplacian noise mechanism, this method provides better data utility while ensuring the same degree of user privacy.

Description of drawings:

Figure 1 is a schematic diagram of multi-dimensional decomposition noise mechanism;

Figure 2 is a schematic diagram of the aggregation process of private data based on multidimensional decomposition;

Figure 3 is a comparison diagram of the noise variance of the multi-dimensional decomposition noise mechanism and the ordinary Laplace noise mechanism under different global sensitivities;

Figure 4 is a comparison of the average relative error between multidimensional decomposition data aggregation and ordinary Laplacian data aggregation under different privacy budgets.

detailed description:

The present invention will be described in further detail below in conjunction with the accompanying drawings.

The privacy data aggregation method based on multidimensional decomposition in the sensor network of the present invention comprises the following steps:

Step1 initialization: given the dimension base b (generally 2, which is consistent with the computer binary representation) and the global sensitivity g (the maximum value of the sensor monitoring value can be taken), the obtained dimension d is

The local sensitivity s _i (where i=1,2,…,d) in each dimension is

Step2 Data Acquisition and Decomposition: Referring to Figure 2, directly obtain the monitoring data through the underlying hardware device, obtain the original monitoring value X _t corresponding to each time slot t, and decompose it into d-dimensional data, thus It can be expressed as

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

in, is the i-th dimension component of the original monitoring value X _t , and b ^i-1 is the dimension weight of the i-th dimension.

Step3 Data perturbation: Referring to Figure 1, according to the local sensitivity _si and privacy budget ε in each dimension, generate d noise components that satisfy ε-differential privacy and are independent of each other The Laplace distribution that obeys the probability density function as expression (4):

$\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ~</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, n is the noise variable, and the parameter λ is jointly determined by the local sensitivity _si and the privacy budget ε in the corresponding dimension, namely In practical applications, random distribution functions such as geometric distribution and Gaussian distribution can be used to replace Laplace distribution, and the expected effect can also be achieved;

Noise results in each dimension The expression is

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

in, is the i-th dimension component of the original monitoring value X _t , is the noise component in the corresponding dimension;

Step4 Privacy aggregation: when time slot t=0, the aggregation results of each dimension is 0; when slot t>0, according to the aggregation result of the i-th dimension of the previous slot and the noised result of the i-th dimension of the current slot Get the aggregation results of privacy protection in each dimension for

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Step5 data synthesis and release: refer to Figure 2, after the privacy calculation of Step4, the results of each dimension are noised according to different dimension weights The aggregation result R _t (the aggregation target can be summation or counting) released externally can be obtained as follows:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; d</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Among them, b ^i-1 represents the dimension weight w _i of the i-th dimension;

Restoring the privacy protection monitoring value Y _t from the published aggregation results is

Y _t =R _t -R _t-1 (8)

Referring to Figure 3, given that the global sensitivity range g is an integer between 2 and 2000, the privacy budget is ε=2, and the dimension bases b are randomly selected to be 3, 8 and 1000 respectively, the multidimensional decomposition noise mechanism used in the present invention generates The variance of the noise is generally smaller than the variance of the noise generated by the ordinary Laplace noise mechanism, and the small noise variance can bring better data utility, which shows that the multidimensional decomposition noise mechanism in the present invention is more effective than the existing mechanism. sexually superior.

Referring to Figure 4, given the same global sensitivity g of 4083, as the privacy budget ε increases, the average relative error generated by multidimensional decomposition data aggregation and ordinary Laplacian data aggregation gradually decreases. This reflects the nature of differential privacy, where there is a trade-off between privacy and utility, i.e., the smaller the privacy budget, the better the data privacy and the lower the data utility, and vice versa. The dimension base b is randomly selected as 2 and 2042. Given the same privacy budget, the average relative error generated by multidimensional decomposition data aggregation is lower than that of ordinary Laplace data aggregation, which reflects that the multidimensional decomposition data aggregation in the present invention can bring more Good utility.

In practical applications, the cascaded buffer counting method can be integrated to improve the performance of the aggregation process by using the characteristics of multidimensional decomposition.

Claims (6)

1. The privacy data aggregation method based on multi-dimensional decomposition in the sensor network is characterized in that noise generated by a multi-dimensional noise decomposition mechanism is added to monitoring data generated in each time slot, and then the generated data is utilized to carry out privacy data aggregation, and the method specifically comprises the following steps:

step1 initializes: given a dimension base b and a global sensitivity g, calculating a dimension degree d, and calculating a local sensitivity s on each dimension_iWhere i is 1,2, …, d is the dimension after decomposition;

step2 data acquisition and decomposition: through the bottom layer hardDirectly acquiring monitoring data by piece equipment to obtain an original monitoring value X corresponding to each time slot t_tAnd decompose it into d-dimensional data

Step3 data perturbation: according to local sensitivity s in each dimension_iAnd a privacy budget for generating d noise components which are subject to a Laplace distribution and are independent of each otherAnd add it toForm a noise result

Step4 privacy Convergence: combining d-dimensional convergence results of last time slotAnd d-dimensional noise results of the current time slotObtaining d dimension convergence result of current time slot

Step5 data synthesis and release: denoising results of each dimension according to different dimension weightsComprehensively obtain and externally release a convergence result R of privacy protection_t。

2. The private data aggregation method based on multidimensional decomposition in the sensor network as claimed in claim 1, wherein Step1 is specifically operated as follows: the dimensionality base number b is a natural number which is more than or equal to 2, the global sensitivity g is the maximum estimation value of monitoring data, and the expression of the dimensionality d is

Local sensitivity s in each dimension_iIs expressed as

Where expression (2) indicates that the local sensitivity in the lower dimension i 1, 2.., d-1 is b-1, while the sensitivity in the highest dimension i d is determined jointly by the dimension base b, the global sensitivity g, and the dimension number d.

3. The private data gathering method based on multidimensional decomposition in sensor network as claimed in claim 1, wherein the original monitoring value X in Step2_tComprises the following steps:

$X_t=\underset{i=1}{\overset{d}{\&Sigma;}}{x}_t^i{b}^{i-1}---\left(3\right)$

wherein,is the original monitoring value X_tThe ith-dimensional component of (c), b^i-1Is the dimension weight of the ith dimension.

4. The private data aggregation method based on multidimensional decomposition in the sensor network as claimed in claim 1, wherein Step3 is specifically operated as follows: generating d noise components satisfying differential privacy and being independent of each otherRequire thatObeying the probability density function to a laplacian distribution of equation (4):

$Lap\left(\mathrm{\&lambda;}\right)~\frac{1}{2\mathrm{\&lambda;}}{e}^{-\frac{\left|n\right|}{\mathrm{\&lambda;}}}---\left(4\right)$

where n is a noise variable and the parameter λ is determined by the local sensitivity s in the corresponding dimension_iDetermined in conjunction with the privacy budget, i.e. $\mathrm{\&lambda;}=\frac{s_i}{\mathrm{\&epsiv;}};$

Noisy results in various dimensionsIs expressed as

$y_t^i=x_t^i+n_t^i---\left(5\right)$

Wherein,is the original monitoring value X_tThe (d) th-dimensional component of (a),is the noise component in the corresponding dimension.

5. The method for gathering private data based on multidimensional decomposition in sensor network as claimed in claim 1, wherein Step4 obtains the gathering result of privacy protection in each dimensionIs composed of

$r_t^i=r_{t-1}^i+y_t^i---\left(6\right)$

Wherein,is the convergence result of the ith dimension of the last time slot, and the convergence result of each dimension when the time slot t is 0Is 0.

6. The method for gathering private data based on multidimensional decomposition in sensor network as claimed in claim 1, wherein Step5 is specifically operated to weight w according to different dimensions_iFor each dimension of noise resultsComprehensively obtain a convergence result R published externally_tIs composed of

$R_t=\underset{i=1}{\overset{d}{\&Sigma;}}{r}_t^i{b}^{i-1}---\left(7\right)$

Wherein, b^i-1Dimension weight w representing the ith dimension_i；

The monitoring value Y after privacy protection is restored from the published convergence result_tIs composed of

Y_t＝R_t-R_t-1(8)。