WO2022107284A1

WO2022107284A1 - Concealment device, concealment method, and program

Info

Publication number: WO2022107284A1
Application number: PCT/JP2020/043234
Authority: WO
Inventors: 聡長谷川; 尭之三浦
Original assignee: 日本電信電話株式会社
Priority date: 2020-11-19
Filing date: 2020-11-19
Publication date: 2022-05-27
Also published as: JPWO2022107284A1; JP7509232B2

Abstract

This concealment device according one embodiment of the present invention is for concealing data through stochastic randomization. The concealment device has: a conversion unit that converts the data to a member of a binary vector set in which a Hamming distance between any two binary vectors is predetermined L or less; and a randomization unit that randomizes elements of the member into 0 or 1 such that each of the elements is in compliance with p=(e^ε/L)/(e^ε/L+1) when the value of the element is 1 and q=1/(e^ε/L+1) (where ε represents a parameter indicating the intensity of privacy) when the value of the element is 0.

Description

Concealment device, concealment method and program

The present invention relates to a concealment device, a concealment method, and a program.

A technique for concealing individual data from a database by a probabilistic method is known (for example, Non-Patent Documents 1 and 2). The techniques described in Non-Patent Documents 1 and 2 randomize data according to a defined probability and have been shown to meet certain privacy criteria called local differential privacy. As a method of randomizing data, there are cases where the input data set and the output data set are the same and different, and the techniques described in Non-Patent Documents 1 and 2 are cases where the input data set and the output data set are different. Corresponds to.

Here, in the techniques described in Non-Patent Documents 1 and 2 described above, a one-dimensional input is converted into a D-dimensional binary vector by one-hot notation, and randomization is performed for each value of each element of the vector. Therefore, the size of the output data set is 2D with respect to the size ^D of the input data set, and the amount of spatial complexity is not good.

One embodiment of the present invention has been made in view of the above points, and an object thereof is to realize data concealment with a good amount of spatial calculation.

In order to achieve the above object, the concealment device according to the embodiment is a concealment device that conceals data by probabilistic randomization, and the humming distance between any two binary vectors is such that the data is concealed. When the value of the element is 1, p = (e ^{ε / L} ) / (e ^ε / L) of the conversion unit that converts to the element of the binary vector set that is less than or equal to the predetermined L, and each element of the element. +1), a randomization unit that randomizes to 0 or 1 so as to follow q = 1 / (e ^{ε / L} +1) (where ε is a parameter representing privacy strength) when the value of the element is 0. Have.

It is possible to realize data concealment with a good amount of spatial complexity.

It is a figure which shows an example of the hardware composition of the concealment apparatus which concerns on this embodiment. It is a figure which shows an example of the functional structure of the concealment apparatus which concerns on this embodiment. It is a flowchart which shows an example of the flow of the data concealment processing. It is a flowchart which shows an example of the flow of the process of creating a vector set in which the Hamming distance is at most L or less.

Hereinafter, an embodiment of the present invention will be described. In this embodiment, a concealment device 10 that realizes data concealment with a good spatial complexity will be described.

<Theoretical composition>
First, the theoretical configuration of this embodiment will be described.

The data x ∈ X contained in the data set X = [D] = {0, ..., D-1} having D kinds of values is input to the stochastic mechanism M: X → Z, and the output z ∈ Z is obtained. Shall get. It is assumed that the stochastic mechanism M: X → Z has a conditional probability Pr [z | x] for the input x ∈ X and the output z ∈ Z, and the randomization process is performed according to the conditional probability.

In the techniques described in Non-Patent Documents 1 and 2 described above, in order to convert the input x into a D-dimensional binary vector, the input x is input to Encode: X → {0,1} ^D. However, the output is a D-dimensional binary vector in one-hot notation. The vector in one-hot notation means a vector in which only one component is 1 and the remaining components are all 0. That is, Vector (x) = (0, ..., 0, 1, 0, ..., 0) = b with respect to the input x (only a certain i-th element is 1, and the others are 0). Vector).

Further, the randomization process Perturb (b) = b'performs a randomization (disturbance) process so as to follow the probability shown in the following equation (1) for each value of each element of the vector.

Here, b [i] is the value of the i-th element of the vector b.

That is, when b [i] = 1, the probability p is Perturb (b [i]) = b'[i] = 1, and the probability 1-p is Perturb (b [i]) = b'[i] =. Randomize to 0. On the other hand, when b [i] = 0, the probability q is Perturb (b [i]) = b'[i] = 1, and the probability 1-q is Perturb (b [i]) = b'[i]. Randomize to = 0.

At this time,

If so, it is known to satisfy the ε-local differential privacy. Note that ε is a parameter representing the privacy strength.

In this embodiment, the techniques described in Non-Patent Documents 1 and 2 are improved and extended, and any two vectors a among the D-dimensional vectors having the output of the Encode as {0,1} as elements a. It is assumed that the Hamming distance of, b is at most L or less. In addition, when performing randomization processing according to the probability shown in the above equation (1),

And. Note that L is an adjustable parameter.

Thereby, in the present embodiment, by adjusting L, the amount of spatial calculation can be reduced as compared with the techniques described in the above-mentioned Non-Patent Documents 1 and 2. Therefore, it is possible to increase the size of the input data set that can be handled. In addition, the strength of randomization can be freely manipulated.

Here, the reason why the method of this embodiment satisfies the ε-local differential privacy will be described. Intuitively, the local differential privacy is "when looking at the output obtained by inputting any two data into the mechanism M, it is difficult to distinguish which input the output was obtained from." It is defined as follows for the mechanism M.

(Definition) Stochastic mechanism M: X → Z satisfies ε-local differential privacy means that the following equation (2) holds for any two inputs x _a and x _b ∈ X. ..

∀z ∈ Z: Pr [M (x _a ) = z] ≤ e ^ε Pr [M (x _b ) = z] (2)
For details of the above definition, refer to Reference 1 "Tianhao Wang, Jeremiah Blocki, Ninghui Li, and Somesh Jha. Locally differentially private protocols for frequency estimation. In 26th USENIX Security Symposium, pp. 729-745, 2017. Please refer to "."

The mechanism M in the above definition corresponds to Perturb. Randomization is performed for each element value of the vector by the above equation (1), but in the above equation (2), the ratio of the probability that the randomization results of any two inputs match is suppressed by e ^ε . It represents what must be done. Therefore, the probability ratio can be suppressed when the vectors input to the Perturb are as close as possible to each other. Specifically, if the Hamming distance between the vectors input to Perturb is L or less, p = (e ^{ε / L} ) / (e ^{ε / L} +1), q = 1 / (e ^{ε / L} +1). When, ε-local differential privacy can be satisfied. In the techniques described in Non-Patent Documents 1 and 2 above, the Hamming distance is 2 or less.

<Hardware configuration>
Next, the hardware configuration of the concealment device 10 according to the present embodiment will be described with reference to FIG. FIG. 1 is a diagram showing an example of the hardware configuration of the concealment device 10 according to the present embodiment.

As shown in FIG. 1, the concealment device 10 according to the present embodiment is realized by a hardware configuration of a general computer or computer system, and includes an input device 11, a display device 12, an external I / F 13, and a communication I. It has / F14, a processor 15, and a memory device 16. Each of these hardware is connected so as to be communicable via the bus 17.

The input device 11 is, for example, a keyboard, a mouse, a touch panel, or the like. The display device 12 is, for example, a display or the like. The concealment device 10 may not have, for example, at least one of the input device 11 and the display device 12.

The external I / F 13 is an interface with an external device such as a recording medium 13a. The concealment device 10 can read or write the recording medium 13a via the external I / F 13. Examples of the recording medium 13a include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, and the like.

The communication I / F 14 is an interface for connecting the concealment device 10 to the communication network. The processor 15 is, for example, various arithmetic units such as a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit). The memory device 16 is, for example, various storage devices such as an HDD (Hard Disk Drive), an SSD (Solid State Drive), a RAM (Random Access Memory), a ROM (Read Only Memory), and a flash memory.

By having the hardware configuration shown in FIG. 1, the concealment device 10 according to the present embodiment can realize various processes described later. The hardware configuration shown in FIG. 1 is an example, and the concealment device 10 may have another hardware configuration. For example, the concealment device 10 may have a plurality of processors 15 or a plurality of memory devices 16.

<Functional configuration>
Next, the functional configuration of the concealment device 10 according to the present embodiment will be described with reference to FIG. FIG. 2 is a diagram showing an example of the functional configuration of the concealment device 10 according to the present embodiment.

As shown in FIG. 2, the concealment device 10 according to the present embodiment has an encoding unit 101, a randomization unit 102, and a vector set creating unit 103. Each of these parts is realized, for example, by a process of causing the processor 15 to execute one or more programs installed in the concealment device 10.

Further, the concealment device 10 according to the present embodiment has a storage unit 104. The storage unit 104 is realized by, for example, a memory device 16. However, the storage unit 104 may be realized by, for example, a storage device (database server or the like) connected to the concealment device 10 via a communication network.

The storage unit 104 stores the data set X = [D] = {0, ..., D-1} to be concealed.

The encoding unit 101 converts (encodes) the data x ∈ X into a D-dimensional vector b having {0, 1} as an element by Encode: X → {0, 1} ^D. However, it is assumed that the Hamming distance of any two output vectors of Encode is L or less. That is, if R ⊆ {0, 1} ^D and the vector set R that satisfies the Hamming distance of a and b of L or less for any a, b ∈ R is used, then Code: X → R.

The randomization unit 102 randomizes Encode (x) = b by Perturb so as to follow the probability shown in the above equation (1). However, p = (e ^{ε / L} ) / (e ^{ε / L} +1) and q = 1 / (e ^{ε / L} +1).

The vector set creation unit 103 creates a vector set R in which R ⊆ {0,1} ^D and the Hamming distance between a and b is L or less with respect to any a, b ∈ R.

<Data concealment processing>
Next, the flow of the process of concealing arbitrary data x ∈ X will be described with reference to FIG. FIG. 3 is a flowchart showing an example of the flow of data concealment processing. When concealing all the data in the data set X, the following steps S101 to S102 may be repeated for each x ∈ X, or after repeating step S101 for each x ∈ X. , Step S102 may be repeated for each b ∈ R obtained in this step S101.

The encoding unit 101 converts the data x ∈ X into a D-dimensional vector b ∈ R by Encode: X → R (step S101). Note that R is an arbitrary vector set in which R ⊆ {0, 1} ^D and the Hamming distance of a and b satisfies L or less with respect to any a, b ∈ R.

The randomization unit 102 randomizes Encode (x) = b by Perturb so as to follow the probability shown in the above equation (1) to obtain Perturb (b) = b'(step S102). However, p = (e ^{ε / L} ) / (e ^{ε / L} +1) and q = 1 / (e ^{ε / L} +1). The randomized data b'is stored in, for example, a storage unit 104.

<Process for creating a vector set whose Hamming distance is at most L or less>
The flow of processing for creating a vector set R in which R ⊆ {0, 1} ^D and the Hamming distance between a and b is L or less with respect to any a, b ∈ R will be described with reference to FIG. do. FIG. 4 is a flowchart showing an example of the flow of the process of creating a vector set in which the Hamming distance is at most L or less. However, the vector set R created in this creation process is an example, and R ⊆ {0,1} ^D , and the Hamming distance between a and b is L or less with respect to any a, b ∈ R. The vector set R of may be created.

The vector set creation unit 103 sets C = {z}, R = {z}, and C'= {}, where z is a D-dimensional vector in which all elements are 0 (step S201).

Next, the vector set creation unit 103 determines whether or not | C | = 0 (step S202). Note that | C | is the number of vectors included in the vector set C (the total number of elements included in C).

If it is not determined in step S202 above that | C | = 0, the vector set creation unit 103 selects v ∈ C and selects v ∈ C.

(Step S203).

Next, the vector set creation unit 103 sets a vector set having a Hamming distance different from v ∈ C selected in step S203 above by 1 as E ⊆ {0, 1} ^D.

(Step S204).

Next, the vector set creation unit 103 executes the following Step1 to Step2 for each of all u ∈ E'(step S205).

Calculate the Hamming distance between Step1: u and each c ∈ R, respectively.

Step2: If all the Hamming distances calculated in Step1 above are L or less,

And.

After the above step S205 is executed, the vector set creation unit 103 returns to the above step S202. As a result, steps S203 to S205 are repeatedly executed until | C | = 0.

When it is determined in step S202 above that | C | = 0, the vector set creation unit 103 outputs the vector set R (step S206). The output destination of the vector set R may be, for example, the storage unit 104.

<Summary>
As described above, the concealment device 10 according to the present embodiment conceals by converting each data x included in the data set X = [D] to be concealed by Encode and then randomizing by Perturb. I do. At this time, the concealment device 10 according to the present embodiment sets the output data set of the Encode to R ⊆ {0, 1} ^D , and the Hamming distance between a and b is L with respect to any a, b ∈ R. Let R be a vector set that satisfies the following. Further, when randomizing by Perturb, p = (e ^{ε / L} ) / (e ^{ε / L} +1), q = 1-p = 1 / (e ^{ε / L} +1), and the above equation (1) is used. Randomize according to the probabilities shown.

Thereby, in the concealment device 10 according to the present embodiment, by adjusting L, the amount of spatial calculation can be reduced as compared with the techniques described in the above-mentioned Non-Patent Documents 1 and 2. Therefore, it is possible to increase the size of the input data set that can be handled. In addition, the strength of randomization can be freely manipulated.

The present invention is not limited to the above-described embodiment disclosed specifically, and various modifications and modifications, combinations with known techniques, and the like are possible without departing from the description of the claims. ..

10 Concealment device 11 Input device 12 Display device 13 External I / F
13a Recording medium 14 Communication I / F
15 Processor 16 Memory device 17 Bus 101 Encoding unit 102 Randomization unit 103 Vector set creation unit 104 Storage unit

Claims

It is a concealment device that conceals data by stochastic randomization.
A conversion unit that converts the data into a binary vector set in which the Hamming distance between any two binary vectors is equal to or less than a predetermined L.
Each of the original elements is p = (e ε / L ) / (e ε / L +1) when the value of the element is 1, and q = 1 / (e ε / ) when the value of the element is 0. L + 1) (where ε is a parameter representing privacy strength), a randomization unit that randomizes to 0 or 1 and
Concealment device with.
It has a set creation unit that creates a binary vector set in which the Hamming distance between any two binary vectors is L or less using a predetermined L.
The conversion unit
The concealment device according to claim 1, wherein the data is converted into a binary vector set created by the set creation unit.
The set creation unit is
After preparing the set C = {z} and R = {z} based on the binary vector z in which all the elements are 0, and the set C'= {},
Arbitrarily select the binary vector v ∈ C, delete the selected binary vector v from the set C, and add the binary vector v to the set C'.
Hamming between each binary vector u included in the set E'excluding the set C'from the set E of the binary vectors having a Hamming distance different from the binary vector v by 1, and each binary vector c included in the set R. Calculating the distance and
Adding a binary vector u whose Hamming distance to all binary vectors c ∈ R is L or less is added to the set R and the set C.
Is repeated until there are no more selectable binary vectors v when arbitrarily selecting the binary vector v ∈ C, thereby creating a set R of binary vectors in which the Hamming distance between any two binary vectors is L or less. , The concealment device according to claim 2.
The randomized part is
When the value of the element is 1, the value of the element is randomized so that the probability of p = (e ε / L ) / (e ε / L +1) is 1 and the probability of 1-p is 0.
When the value of the element is 0, the value of the element is randomized so that the probability of q = 1 / (e ε / L + 1) is 1 and the probability of 1-q is 0. The concealment device according to any one of 3.
Computers that conceal data by stochastic randomization
A conversion procedure for converting the data into a binary vector set in which the Hamming distance between any two binary vectors is less than or equal to a predetermined L, and
Each of the original elements is p = (e ε / L ) / (e ε / L +1) when the value of the element is 1, and q = 1 / (e ε / ) when the value of the element is 0. A randomization procedure that randomizes to 0 or 1 to follow L + 1) (where ε is a parameter representing privacy strength), and
Concealment method to execute.
A program that causes a computer to function as a concealment device according to any one of claims 1 to 4.