JP5875535B2 - Anonymization device, anonymization method, program - Google Patents

Description

  The present invention relates to an anonymization device, an anonymization method, and a program that conceal privacy information of individual data in a database by a probabilistic method.

  In recent years, there has been a desire to accumulate and analyze data such as purchase history and behavior history and utilize it for product recommendations and better urban development. However, utilization of data associated with such individuals has a privacy problem, and it is difficult to provide data to a third party or outsource analysis. In addition, there is a problem that a person who collects data is required to handle the data delicately. To deal with this problem, anonymization technology that achieves both privacy protection and statistical analysis by taking appropriate privacy protection measures for data has attracted attention. In the anonymization technique, several privacy indexes have been proposed to quantitatively represent how much data can protect privacy. Among them, k-anonymity and algorithms that satisfy them are one of the most anonymizing techniques that have been most studied in recent years. However, since there is a problem that k-anonymity and its derivation cannot be applied to a probabilistic method, a privacy protection index called Pk-anonymity that extends k-anonymity to a probability space has been proposed.

  Pk-anonymity is an index for measuring how much privacy information of individual data in a database is concealed for a probabilistic method. Non-Patent Documents 1, 2, 3, and 4 are disclosed as concealment techniques that satisfy Pk-anonymity.

Rakesh Agrawal, Ramakrishnan Srikant, and Dilys Thomas. "Privacy preserving olap. In Fatma Ozcan", editor, SIGMOD Conference, pp.251-262. ACM, 2005. University of Igarashi, Koji Senda, Katsumi Takahashi, “Extension to k-anonymity and its application example”, InCSS, 2009. University of Igarashi, Koji Senda, Katsumi Takahashi, “Randomization method that satisfies k-anonymity in numerical attributes”, InCSS, 2011. Igarashi Univ., Satoshi Hasegawa, Tatsuya Naya, Ryo Kikuchi, Koji Senda, “Privacy Protection Cross-tabulation that Guarantees K-Anonymity by Randomization,” InCSS, 2012.

  In the present invention, a model in which there are three persons, a provider, a processor, and an analyst, is considered. The provider passes information related to the individual (hereinafter referred to as personal information) to the processor. Examples of personal information include smartphone location information. A processor is a person who collects personal information of a plurality of providers, performs anonymization processing in a batch using an anonymization device (anonymization method), and provides the analyst. An analyst is a person who gives and receives anonymized data from a processor.

  There is Pk-anonymity described above as an index indicating how much privacy information is concealed. A method that satisfies this index is called Pk-anonymization, and a specific process of Pk-anonymization is called an anonymization process. I will do it. Several Pk-anonymizations have already been proposed, but all of them need to perform the same process regardless of the distribution of data to be anonymized. In the model to which the present invention is applied, since the anonymization process is performed in a lump, the entire original data is known when the anonymization process is performed. Therefore, a better anonymization becomes possible by making the anonymization process dependent on the data. For example, if the original data has some degree of anonymity in the first place, it can be considered that “weak” anonymization processing is performed as compared with data having low anonymity.

  However, existing Pk-anonymization cannot perform such anonymization processing depending on the anonymity of the original data. Therefore, even if the original data has some degree of anonymity in the first place, it is necessary to perform the same processing as when the anonymity of the original data is low, and as a result, the usefulness of the obtained anonymized data is reduced. There is a problem. Therefore, an object of the present invention is to provide an anonymization device that can satisfy desired anonymity with weaker anonymization when performing anonymization processing on data collectively.

  The anonymization device of the present invention includes a sorting unit, a maintenance probability calculation unit, a matrix calculation unit, and a table transition unit.

Each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and a set of values that a certain attribute a∈AS can take V _a , its specific value v _a , the original table before anonymization τ, the anonymization table τ ′, and the distance D between records r ₁ and r _{2 of the} original table δ ^ Is the Kronecker delta,

And a sorting function for the set φ having integer values as elements,

It is defined as

  The sorting unit performs the processing for all records rεR from the original table τ.

Calculate

Calculate

Maintaining probability calculation unit anonymization parameter k, the n _i

and,

The parameter _ρaj , which is the maintenance probability of each attribute, is obtained so as to satisfy

  The matrix calculator is a transition probability matrix of attribute a

Calculate

  The table transition unit transitions the value of each attribute of the table using a transition probability matrix.

Transition, when the value of the attribute a of a table record was v _a, indicating that changing the value to v _'a probability that is determined based on the transition probability matrix.

  According to the anonymization device of the present invention, when anonymization processing is performed on data collectively, anonymity desired by weaker anonymization can be satisfied.

The figure which shows the example of the table used as the object of anonymization in this invention. The figure which shows the outline | summary of the input / output of the anonymization apparatus of this invention. The block diagram which shows the structure of the anonymization apparatus of Example 1 of this invention. The flowchart which shows operation | movement of the anonymization apparatus of Example 1 of this invention. The figure which shows the example of the original table which the sort part of the anonymization apparatus of Example 1 processes. The figure which shows the process example of the sort part of the anonymization apparatus of Example 1. FIG. The block diagram which shows the structure of the anonymization apparatus of the modification 1 of this invention. The flowchart which shows operation | movement of the anonymization apparatus of the modification 1 of this invention. The block diagram which shows the structure of the anonymization apparatus of Example 2 of this invention. The flowchart which shows operation | movement of the anonymization apparatus of Example 2 of this invention. The figure which illustrates set R _L ^(k) , V _L ^(k) . The block diagram which shows the structure of the anonymization apparatus of the modification 2 of this invention. The flowchart which shows operation | movement of the anonymization apparatus of the modification 2 of this invention.

  Hereinafter, embodiments of the present invention will be described in detail. In addition, the same number is attached | subjected to the structure part which has the same function, and duplication description is abbreviate | omitted.

<Prerequisites>
The anonymization target of the present invention will be described with reference to FIG. FIG. 1 is a diagram showing an example of a table to be anonymized in the present invention. As shown in FIG. 1, in the table used for anonymization in the present invention, each row represents one person's data (this is called a record r), and each column has a value of each attribute (for example, age, annual income, etc.). It is assumed that it has been entered. In the privacy protection index Pk-anonymity that the present invention satisfies, the degree of privacy protection is determined by a parameter k (hereinafter referred to as an anonymization parameter). Therefore, it is assumed that the anonymization parameter k is first given in the anonymization process.

  The input / output of the anonymization device of the present invention will be described with reference to FIG. FIG. 2 is a diagram showing an outline of input / output of the anonymization device of the present invention. As shown in FIG. 2, the anonymization apparatus receives as input an original table to be anonymized and a parameter (anonymization parameter k) that determines how much anonymity is given. The anonymization device executes an anonymization process, and an anonymization table and parameters (such as a transition probability matrix) used for the anonymization process are output.

In the following, terms and functions are defined in order to describe the present invention in detail. Assume that a set of attributes of the table is AS, a set of records r is R, a set of values that a certain attribute aεAS can take is V _a , and a specific value thereof is v _a . Let the original table before anonymization be τ and the anonymization table be τ ′. The distance D between the records r ₁ and r _{2 of the} original table is defined as follows. When δ ^ is the Kronecker delta,

And a sorting function for the set φ having integer values as elements,

It is defined as

  Hereinafter, the anonymization device 1 according to the first embodiment of the present invention will be described with reference to FIGS. FIG. 3 is a block diagram showing the configuration of the anonymization device 1 of this embodiment. FIG. 4 is a flowchart showing the operation of the anonymization device 1 of this embodiment.

  As shown in FIG. 3, the anonymization device 1 of this embodiment includes a sorting unit 11, a maintenance probability calculation unit 12, a matrix calculation unit 13, and a table transition unit 14. The anonymization device 1 receives the anonymization parameter k and the original table τ. First, the sorting unit 11 performs the processing for all records rεR from the original table τ.

Calculate

Is calculated (S11).

The sorting performed by the sorting unit 11 and the calculation of n will be supplementarily described with reference to FIGS. FIG. 5 is a diagram illustrating an example of original data processed by the sorting unit 11 of the anonymization device 1 according to the present embodiment. FIG. 6 is a diagram illustrating a processing example of the sorting unit 11 of the anonymization apparatus 1 according to the present embodiment. As shown in FIG. 5, let us consider a case where the attributes are age, gender, and annual income, and the original table composed of records r ₁ , r ₂ , r ₃ , and r ₄ is sorted. In this case, as shown in FIG. 6, the sorting unit 11 calculates the distance D between the records, executes sorting to sort the distance D in ascending order for each record, and calculates n from the maximum value of each rank after sorting. = (N ₁ , n ₂ , n ₃ ) is calculated.

Then, maintaining the probability calculation section 12, the n _i determined given anonymous parameters k and earlier

and,

A parameter _ρaj , which is a maintenance probability of each attribute, is obtained so as to satisfy (S12).

  Next, the matrix calculation unit 13 uses the transition probability matrix of the attribute a

Is calculated (S13). Next, the table transition unit 14 causes the value of each attribute of the table to transition using the upper transition probability matrix (S14). Transition, when the value of the attribute a of a table record was v _a, the probability

In v 'is meant to change the value to _a. The result of performing this operation on all attribute values of all records is defined as an anonymization table τ ′.

The anonymization device 1 includes an anonymization table τ ′, a transition probability matrix {A _a | a∈AS} for each attribute,

Is output.

  According to the anonymization apparatus 1 of the present embodiment, when anonymization processing is performed on data collectively, anonymity desired by weaker anonymization can be satisfied.

  Further, according to the anonymization device 1 of the present embodiment, since the information n → of the original data table that did not exist in the conventional method is disclosed, the maintenance probability can be increased. The maintenance probability is the “probability that the data will remain as it is without transition”, and the higher the value, the closer to the original data, the more useful the data than the conventional method.

[Modification 1]
Hereinafter, with reference to FIG. 7 and FIG. 8, the anonymization apparatus 10 of the modification 1 which changed a part of Example 1 is demonstrated. FIG. 7 is a block diagram showing a configuration of the anonymization device 10 of the present modification. FIG. 8 is a flowchart showing the operation of the anonymization device 10 of this modification.

<Prerequisites>
As in the first embodiment, each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and an attribute aε Assume that a set of values that AS can take is V _a , and its specific value is v _a . Further, when V is a set of attribute combinations, that is, _直 represents a direct product, V = Π _aεAS V _a and its element is v. Similarly, a set of values that an attribute aεAS of the anonymization table can take is V ′ _a , a specific value is v ′ _a, and V ′ is a set of combinations of attributes of the anonymization table, and anonymization is performed. Let τ be the original table before being processed, and τ ′ be the anonymization table.

As shown in FIG. 7, the anonymization device 10 of the present modification includes a distance calculation unit 110, a probability calculation unit 120, a matrix calculation unit 130, and a table transition unit 14. Similar to the first embodiment, the anonymization device 10 of the present modification takes the anonymization parameter k and the original table τ as inputs. First, the distance calculation unit 110 calculates the inter-record distance D for all the records rεR of the original table τ, and sets the largest one among them as D ^* . Here, a set of tables in which the largest inter-record distance is D ^* in the table space T is T ^. The space of the anonymization table is T ′. Also,

Is the attribute of the sth record of a certain table τ ^ (this is written as τ ^ (s)), and the attribute of the s'th record of the anonymization table τ ′ (this is τ ′ (s ′) Is defined as the probability of changing.

  Next, the probability calculation unit 120 calculates a given anonymity parameter k and T ^, T ′ from

To meet

Is calculated (S120). Here, π is a replacement in an arbitrary record order.

  Next, the matrix calculation unit 130

And satisfy

| V | × | V ′ | matrix A is calculated (S130). The table transition unit 14 transitions the value of each attribute of the original table according to the matrix A obtained in step S130. Specifically, step S14 is a process of changing the value to _{v ′} with the probability A _{v, v ′} when the attribute of the record in the original table is vεV. The result of performing this processing on all attribute values of all records is defined as an anonymization table τ ′. The anonymization device 10 outputs an anonymization table τ ′ and a transition probability matrix A ^{τ ^, τ ′} , D ^* .

  According to the anonymization device 10 of the present modification, as in the first embodiment, when anonymization processing is performed on data collectively, anonymity desired by weaker anonymization can be satisfied.

  Further, in the present modification example, if the inter-record distance D is embodied as the Hamming distance between the records and n → calculated by the Kronecker δ and the sort function, as in the first embodiment, the conventional method does not exist. Since the information n → of the original data table is disclosed, the maintenance probability can be increased. The maintenance probability is the “probability that the data will remain as it is without transition”, and the higher the value, the closer to the original data, the more useful the data than the conventional method.

<Prerequisites>
As in the first embodiment, AS is a set of table attributes, R is a set of records, V _{a is a} set of values that a certain attribute aεAS can take, and v _a is a specific value thereof. The original table before anonymization is written as τ, and the anonymization table is written as τ ′. The table is a mapping connecting the record and the attribute value. For example, if the attribute value of the record 1 is A, τ (1) = A is expressed. Here, the operation symbol # _τ (*)

It is defined as That is, # _τ (v) represents the number of records having the attribute value v in the table τ. Let R _L ^(k) and V _L ^{(k) be} a set of records r and a set of attributes τ (r) where # _τ (τ (r)) <k in the table τ. In addition, this system needs to satisfy | R _L ^(k) | ≧ k. R _L ^(k) and V _L ^(k) will be supplementarily described with reference to the specific example of FIG. FIG. 11 is a diagram illustrating the sets R _L ^(k) and V _L ^(k) . Assuming the case where k = 3, with the attributes r _{1 to} r ₁₀ as shown in FIG. 11 as an example, the set R _L ^(k) is a record corresponding to less than k (= 3) attribute values. A set of numbers. Therefore, in this case, the set R _L ^(k) = {4, 5, 6}. The set V _L ^(k) is a set of attribute values less than k (= 3). Therefore, in this case, the set V _L ^(k) = {30s, 40s}.

  Hereinafter, the anonymization device 2 according to the second embodiment will be described with reference to FIGS. 9 and 10. FIG. 9 is a block diagram showing the configuration of the anonymization device 2 of this embodiment. FIG. 10 is a flowchart showing the operation of the anonymization device 2 of this embodiment. As shown in FIG. 9, the anonymization device 2 of this embodiment includes a set calculation unit 21, a parameter calculation unit 22, a matrix calculation unit 23, and a table transition unit 14. Similar to the first embodiment, the anonymization device 2 receives the anonymization parameter k and the original table τ.

First, the set calculation unit 21 calculates the sets R _L ^(k) and V _L ^(k) from the anonymization parameter k and the original table τ. If | R _L ^(k) | ≧ k, the set calculation unit 21 outputs ⊥ (reject). (S21). Next, the parameter calculation unit 22 uses the given anonymization parameter k and R _L ^(k) obtained in step S21,

Parameters ρ, cε [0, 1] that satisfy the above are calculated (S22). Next, the matrix calculation unit 23 uses the parameters ρ and c obtained in step S22 to change the transition probability matrix A to # _τ (v) ≧ k.

When # _τ (v) <k,

(S23). Next, the table transition unit 14 creates an anonymization table τ ′ according to the transition probability matrix A (S14). The operation of the table transition unit 14 of the present embodiment is the same as the operation of the table transition unit 14 of the first embodiment.

  The anonymization device 2 outputs the anonymization table τ ′ and the transition probability matrix A.

[Modification 2]
Hereinafter, with reference to FIG. 12 and FIG. 13, an anonymization device 20 of Modification 2 in which a part of Embodiment 2 is modified will be described. FIG. 12 is a block diagram showing the configuration of the anonymization device 20 of this modification. FIG. 13 is a flowchart showing the operation of the anonymization device 20 of this modification. In this modification, the <precondition> shown in the second embodiment is continuously used.

  As illustrated in FIG. 12, the anonymization device 20 of the present modification includes a set calculation unit 21, a function calculation unit 220, a matrix calculation unit 230, and a table transition unit 14. Since the operations of the set calculation unit 21 and the table transition unit 14 are the same as those in the second embodiment, a description thereof will be omitted. Similar to the second embodiment, the anonymization device 20 receives the anonymization parameter k and the original table τ.

From the given anonymization parameter k and R _L ^(k) obtained in step S21, the function calculator 220 calculates

A function fε [0,1], αε [0,1], βε [0,1] that satisfies the above is calculated (S220). Next, the matrix calculation unit 230 uses the f, α, and β obtained in step S220 to set | V | × | V ′ | matrix A to # _τ (v) ≧ k.

When # _τ (v) <k, the value included in any [0,1],

(S230).

Hereinafter, in steps S220 and S230 in this modification, α and β are embodied as α = 1 + (1−ρ) / | V | and β = (1−ρ) / | V | using ρ as ρ. State. In this case, in step S220 described above, the function calculation unit 220 calculates from the given anonymization parameter k and R _L ^(k) obtained in step S21.

A function fε [0,1], ρ [0,1] that satisfies the above is calculated. Next, in step S230, the matrix calculation unit 230 uses the parameters f and ρ obtained in step S220 and sets | V | × | V ′ | matrix A to # _τ (v) ≧ k.

When # _τ (v) <k,

Calculate as

  According to the anonymization devices 2 and 20 of the second embodiment and the second modification, as in the first embodiment, when anonymization processing is performed on data collectively, the desired anonymity is satisfied with weaker anonymization. Can do.

In addition, according to the anonymization devices 2 and 20 of the second embodiment and the second modification, by using the sets R _L ^(k) and V _L ^(k) that do not exist in the conventional technique, the sets R _L ^(k) , Since data processing can be changed depending on V _L ^(k) , it is possible to reduce changes in the original data while maintaining anonymity equivalent to that of the conventional method, and the usefulness of the data compared to the conventional method. Is expensive.

<Comparison of Anonymization Device 1 of Example 1 and Anonymization Device 2 of Example 2>
The method of the anonymization device 1 has a property that should be called a data-dependent maintenance replacement disturbance method. In the method of the anonymization device 1, the distribution of the entire table is not maintained so much, but the relationship between the attributes in the table is maintained. Therefore, the method of the anonymization device 1 is an effective method when an analyst acquires one large anonymization table and analyzes using partial attributes therein.

  On the other hand, the method of the anonymization device 2 has a property that should be called a data-dependent cross-value disturbance method. In the method of the anonymizing device 2, the distribution of the entire table is maintained, but the relationship between individual attributes is not so much maintained. Therefore, the method of the anonymization device 2 is an effective method for custom-made anonymization, for example, when an analyst acquires a table for each analysis.

  The various processes described above are not only executed in time series according to the description, but may also be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes. Needless to say, other modifications are possible without departing from the spirit of the present invention.

  Further, when the above-described configuration is realized by a computer, processing contents of functions that each device should have are described by a program. The processing functions are realized on the computer by executing the program on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its own storage device. When executing the process, the computer reads a program stored in its own recording medium and executes a process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Also, the program is not transferred from the server computer to the computer, and the above-described processing is executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. It is good.

Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer). In this embodiment, the present apparatus is configured by executing a predetermined program on a computer. However, at least a part of these processing contents may be realized by hardware.

Claims (7)

Each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and a set of values that a certain attribute a∈AS can take V _a , its specific value v _a , the original table before anonymization τ, the anonymization table τ ′, and the distance D between records r ₁ and r _{2 of the} original table δ ^ Is the Kronecker delta,

And a sorting function for the set φ having integer values as elements,

And define
For all records r∈R from the original table τ

Calculate

A sort part for calculating
Anonymous parameter k, from _{n i}

and,

A maintenance probability calculation unit for _obtaining a parameter ρ _aj that is a maintenance probability of each attribute so as to satisfy
Transition probability matrix of attribute a

A matrix calculator for calculating
A table transition unit that transitions the value of each attribute of the table using a transition probability matrix,
Transition, when the value of the attribute a of a table record was v _a, anonymous device indicating that change the value to v _'a probability that is determined based on the transition probability matrix. Each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and a set of values that a certain attribute a∈AS can take _Is V _a , its specific value is v _a, and V is a set of attribute combinations, that is, Π represents a Cartesian product, V = Ａ _a∈AS V _a , its element is v, and anonymization A set of values that a table attribute aεAS can take is V ′ _a , its specific value is v ′ _a, and V ′ is a set of combinations of attributes of the anonymization table. When the table is τ and the anonymization table is τ ′,
A distance calculation unit that calculates a distance D between records for all records rεR of the original table τ, and sets the largest one among them as D ^* ;
Of the table space T, let T ^ be the set of tables whose distance between records is D ^* , and let T 'be the anonymized table space.

Is defined as representing the probability that the attribute τ ^ (s) of the sth record of a table τ ^ will change to the attribute τ '(s') of the s'th record of the anonymization table τ', Let π be any record order permutation,
From given anonymity parameters k and T ^, T '

To meet

A probability calculation unit for calculating

And satisfy

A matrix calculator for calculating | V | × | V ′ | matrix A such that
A table transition unit that transitions the value of each attribute of the table using | V | × | V ′ | matrix A,
Transition is an anonymization device that indicates that when the attribute of a record in the table is vεV, the value is changed to v ′ with a probability determined based on the transition probability matrix. The anonymization device according to claim 2,
An anonymization device that uses a distance D between records as a Hamming distance between records. An anonymization method executed by an anonymization device,
Each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and a set of values that a certain attribute a∈AS can take V _a , its specific value v _a , the original table before anonymization τ, the anonymization table τ ′, and the distance D between records r ₁ and r _{2 of the} original table δ ^ Is the Kronecker delta,

And a sorting function for the set φ having integer values as elements,

And define
The anonymization device
For all records r∈R from the original table τ

Calculate

A sorting step that calculates
Anonymous parameter k, from _{n i}

and,

A maintenance probability calculation step for _obtaining a parameter ρ _aj that is a maintenance probability of each attribute so as to satisfy
Transition probability matrix of attribute a

A matrix calculation step for calculating
A table transition step for transitioning the values of the attributes of the table using the transition probability matrix ,
Transition is an anonymization method indicating that when _a value of attribute a of a record in a table is va, the value is changed to va 'with _a probability determined based on a transition probability matrix. An anonymization method executed by an anonymization device,
Each row of the table is a record r representing one person's data, each column of the table is a value of each attribute, AS is a set of attributes of the table, R is a set of records r, and a set of values that a certain attribute a∈AS can take _Is V _a , its specific value is v _a, and V is a set of attribute combinations, that is, Π represents a Cartesian product, V = Ａ _a∈AS V _a , its element is v, and anonymization A set of values that a table attribute aεAS can take is V ′ _a , its specific value is v ′ _a, and V ′ is a set of combinations of attributes of the anonymization table. When the table is τ and the anonymization table is τ ′,
The anonymization device
A distance calculating step of calculating a distance D between the records for all records r∈R of the original table τ, and setting D ^{* as} the largest one among them,
Of the table space T, let T ^ be the set of tables whose distance between records is D ^* , and let T 'be the anonymized table space.

Is defined as representing the probability that the attribute τ ^ (s) of the sth record of a table τ ^ will change to the attribute τ '(s') of the s'th record of the anonymization table τ', Let π be any record order permutation,
From given anonymity parameters k and T ^, T '

To meet

A probability calculating step for calculating

And satisfy

A matrix calculation step of calculating | V | × | V ′ | matrix A such that
A table transition step of transitioning the value of each attribute of the table using | V | × | V ′ | matrix A ;
Transition is an anonymization method indicating that when the attribute of a record in the table is vεV, the value is changed to v ′ with a probability determined based on the transition probability matrix. The anonymization method according to claim 5,
An anonymization method in which the inter-record distance D is a Hamming distance between records.   The program for making a computer perform each step of the anonymization method described in any one of Claim 4 to 6.