CN109033766A - Database water mark method based on local difference privacy - Google Patents
Database water mark method based on local difference privacy Download PDFInfo
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- G06F21/10—Protecting distributed programs or content, e.g. vending or licensing of copyrighted material ; Digital rights management [DRM]
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/10—Protecting distributed programs or content, e.g. vending or licensing of copyrighted material ; Digital rights management [DRM]
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Abstract
The invention discloses a kind of database water mark method based on local difference privacy, attribute is ranked up according to the attribute-name of database, tuple grouping is embedded in for watermark according to the major key of tuple in database；Difference privacy is carried out to the Sensitive Attributes in database；Feature according to data in the database after difference privacy carries out watermark insertion, then by Database Publishing after watermark to cloud；Database of the user from cloud downloading publication, integrity verification of the watermark for copyright tracking and data is extracted from the database of publication, the property for not only maintaining difference privacy the present invention is based on the database water mark method of local difference privacy also reduces data distortion caused by difference privacy, has very high robustness for attacks such as the increases, modification, deletion of database for various.The present invention is used for the safety of database privacy, distorts integrality and reliability of source etc. and provide integrated protection mechanism.
Description
Technical field
The invention belongs to database security fields, more particularly to a kind of database water mark based on local difference privacy.
Background technique
With network technology and digital multimedia technology fast development and the extensive use of database, people can be easily
Ground is modified or even distorted by the data in database.The shared of data may cause individual privacy even under big data environment
The leakage of national intelligence.For the Privacy Protection of database, the methods of difference privacy, k- anonymity and encryption are suggested；Its
The problem of middle local difference privacy can solve user sensitive information leakage, but data distortion problem caused by it needs into one
Step research and improvement.Trace to the source for complicated, multi-source big data, copyright protection the problems such as, database water mark technology has obtained height
Degree is paid attention to.Difference privacy technology and database digital watermark are all the digital multimedia safe practices newly risen, although they are
Good development has been obtained, still, database privacy concern and copyright can be solved simultaneously currently without a kind of method
Protection problem.
There is also following disadvantages for current difference privacy technology and database digital watermark:
1, when in database including a large amount of individual subscriber sensitive information, secret protection is extremely important and Database vendors
When database trace to the source, the integrity verification of copyright protection and data the problems such as be also required to solve.Current database water mark skill
Art can only the integrality to database carry out verifying and copyright protection carried out to database, but privacy cannot be protected.
2, at present there is no database privacy protection can be provided and provide initial data copyright tracking, integrity verification
Database water mark method.
3, data distortion caused by when current difference privacy technology carries out secret protection is bigger.
4, it still needs further improvement for the robustness of current database water mark technology, and distortion caused by insertion watermark makes
Quality of data decline is further improved.
Summary of the invention
The present invention is to provide a kind of data based on local difference privacy to avoid above-mentioned deficiency of the prior art
Library watermark, to database security of private data, distort integrality and reliability of source etc. and make integrated protection.
The present invention adopts the following technical scheme that in order to solve the technical problem
The present invention is based on the characteristics of database water mark method of local difference privacy to be: according to the attribute-name of database to category
Property be ranked up, according to the major key of tuple in database to tuple grouping for watermark be embedded in；To the Sensitive Attributes in database
Carry out difference privacy；Feature according to data in the database after difference privacy carries out watermark insertion, then by data after watermark
Library is distributed to cloud；User extracts watermark from the database of publication and tracks for copyright from the database of cloud downloading publication
With the integrity verification of data.
It is to carry out as follows the present invention is based on the characteristics of database water mark method of local difference privacy:
Step 1: attribute is ranked up according to the attribute-name of database, according to the major key of tuple in database to first component
Group:
1.1, the database after being sorted is ranked up to attribute according to the ascending order of the attribute-name of database or descending
D；
1.2, it is grouped to obtain the number of each tuple in database to database D using formula (1),
ni=H (Ks | | H (Ks | | tu.PK)) %Ng(1),
In formula (1), niIt is the number of tuple in the database after being grouped, ni=1,2 ... Ng, NgFor watermark length；H () table
Show hash algorithm, " | | " it is bound symbol, Ks is key, and tu.PK is the major key of tuple；
Step 2: local difference secret protection being carried out to the Sensitive Attributes x in database and obtains the attribute with secret protection
Y:
Realize local difference secret protection using Laplce's mechanism, in Laplce's mechanism global susceptibility be attribute most
The difference of big value and attribute minimum value, it is assumed that attribute maximum value is t, and attribute minimum value is 1, then global susceptibility is t-1, for
Attribute value is the database of integer, the attribute value of database is mapped to integer 1,2 ... on t, and modifies attribute value according to formula (2)
xiObtain attribute value yi, realize the secret protection to the Sensitive Attributes in database；
In formula (2), ck=k+0.5, k=1,2 ... t-1；Lap () is Laplace function；ε is secret protection budget；
Step 3: initialize array mark, according to Sensitive Attributes x through difference privacy obtain brought by attribute y distortion d into
Row watermark insertion, then by database D after watermark 'wIt is distributed to cloud；
3.1, initialize array mark；
3.2, it calculates and obtains attribute value yiCaused by data distortion d are as follows: d=| yi-xi|；The distortion of user's Custom Attributes value
Range is ξ, if data distortion d is more than user's Custom Attributes value distortion range ξ, the record attribute value y in array markiInstitute
Position in the database, and in attribute value yiMiddle insertion watermark；
It is described in attribute value yiMiddle insertion watermark is to carry out as follows:
According to the number n of tuple each in databaseiWatermark insertion is carried out, the tuple insertion of number having the same is identical
Watermark w；Watermark telescopiny are as follows:
First according to the watermark w to be embedded in modification attribute value yiThe attribute value y ' updatedi, when the watermark of insertion is 1
When, by attribute value yiBecome odd number, when watermark is 0, by attribute value yiBecome even number；
For all groupings complete the database D after watermarks are embedded in obtain watermark 'w；
3.2, publication database D 'wTo cloud；
Step 4: user from cloud download to obtain database D 'w, according to the ascending order or descending pair of the attribute-name of database
Attribute is ranked up to obtain the identical database D of number for identical and each tuple that sorts with attribute in step 1 "w；
Step 5: possess key legitimate user extract watermark, not the ordinary user of key be only able to use database but
Watermark cannot be extracted；Initializing variable ones is 0, zeros 0；According to database D "wThe number of middle grouping is successively in every group
All tuples carry out watermark extracting；It is extracted if the location information of the attribute of tuple each in every group is present in array mark
Watermark；The process for extracting watermark is as follows:
When attribute value is odd number, ones adds 1, and when attribute value is even number, zeros adds 1；When all properties value is all in one group
Traversal is completed, and the size of ones and zeros are compared, if ones > zeros, the watermark w extracted is 1, the watermark otherwise extracted
W is 0；If ones and zeros are not 0, it is judged as that database has been tampered, the integrality of data is destroyed.
The present invention is based on the characteristics of database water mark method of local difference privacy to lie also in: the secret protection budget ε
It can be set to 1, ln (2) or ln (3).
The present invention is based on the characteristics of database water mark method of local difference privacy to lie also in: being directed to attribute value yiOdd number or
The modification of even number is to carry out as follows:
If w=1 works as yi> xiWhen, if attribute value xiIt is that odd number then modifies yiFor xiIf attribute value xiIt is even number, then will repairs
Change attribute value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that odd number is then constant, if attribute value yiIt is even number, then by attribute value
yiIt is revised as yi-1；
If w=0 works as yi> xiWhen, if attribute value xiIt is that even number then modifies yiFor xiIf attribute value xiIt is odd number, then will repairs
Change attribute value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that even number is then constant, if attribute value yiIt is odd number, then by attribute value
yiIt is revised as yi-1。
For application of the invention, the present invention is can be used to protect database copyright and privacy to believe in database owner
Breath.Ordinary user can download from cloud and use database, but cannot analyze to obtain by data personal in database
Sensitive information；The legitimate user for possessing key can not only use database as general user, but also can extract watermark
For copyright and data integrity validation.Compared with the prior art, the invention has the advantages that:
1, the present invention not only realize the secret protection to database and also realize to the copyright protection of database and
Integrity verification.
2, database water mark improves the quality of data of the database after difference privacy in the present invention, reduces difference privacy
Caused by data distortion.
3, database still can after the database water mark designed the present invention is based on local difference privacy is embedded in watermark
Enough keep the characteristic of difference privacy.
4, database water mark has very high robustness in the present invention, i.e., when database is inserted into or is modified attack,
User still is able to correctly and completely extract watermark.
5, the present invention can apply to big data processing mechanism, apply to the copyright protection of initial data in database, complete
The protection of whole property and the secret protection of publication data, user may determine that the source of database, verify data integrality and
It cannot obtain exact privacy of user data.
Detailed description of the invention
Fig. 1 is the application scenarios of the database water mark model based on local difference privacy in the present invention；
Fig. 2 is the database water mark model general illustration based on local difference privacy in the present invention；
Fig. 3 is the watermark telescopiny schematic diagram that model is directed in the present invention；
Fig. 4 is the watermark extraction process schematic diagram that model is directed in the present invention；
Fig. 5 is the watermark robustness schematic diagram of model in the present invention；
Specific embodiment
Referring to Fig. 1, the database water mark method based on local difference privacy in this example is: according to the attribute-name of database
Attribute is ranked up, tuple grouping is embedded in for watermark according to the major key of tuple in database；To the sensitivity in database
Attribute carries out difference privacy, and carries out watermark insertion according to the distortion of the data after difference privacy, then by database after watermark
It is distributed to cloud；All users can download the database of publication from cloud, and using database but cannot pass through data
Analysis obtains the sensitive data of some individual in database, and the legitimate user for possessing key not only can be used database, may be used also
With from the database of publication extract watermark for copyright tracking and data integrity verification, attacker can to database into
Row is attacked and it is distributed to cloud again.
Referring to fig. 2, the database water mark method based on local difference privacy in the present embodiment carries out as follows:
Step 1: attribute being ranked up according to the attribute-name of database as follows, according to the master of tuple in database
Key is grouped tuple:
1.1, the database after being sorted is ranked up to attribute according to the ascending order of the attribute-name of database or descending
D；
1.2, it is grouped to obtain the number n of each tuple in database to database D using formula (1)i,
ni=H (Ks | | H (Ks | | tu.PK)) %Ng(1),
In formula (1), niIt is the number of tuple in the database after being grouped, ni=1,2 ... Ng, NgFor watermark length；H () table
Show hash algorithm, " | | " it is bound symbol, Ks is key, and tu.PK is the major key of tuple.
Step 2: local difference secret protection being carried out to the Sensitive Attributes x in database and obtains the attribute with secret protection
Y:
Realize local difference secret protection using Laplce's mechanism, in Laplce's mechanism global susceptibility be attribute most
The difference of big value and attribute minimum value, it is assumed that attribute maximum value is t, and attribute minimum value is 1, then global susceptibility is t-1, for
Attribute value is the database of integer, the attribute value of database is mapped to integer 1,2 ... on t, and modifies attribute value according to formula (2)
xiObtain attribute value yi, realize the secret protection to the Sensitive Attributes in database；
In formula (2), ck=k+0.5, k=1,2 ... t-1；Lap () is Laplace function；ε is secret protection budget, and ε is got over
The degree of small secret protection is higher, but data distortion is bigger simultaneously, flat according to secret protection and availability of data in concrete application
The demand of weighing apparatus is configured, and in specific implementation, secret protection budget ε can be set to 1, ln (2) or ln (3).
Step 3: initialize array mark, according to Sensitive Attributes x through difference privacy obtain brought by attribute y distortion d into
Row watermark insertion, then by database D after watermark 'wIt is distributed to cloud；
3.1, initialize array mark；
3.2, it calculates and obtains attribute value yiCaused by data distortion d are as follows: d=| yi-xi|；The distortion of user's Custom Attributes value
Range is ξ, if data distortion d is more than user's Custom Attributes value distortion range ξ, the record attribute value y in array markiInstitute
Position in the database, and in attribute value yiMiddle insertion watermark；
It is described in attribute value yiMiddle insertion watermark is to carry out as follows:
According to the number n of tuple each in databaseiWatermark insertion is carried out, the tuple insertion of number having the same is identical
Watermark w；Watermark telescopiny are as follows:
First according to the watermark w to be embedded in modification attribute value yiThe attribute value y ' updatedi, when the watermark of insertion is 1
When, by attribute value yiBecome odd number, when watermark is 0, by attribute value yiBecome even number；
In specific implementation, for attribute value yiThe modification of odd number or even number carries out as follows:
If w=1 works as yi> xiWhen, if attribute value xiIt is that odd number then modifies yiFor xiIf attribute value xiIt is even number, then will repairs
Change attribute value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that odd number is then constant, if attribute value yiIt is even number, then by attribute value
yiIt is revised as yi-1；
If w=0 works as yi> xiWhen, if attribute value xiIt is that even number then modifies yiFor xiIf attribute value xiIt is odd number, then will repairs
Change attribute value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that even number is then constant, if attribute value yiIt is odd number, then by attribute value
yiIt is revised as yi-1。
For all groupings complete the database D after watermarks are embedded in obtain watermark 'w；
3.2, publication database D 'wTo cloud；
Step 4: user from cloud download to obtain database D 'w, according to the ascending order or descending pair of the attribute-name of database
Attribute is ranked up to obtain the identical database D of number for identical and each tuple that sorts with attribute in step 1 "w；
Step 5: possess key legitimate user extract watermark, not the ordinary user of key be only able to use database but
Watermark cannot be extracted；Initializing variable ones is 0, zeros 0；According to database D "wThe number of middle grouping is successively in every group
All tuples carry out watermark extracting；It is extracted if the location information of the attribute of tuple each in every group is present in array mark
Watermark；The process for extracting watermark is as follows:
When attribute value is odd number, ones adds 1, and when attribute value is even number, zeros adds 1；When all properties value is all in one group
Traversal is completed, and the size of ones and zeros are compared, if ones > zeros, the watermark w extracted is 1, the watermark otherwise extracted
W is 0；If ones and zeros are not 0, it is judged as that database has been tampered, the integrality of data is destroyed.
Referring to Fig. 3, the telescopiny of watermark carries out as follows:
1.1: input database D, key Ks, secret protection budget ε, distortion toleance degree ξ and watermark W；
It is tested by taking the database of adult income forecast as an example, 32,560 adult information is contained in database,
Two kinds of Sensitive Attributes are respectively age (age) and per work hours per week (hours-per-week), by taking two kinds of Sensitive Attributes as an example
And it generates a column and is tested as major key.Key Ks is generated at random, and distortion toleance degree ξ and watermark W are customized by the user, hidden
Private protection budget ε trains optimal value according to user demand and combined data library.
Sensitive Attributes value such as table 1 in raw data base, table 1 be by part attribute value and for:
Table 1
| age | hours-per-week |
| 39 | 40 |
| 50 | 13 |
| 38 | 40 |
| 53 | 40 |
| 28 | 40 |
| 37 | 40 |
| 49 | 16 |
| 52 | 45 |
| 31 | 50 |
| 42 | 40 |
| 37 | 80 |
| 30 | 40 |
| 23 | 30 |
| 32 | 50 |
1.2:Ng=strlen (W), grouping number NgEqual to the length of watermark W；
1.3: database being grouped to obtain N using formula (1)gA grouping G1,
1.4:DwDatabase is copied to D by ' ← Dw' in；
1.5: the insertion watermark stage, first to Sensitive Attributes xiLocal difference secret protection is carried out to obtain with secret protection
Attribute yi；
1.6: if the attribute value y after difference privacyiMore than distortion toleance degree, i.e., | yi-xi| > ξ, then in array mark
It records the position of the Sensitive Attributes in the database and prepares to extract watermark, be then inserted into watermark；It is obtained by theory analysis
When the variation c of data meets [- 2 Δ f, 0] when being embedded in watermark, watermark will not destroy difference privacy, wherein -2 Δ f are insertion watermark
When data variation lower limit, Δ f is global susceptibility (as t-1), and 0 is the upper limit of data variation when being embedded in watermark.
It is embedded in the process of watermark are as follows: check the grouping serial number n where the attribute valuei, find corresponding watermark bitIt is embedding
Enter watermarkIfIt is 1, then attribute value is revised as odd number, is otherwise revised as even number；Due to yi-xi-1(yi-xi< t-
1) and -1 belongs to range [- 2 (t-1), 0], so difference privacy will not be destroyed.
Assuming that recording attribute value y in mark array when distortion toleance degree ξ=8, ε=1iPosition in the database,
Initializing all data in mark [n] [m] array is 0, and wherein n is the number of tuple in database, and m is the number of Sensitive Attributes
Amount, when being embedded in watermark in c-th of attribute in tuple tu, then modifying mark [tu] [c] is 1；Then attribute is modified according to watermark
Value yiIt is embedded in watermark.Such as: the attribute value after the first row first row difference privacy is 17, has been more than distortion toleance degree, has then modified
Mark [1] [1]=1, and the watermark 1 being embedded in as needed are embedded in watermark, due to the attribute value 17 < 39 after difference privacy, and 17
It is odd number so not having to modification attribute value, the attribute value after watermark is 17；Category after 8th row secondary series difference privacy for another example
Property value be 99,99 to be greater than original attribute value 50, be embedded in watermark 1, since 50 be even number, modification 50 is 49, so after watermark
Attribute value is 49；And so on to obtain the Sensitive Attributes value after watermark as shown in table 2:
Table 2
| age | hours-per-week |
| 17 | 19 |
| 50 | 0 |
| 16 | 40 |
| 17 | 1 |
| 17 | 1 |
| 37 | 39 |
| 48 | 21 |
| 52 | 44 |
| 17 | 49 |
| 42 | 0 |
| 36 | 12 |
| 16 | 40 |
| 17 | 1 |
| 31 | 1 |
1.7: the database D after output watermarkw' array the mark with record position information；
Referring to fig. 4, the extraction process of watermark carries out as follows:
2.1: the database D after input watermarkw', the array mark of key Ks and record position information；
2.2: initialization zeros=0, ones=0, data integrity integrity=TRUE；
2.3: database being grouped to obtain the number n of tuple using formula (3)i；
2.4: extracting the watermark stage, Sensitive Attributes are performed the following operation: if attribute value is odd number, ones++；It is no
Then zeros++；Until all tuples all iteration are completed in grouping；
2.5: the size of zeros and ones in more every group, if zeros is bigger, then it is assumed that the n-th of insertioniA water
Print is 0；Otherwise it is assumed that the watermark of insertion is 1；
2.6: if zeros and ones are not 0, data are tampered, integrity=FALSE；
2.7: repeating step 2.4 to step 2.6 until all groupings all iteration are completed；
2.8: the watermark and integrality for exporting extraction judge integrity.
The robustness experimental result of watermark is as shown in figure 5, operating process is as follows:
The robustness of database is measured by error rate BER, that is, the accuracy of the watermark bit extracted.
In formula (3), NgIt is packet count, wiIt is the watermark bit of insertion,It is the watermark bit extracted.
Consider three kinds of typical attack types: increasing, deletes and modify.Each attack respectively repairs database
Change 10%, 20% ..., 90%, then extracts watermark in the database after attack, it is as shown in Figure 5 to obtain the bit error rate.In Fig. 5
Abscissa indicates that the tuple number attacked accounts for total number of tuples purpose ratio, and ordinate indicates error rate BER, can from figure
The extraction of watermark is not influenced to attack is increased；When modification attack reaches 80%, modification attack does not also influence watermark；
It deletes influence maximum of the attack to watermark and is also only 4.58%, therefore visible the method for the present invention has very high robustness.
Table 3 is that the attribute value of model proposed by the present invention statisticallys analyze situation:
Attribute before and after the data distortion problem for caused by watermark, statistical data analysis library difference privacy and insertion watermark
Mean value and standard deviation.And carry out data distortion caused by the watermark of quantized data library using mean absolute error MAE.
In formula (4), n is number of tuples, AiWithIt is the attribute value being embedded in front of and after watermark respectively.
Table 3
By table 3 it can be found that watermark reduces data distortion, the availability of data is improved.
Claims (4)
1. a kind of database water mark method based on local difference privacy, it is characterized in that: according to the attribute-name of database to attribute
It is ranked up, tuple grouping is embedded in for watermark according to the major key of tuple in database；To the Sensitive Attributes in database into
Row difference privacy；Feature according to data in the database after difference privacy carries out watermark insertion, then by database after watermark
It is distributed to cloud；User from cloud downloading publication database, from the database of publication extract watermark for copyright tracking and
The integrity verification of data.
2. the database water mark method according to claim 1 based on local difference privacy, it is characterized in that as follows
It carries out:
Step 1: attribute is ranked up according to the attribute-name of database, tuple is grouped according to the major key of tuple in database:
1.1, the database D after being sorted is ranked up to attribute according to the ascending order of the attribute-name of database or descending；
1.2, it is grouped to obtain the number of each tuple in database to database D using formula (1),
ni=H (Ks | | H (Ks | | tu.PK)) %Ng(1),
In formula (1), niIt is the number of tuple in the database after being grouped, ni=1,2 ... Ng, NgFor watermark length；H () is indicated
Hash algorithm, " | | " it is bound symbol, Ks is key, and tu.PK is the major key of tuple；
Step 2: local difference secret protection is carried out to the Sensitive Attributes x in database and obtains the attribute y with secret protection:
Local difference secret protection is realized using Laplce's mechanism, and global susceptibility is attribute maximum value in Laplce's mechanism
With the difference of attribute minimum value, it is assumed that attribute maximum value is t, and attribute minimum value is 1, then global susceptibility is t-1, for attribute
Value is the database of integer, the attribute value of database is mapped to integer 1,2 ... on t, and modifies attribute value x according to formula (2)i?
To attribute value yi, realize the secret protection to the Sensitive Attributes in database；
In formula (2), ck=k+0.5, k=1,2 ... t-1；Lap () is Laplace function；ε is secret protection budget；
Step 3: initialize array mark obtains distortion d brought by attribute y through difference privacy according to Sensitive Attributes x and carries out water
Print insertion, then by database D after watermark 'wIt is distributed to cloud；
3.1, initialize array mark；
3.2, it calculates and obtains attribute value yiCaused by data distortion d are as follows: d=| yi-xi|；User's Custom Attributes value distortion range
For ξ, if data distortion d is more than user's Custom Attributes value distortion range ξ, the record attribute value y in array markiPlace number
According to the position in library, and in attribute value yiMiddle insertion watermark；
It is described in attribute value yiMiddle insertion watermark is to carry out as follows:
According to the number n of tuple each in databaseiWatermark insertion is carried out, the tuple of number having the same is embedded in identical watermark
w；Watermark telescopiny are as follows:
First according to the watermark w to be embedded in modification attribute value yiThe attribute value y ' updatedi, will when the watermark of insertion is 1
Attribute value yiBecome odd number, when watermark is 0, by attribute value yiBecome even number；
For all groupings complete the database D after watermarks are embedded in obtain watermark 'w；
3.2, publication database D 'wTo cloud；
Step 4: user from cloud download to obtain database D 'w, according to the ascending order of the attribute-name of database or descending to attribute into
Row sequence obtains sorting with attribute in step 1 the identical database D of number of identical and each tuple "w；
Step 5: the legitimate user for possessing key extracts watermark, and the ordinary user of key is not only able to use database but cannot
Extract watermark；Initializing variable ones is 0, zeros 0；According to database D "wThe number of middle grouping is successively to the institute in every group
There is tuple to carry out watermark extracting；Water is extracted if the location information of the attribute of tuple each in every group is present in array mark
Print；The process for extracting watermark is as follows:
When attribute value is odd number, ones adds 1, and when attribute value is even number, zeros adds 1；When all properties value all traverses in one group
It completes, compares the size of ones and zeros, if ones > zeros, the watermark w extracted is 1, and the watermark w otherwise extracted is
0；If ones and zeros are not 0, it is judged as that database has been tampered, the integrality of data is destroyed.
3. the database water mark method according to claim 2 based on local difference privacy, it is characterized in that: the secret protection
Budget ε can be set to 1, ln (2) or ln (3).
4. the database water mark method according to claim 2 based on local difference privacy, it is characterized in that: being directed to attribute value yi
The modification of odd number or even number is to carry out as follows:
If w=1 works as yi> xiWhen, if attribute value xiIt is that odd number then modifies yiFor xiIf attribute value xiIt is even number, then belongs to modification
Property value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that odd number is then constant, if attribute value yiIt is even number, then by attribute value yiIt repairs
It is changed to yi-1；
If w=0 works as yi> xiWhen, if attribute value xiIt is that even number then modifies yiFor xiIf attribute value xiIt is odd number, then belongs to modification
Property value yiFor xi-1；Work as yi< xiWhen, if attribute value yiIt is that even number is then constant, if attribute value yiIt is odd number, then by attribute value yiIt repairs
It is changed to yi-1。
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