CN110378144A - The method for secret protection and system of range query are supported under data, that is, service mode - Google Patents

Abstract

The invention relates to a privacy protection method and system supporting range query in a data-as-a-service mode. In the data-as-a-service management model, the security policy of the data service provider may not be complete, and the data owner does not fully trust it. In such an environment, it is necessary to design a complete mechanism that can ensure data privacy and security while data query is relatively efficient. The existing data-as-a-service management model has low time efficiency and risks of privacy information attacks. The present invention proposes a complete, privacy-safe solution that supports range query and data verification, the core of which is to partition the data and obtain an index by means of a partial sum of hash functions for data in the same partition; in order to avoid False hit data and data validation, introducing query accuracy and validation matrix. It is verified by experiments that the present invention has good time efficiency, and at the same time can well reduce data information leakage.

Description

Privacy protection method and system supporting range query in data-as-a-service mode

technical field

The invention belongs to the technical field of data security such as data management and privacy protection, and specifically designs a data-as-a-service (DaaS) data management mode that ensures user privacy and security.

Background technique

Data as a Service (DaaS) is already a data management model in the era of cloud computing. Data organizers obtain on-demand data storage services by purchasing services. By placing storage tasks in the cloud, they can reduce enterprise costs and increase data management capabilities. However, data privacy security has become an issue that data organizers must consider. At present, the leakage of user privacy has caused serious social problems.

In the user privacy protection technology, the first is to set up a reasonable access authority mechanism, and illegal identities cannot obtain data access authority. The second is to implement data encryption technology, encrypt and store key data or all data, and store encrypted data. When using the data, the original data is obtained by decrypting the data, and then specific statistical analysis is performed. Currently, the data-as-a-service model (DaaS) is an effective way to manage data usage. The data is often stored in the server of the data service provider. Data users need to obtain data from the server of the data service provider when using the data. The advantage of the data-as-a-service model is that data access is not limited to time and place, and data organizers do not need to use corresponding hardware to build data servers. However, data storage in data service providers increases the hidden danger of data privacy leakage.

In the DaaS model, the entire business process role can be divided into three: (1) data organizer. is the owner of the data. (2) Data service provider. Store user's encrypted data. (3) Data usage customers. Use the services provided by the data service provider to query. As shown in Figure 1, the data user uses the data storage service of the data service provider. For example, if a data organizer wants to deploy its own data TRADE (tno cost, date) to a data service provider, first, in order to protect data privacy, the data item is encrypted to obtain Entrypt (TRADE) and then submitted to the data service provider. After obtaining the consent of the data organizer and the codebook, the data user can query the data and decrypt it to obtain the original data. The trust relationship and service mode among them are also shown in Figure 1. There is a trust relationship between the data user and the data organizer, and the data user can obtain the password policy of the data to obtain the data query service. However, data service providers do not have an absolute trust relationship with them. The reason why data service providers are untrustworthy is that their storage strategies are not completely reliable, and there may be the possibility of illegal theft and tampering.

For data privacy and security, when the data service provider is not trustworthy, the data needs to be encrypted and stored, and when the query service is performed, the data query request for the operation is also processed, so that the data service provider does not know the specific data. At the same time, it is necessary to improve the operability on encrypted data and to be able to verify query results.

Range query on encrypted data and verification of query results are the core technologies to ensure the availability of data and services. The method of performing range query on the encryption technology includes the encryption algorithm and the bucket division method that maintains the sequence. When using encryption that maintains the order, that is to say, when the number d ₁ <d ₂ , after encryption, Encrypt(d ₁ )<Encrypt(d ₂ ). This method has already been implemented by algorithms, and related algorithms include OPE and OPES, but the above method is time-consuming, and the complexity is high when inserting new data, which will consume more computing resources. The method of bucketing is to divide the data range into several discrete intervals, and assign an identifier to each bucket. In an ideal state, if each bucket has at most one data, there will be no false hits in the query, but In reality, data is often not evenly distributed, and queries often have false hits. In terms of data verification technology, the current technology generally uses Merkle hash trees for verification. This method is difficult for multi-dimensional data verification and requires relatively high space requirements. For example, for two-dimensional data, the required space complexity is O(n ² ). At the same time, when updating data, it is necessary to update the hash values of all parent nodes of the Merkle node of the data, and all data in the data set is required to participate in the calculation.

Contents of the invention

Aiming at the above problems, the present invention provides a verifiable data privacy protection method in a data service model (DaaS), which can simultaneously support range query and correctness verification of query results.

Overall technical scheme of the present invention is as follows:

1. By dividing the value range interval U, divide it into N intervals, and assign a unique identifier to each interval. This interval is the update unit of the hash index and hash signature chain when data is inserted, and is the update unit of the security policy. The update of the security policy means that the identifier of the interval can be updated to prevent the importance attack due to the frequency of access, and the encryption key can also be changed to automatically expire the data permissions of certain data users, which can prevent data access permissions from being abused .

2. Introduce query accuracy Φ and flag records, so that you can locate a specific location according to the boundary range when performing range search.

3. In the same partition, calculate the hash index that is consistent with the order of the attribute values of the data. When obtaining a hash index that maintains the order, the order is maintained by accumulating the hash function values of the partition elements.

4. The present invention calculates a hash signature chain and verification matrix for data verification. Each hash signature in the hash signature chain is obtained by hashing its own data item and its adjacent data items. The hash signature chain is stored in the data service provider. In order to verify the hash signature chain and data items, the present invention designs a verification matrix to verify the query result. Through the verification matrix, the correctness and integrity of the data can be verified in three ways: self-certification, other certification, and co-certification.

Specifically, the technical scheme adopted in the present invention is as follows:

A privacy protection method supporting range query in a data-as-a-service mode, comprising the following steps:

1) The data organization end divides the value range of the data into several intervals, each interval is assigned a unique identifier, and the mapping relationship between intervals and identifiers is used as a part of the codebook; the data organization end authorizes the codebook to trusted data user;

2) The data organization end establishes a sequential hash index for the data items in the same interval, and calculates the hash signature chain; each hash signature in the hash signature chain passes the data item itself and the data connected to it The hash of the item is obtained;

3) When the data organization end inserts data, set a flag record in the hash index, and then submit the encrypted data items in each interval, the corresponding hash index, and the hash signature chain to the data server;

4) When the data user end searches for the range from the data server end, it locates the specific location according to the boundary range through the query accuracy and mark records set by the data organization end;

5) After receiving the data returned by the data server, the data user uses the codebook authorized by the data organization to decrypt the data, and uses the verification matrix of the hash signature to verify the data.

A privacy protection system supporting range query under the data-as-a-service mode, including a data organization end, a data server end, and a data use end;

The data organization end divides the value range of the data into several intervals, each interval is assigned a unique identifier, and the mapping relationship between intervals and identifiers is used as a part of the codebook; the data organization end authorizes the codebook to be used by trusted data end;

The data organization end establishes a sequential hash index for the data items in the same interval, and calculates the hash signature chain; each hash signature in the hash signature chain is passed through the data item itself and the data item connected to it. get the hash;

When the data organization end inserts data, set the flag record in the hash index, and then submit the encrypted data items in each interval, the corresponding hash index, and the hash signature chain to the data server;

When the data user end searches for the range from the data server end, it locates the specific location according to the boundary range through the query accuracy and mark records set by the data organization end;

After the data user receives the data returned by the data server, it decrypts the data with the codebook authorized by the data organization, and verifies the data with the verification matrix of the hash signature.

The present invention designs an efficient and safe data service model (DaaS), through the design of data submission, query and verification, it can provide security guarantee in the whole life cycle of data, and can provide a A complete and secure DaaS model provides data management and ensures data privacy and security. The program has the following advantages and effects:

1. It can realize accurate range query on encrypted data, and there is no false hit in the query result. By defining the query precision Φ, the boundary data that can be queried in the range can be located at the boundary of the data set even if it is not in the data set.

2. It has good time efficiency. Through value domain partitioning, all operations can be completed with a time complexity of O(1) for the overall n of the data set. Data is time-efficient during submission, update, and query.

3. Added the verification of the correctness of the query results. The data hash signature for data verification is stored in the data service provider to maximize the use of the data service provider's services. At the same time, for more complete verification, the signature and data items are verified in three ways through the verification matrix. Existence of deletion, falsification and destruction is verified.

4. Data privacy and security protection throughout the data life cycle. From data submission, to data storage, data query, and data correctness verification, the entire data transmission process protects data privacy and security, effectively reducing real data leakage and preventing malicious statistical analysis of data.

5. Through data partitioning, the data security policy can be upgraded in units of partitions. By gradually updating the data identifier and data partition by partition, the codebook in the hands of the data user can be invalidated, which is beneficial to the security control of the data.

Description of drawings

Figure 1 is a schematic diagram of the organizational structure of the data service model (DaaS) and their trust relationship.

Fig. 2 is an overall schematic flow chart of the solution of the present invention. It is mainly divided into three parts, data organizers, data service providers, and data users. Five interfaces, the data management interface and query interface of data organizers and data service providers, the query matching and data verification interfaces of data users.

Fig. 3 is a schematic diagram of a hash signature designed by the solution of the present invention, wherein the character d represents a data item, and s represents a hash signature stored together with the data item.

Fig. 4 is a schematic diagram describing the hash signature of the data when the solution of the present invention queries data in multiple dimensions. Among them, A and B represent the attributes of two queries, and the data items in a partition of attribute A are also kept in order according to attribute B.

Fig. 5 is a schematic diagram of data range query in the scheme of the present invention, Q represents query, a and b are query range boundaries, and id is an identifier of a specific value domain partition.

Fig. 6 is a comparison result graph of the processing time of the CPS query.

Fig. 7 is a comparison result diagram of data index value and data original value.

Detailed ways

The main technical points of the present invention include core steps such as value domain division, obtaining hash index, calculating hash signature chain, submitting, querying and verifying data. Fig. 2 is an overall schematic flow chart of the solution of the present invention, which is mainly divided into three parts, data organizer, data service provider, and data user. These three parts can also be called data organization end, data server end and data use end respectively. The implementation of each part is described in detail below.

1. Value range division.

The data organizer sets the value range of the index item of the query to be established as U, divides it into N intervals according to its distribution, and assigns an identifier id _i to each interval. This identifier can uniquely match a range, and the mapping relationship between each range and its identifier is used as a part of the codebook, and the codebook is owned by the data organizer.

2. Get the hash index.

This part is mainly to get the sequential hash index, which is done by the data organizer. For data d ₁ <d ₂ , its index value Index(d ₁ )<Index(d ₂ ). In order to obtain the hash value that maintains the order and can quickly calculate the hash value, the partial sum of the hash value is used in the same partition. That is, the data D _i ={d ₁ , d ₂ , . . . , d _Ni } for the partition U _i . Its hash index is obtained by:

3. Get the hash signature chain and verification matrix.

This part is mainly to verify the correctness and completeness of the query results and is completed by the data organizer. The calculation unit of the hash signature chain is also a partition. In each data record, as shown in FIG. 3 , the data items have been sorted in order, and each data item records a hash signature calculated jointly by its own data item and the hash value of the next data item. The signature formula is:

S(data)＝MaxP(SHash(d _i ), 1/ε ₁ )+MaxP(SHash(d _i-1 ), 1/ε ₂ ) (1)

Among them, ε ₁ and ε ₂ are the calculation parameters, S(data) represents the hash signature of the data data, MaxP(a,b) represents the greatest common multiple of the integer b less than a (a does not have to be an integer), and SHash is applied to the data Hash function for item d _i . ε ₁ and ε ₂ determine the collision rate of the signature formula. According to the signature formula, when ε ₁ and ε ₂ are smaller, at the same time When a prime number is selected, the signature formula conflict rate is lower. At the same time, ε ₁ and ε ₂ should be determined by the data organizer. For the reliability of data verification, this parameter is unknown to the data service provider.

Through this formula, each data item or hash signature can be proved in three ways: 1) Self-certification. 2) Other certificates. The hash signature is proved by the next data item, and the data item is proved by the previous hash chain. 3) Co-certification. Satisfy the signature formula. Then design a hash signature verification matrix based on this:

in s _ij indicates whether the hash signature or data item satisfies the three proof methods. The ways of other proof and self proof are the following formulas (2), (3). Where s _i is the hash signature of data d _i obtained by requesting data from the data service provider. s ₁₁ , s ₁₂ , s ₁₃ indicate whether the hash signature satisfies self-certification, other certification and joint certification, and s ₂₁ , s ₂₂ , s ₂₃ respectively indicate whether the data item satisfies self-certification, other certification and joint certification. 1 means satisfied, 0 means not satisfied.

in β ₁ =1-ε ₁ , β ₂ =1-ε ₂ , and β ₃ show the errors of the three proofs β ₃ =1-ε ₁ ·ε ₂ . Also define the calculation "*":

Au=S*A, au _ij =max(S _ik ×a _kj ).

Among them, s _ik represents the elements of matrix S, i and k represent the subscripts of rows and columns; a _kj represents the elements of matrix A, and k and j represent the subscripts of rows and columns.

4. Submit data

When the data organizer submits data items to the data service provider, it mainly involves two aspects, the calculation of hash index and hash signature. The first is to obtain the identifier id of the partition of the data. After matching the data identifier id through the codebook, in order to keep the hash index and hash signature of the data in the same partition correct, it is necessary to request the data service provider based on the id. All the data of the partition (requesting all the data of the partition is a general step of data insertion, if the data is submitted for the first time, you will get empty data after the request). Then insert the new data to be submitted and sort the data in the partition, and then get the hash index and hash signature according to the signature formula and index formula. Finally, all the data of the partition is submitted to the data service provider.

When indexed, it may be necessary to insert flag records. For the partition [a, b), its query precision Φ needs to insert the identification data in front of the inserted data v, that is, the label record v'. According to the previous method of obtaining the hash index, it can be known that for a boundary data value that does not exist in a data set, the smallest value greater than it and the largest value smaller than it cannot be obtained. That is, for the query interval Q(c,d), it is impossible to locate the boundary values c and d. Query precision is to solve this problem. The query precision Φ is the minimum query precision of data in an interval. The query precision is determined by the array organizer. Data users need to know the query accuracy when querying, and this information is given by the data organizer. If the query accuracy of the partition [a,b) is Φ, the interval [a,b) can be divided into discrete data of {a,a+Φ,...,a+iΦ,...,b}, this When the query boundaries c and d are converted to a+iΦ respectively, this value can be located to the specific position of the data set through the flag record v'. For the flag record v'<v, in this partition, the index can still maintain the order. At the same time, for the flag record v', v'=a+iΦ, the additional value i of the flag record needs to be recorded. The partition identifier id of the flag record is the same as Data v is the same. The calculation formula of i is (v-a)/Φ, and this value is taken as an integer.

For Φ, it should be defined according to the data distribution of the partition. At the same time, the Φ defined by different partitions is not necessarily the same. If the data is relatively sparse, then Φ can be larger. For relatively dense data in the partition, Φ is relatively small, such as for integer data. , Φ can be set to 1. At the same time, Φ is also agnostic to data service providers.

When submitting a data item, a record may have multiple attributes that are indexed. The partitions on different attributes are different. In order to enable the calculation of index values and hash signatures of multiple attributes, it is necessary to operate in the order of attributes. Assuming that an inserted data item has two attributes A and B, first obtain the data item of the entire partition according to the partition identifier of the A value, and then recalculate the index and hash signature after inserting the entire data item. Then obtain all the data items of the partition by obtaining the partition identifier of attribute B, and then update the index and signature data of these data items and submit them to the server in the data service provider. As shown in Figure 4, where A and B represent two query attributes, the data items in an attribute range A are also kept in order according to attribute B.

5. Query data

When searching for a data range, the range area can be divided into two types: 1) The entire range of data satisfies the query. 2) In the interval of the query boundary, some may not be in the query range. After the scope is divided into these two categories, the partition identifier is matched with the calculated index value and the additional value of the flag record. After submitting this information to the server in the data service provider, the server returns the data to the data user. After the data user obtains the data, he decrypts the data (using the password book authorized by the data organizer to decrypt the data) and verifies the data. Fig. 5 is a schematic diagram of a range query, where q ₁ and q ₂ represent flag records obtained by calculating values a and b.

After the data user obtains the queried data, each data includes data item d _i and hash signature s _i . Then calculate the signature matrix for each data i from this According to the definition of Au above, the following results can be judged by Au: the possibility of no missing data before the data item is au ₁₂ , the possibility of no missing data behind the data item is au ₂₂ , and the possibility of correct data item is au ₂₁ , the probability that the hash signature is correct is au ₁₁ .

6. Experimental data and conclusion

The scheme of the present invention verifies the scheme based on time efficiency and data distribution, and verifies the feasibility of the scheme and has good time efficiency in time. The advantages of this scheme are analyzed through further experiments in the following. The scheme is based on a simulation-generated dataset TRADE(tno cost,date) and a public database TLSPD from labor statistics.

1) Time efficiency verification.

A major performance index of the present invention is time efficiency. First of all, the time efficiency of our program. The execution time of the solution of the present invention is compared with that of OPHF, as shown in Table 1. OPHF is a sequential indexing algorithm that does not use partitions.

Table 1: Statistical table of execution time of different schemes (milliseconds/each data item)

Number of partitions (N) all the time Encryption and decryption time Data query preprocessing time The query time of the data service provider 500 54.90754 0.52868 0.3628 54.01606 1000 54.6431 0.45218 0.22302 53.9679 2000 52.6859 0.40784 0.14428 52.13378 OPHF 4957.006 4.842 4929.932 22.096

During the experiment, the simulated data TRADE(tno cost, date) has 10,000 pieces of data, where the cost is randomly generated from a uniform distribution ranging from 0 to 10,000,000. During the experiment, we first adopted our scheme CPS, indexed the cost attribute, and carried out the experiment according to the number of intervals divided into 500, 1000, and 2000. The experimental results are shown in Figure 6. It can be seen that the smaller the interval division, the Less time is consumed. However, the fewer division intervals, the data codebook that the data owner needs to record contains too much data. At the same time, compared with OPHF, the solution of the present invention has good time efficiency.

2) Data privacy protection

This part mainly proves that the data index of the present invention will not leak data privacy. It mainly includes the distribution of the data that will not be leaked and the maximum and minimum values of the data. The experimental results are shown in Figure 7. It can be seen that the data index is increasing in the same partition, and the increase is linear, regardless of the data distribution. In Figure 7, (a) is the uniformly distributed data generated by simulation, and (b) is the actual database. It can be seen that no matter how the actual data is distributed, as long as the partitions are set reasonably, the data items in each partition are as large as possible. same, then importance attacks can be avoided. At the same time, the dynamic update of the identifier of each partition avoids malicious analysis according to the query frequency.

This scheme has been verified experimentally from the perspective of time efficiency and data privacy security, and the experiment shows that the scheme has good time efficiency. There is very little computational consumption in the data submission, data query, and data validation phases. Moreover, this scheme is a complete scheme. In the data relationship model, through the scheme of the present invention, data can be managed effectively and safely, and encrypted data can be queried safely and effectively when the data service provider is not credible, and can verify Integrity and correctness of query results.

Another embodiment of the present invention provides a privacy protection system supporting range query in the data-as-a-service mode, including a data organization end, a data server end, and a data use end;

The data organization end divides the value range of the data into several intervals, each interval is assigned a unique identifier, and the mapping relationship between intervals and identifiers is used as a part of the codebook; the data organization end authorizes the codebook to be used by trusted data end;

The data organization end establishes a sequential hash index for the data items in the same interval, and calculates the hash signature chain; each hash signature in the hash signature chain is passed through the data item itself and the data item connected to it. get the hash;

When the data organization end inserts data, set the flag record in the hash index, and then submit the encrypted data items in each interval, the corresponding hash index, and the hash signature chain to the data server;

When the data user end searches for the range from the data server end, it locates the specific location according to the boundary range through the query accuracy and mark records set by the data organization end;

After the data user receives the data returned by the data server, it decrypts the data with the codebook authorized by the data organization, and verifies the data with the verification matrix of the hash signature.

The above embodiments are only used to illustrate the technical solution of the present invention and not to limit it. Those of ordinary skill in the art can modify or equivalently replace the technical solution of the present invention without departing from the spirit and scope of the present invention. The scope of protection should be determined by the claims.

Claims (10)

1. A privacy protection method supporting range query under a data-as-a-service mode, characterized in that it comprises the following steps: 1) The data organization end divides the value range of the data into several intervals, each interval is assigned a unique identifier, and the mapping relationship between intervals and identifiers is used as a part of the codebook; the data organization end authorizes the codebook to trusted data user; 2) The data organization end establishes a sequential hash index for the data items in the same interval, and calculates the hash signature chain; each hash signature in the hash signature chain passes the data item itself and the data connected to it The hash of the item is obtained; 3) When the data organization end inserts data, set a flag record in the hash index, and then submit the encrypted data items in each interval, the corresponding hash index, and the hash signature chain to the data server; 4) When the data user end searches for the range from the data server end, it locates the specific location according to the boundary range through the query accuracy and mark records set by the data organization end; 5) After receiving the data returned by the data server, the data user uses the codebook authorized by the data organization to decrypt the data, and uses the verification matrix of the hash signature to verify the data. 2. The method according to claim 1, wherein each interval is an update unit of a hash index and a hash signature chain when inserting data, and is an update unit of a security policy; the update of the security policy refers to the update of the security policy by Update the identifier of the interval to prevent importance attacks due to access frequency, and change the encryption key to automatically expire the data permissions of certain data users, thereby preventing data access permissions from being abused. 3. The method according to claim 1, wherein when establishing the hash index maintaining the order, the order is maintained by superimposing the hash function values of the elements in the interval. 4. The method according to claim 1, wherein the query accuracy can be positioned to the query boundary when the range query is performed, and setting different query precisions in different intervals will not cause data distribution leakage; when the range query is performed by comparing the marks Record markers and boundary values to avoid false hits for queries. 5. The method according to claim 1, wherein the hash index is in the same interval, the index value is in the same order as the data record, and when querying ranges, only the location of the boundary is needed to obtain the query range. 6. The method according to claim 1, wherein the verification matrix is calculated according to the hash signature, and both the hash signature and the data items can be verified; The proof method verifies the data, and can verify whether the data has been deleted, forged and destroyed. 7. The method according to claim 6, wherein the calculation formula of the hash signature is: S(data)＝MaxP(SHash(d _i ), 1/ε ₁ )+MaxP(SHash(d _i-1 ), 1/ε ₂ ) Among them, ε ₁ and ε ₂ are the calculation parameters, S(data) represents the hash signature of the data data, MaxP(a, b) represents the greatest common multiple of the integer b less than a, and SHash is the hash applied to the data item d _i Hive function; ε ₁ and ε ₂ determine the collision rate of the signature formula. According to the signature formula, when ε ₁ and ε ₂ are smaller, and When a prime number is selected, the signature formula conflict rate is lower. 8. The method according to claim 7, wherein the verification matrix is: in, s _ij indicates whether the hash signature or data item satisfies the three proof methods, s ₁₁ , s ₁₂ , s ₁₃ Indicates whether the hash signature satisfies self-certification, other certification and joint certification, s ₂₁ , s ₂₂ , and s ₂₃ respectively indicate whether the data item satisfies self-certification, other certification and joint certification; in, β ₁ =1-ε ₁ , β ₂ =1-ε ₂ , β ₃ indicates the errors of the three proofs, β ₃ =1-ε ₁ ·ε ₂ ; Among them, Au=S*A, au _ij =max(s _ik ×a _kj ); s _ik represents the elements of matrix S, i and k represent the subscripts of rows and columns; a _kj represents the elements of matrix A, k and j Indicates row and column subscripts. 9. The method according to claim 1, wherein after the data user obtains the queried data, each data includes a data item d _i and a hash signature _si , and then calculates each data signature matrix of i Among them: the possibility of not missing the front of the data item is au ₁₂ , the possibility of not missing data behind the data item is au ₂₂ , the possibility of the correct data item is au ₂₁ , and the correct possibility of the hash signature is au ₁₁ . 10. A privacy protection system supporting range query under the data-as-a-service mode, characterized in that it includes a data organization end, a data server end, and a data use end; The data organization end divides the value range of the data into several intervals, each interval is assigned a unique identifier, and the mapping relationship between intervals and identifiers is used as a part of the codebook; the data organization end authorizes the codebook to be used by trusted data end; The data organization end establishes a sequential hash index for the data items in the same interval, and calculates the hash signature chain; each hash signature in the hash signature chain is passed through the data item itself and the data item connected to it. get the hash; When the data organization end inserts data, set the flag record in the hash index, and then submit the encrypted data items in each interval, the corresponding hash index, and the hash signature chain to the data server; When the data user end searches for the range from the data server end, it locates the specific location according to the boundary range through the query accuracy and mark records set by the data organization end; After the data user receives the data returned by the data server, it decrypts the data with the codebook authorized by the data organization, and verifies the data with the verification matrix of the hash signature.