Patent Publication Number: US-10783263-B2

Title: System and architecture for supporting analytics on encrypted databases

Description:
BACKGROUND 
     The subject matter of the present specification generally relates to the art of data security. Exemplary embodiments disclosed herein find particular application in conjunction with a Structured Query Language (SQL) database (DB) and/or a Database Management System (DBMS) (e.g., such as MySQL), and they will be described herein with particular reference thereto at times. However, it is to be appreciated that various exemplary embodiments such as those disclosed herein are also amenable to other like applications including other types of relational databases as well as graphic and/or other types of databases. 
     In the field of data security, certain types of encrypted databases are not unknown. However, heretofore, there has been no strong consensus about a suitable architecture that incorporates sufficient privacy by design in data analytics. For example, there has been no strong consensus about how encrypted data should be arranged or stored such that it remains amenable to otherwise traditional database queries, how key management is to be performed and/or what measures should be taken to perform private analytics efficiently. 
     One proposed architecture is known as “CryptDB.” In general, it involves storing data in an encrypted format using “onions of encryption,” in which different encryptions are successively applied to the data. Accordingly, depending upon a query, layers of encryption can be removed (like peeling an onion), until one can access the data in the appropriate encrypted format, and perform sufficient computations thereon to answer the query. While this approach has been shown to support a subset of SQL queries, making it useful to data scientists who are already skilled in analytics for plaintext databases, there are some potential disadvantages. 
     One potential disadvantage to the foregoing approach is that not all the cryptosystems employed in CryptDB have sufficiently strong security properties. For instance, deterministic encryption and order preserving encryption may leak more information than is sufficient to answer a given query. In particular, in order to execute SQL WHERE queries, CryptDB has to access the deterministic encryption layer, which may leak additional information to someone that knows the distribution and cardinality of the data. 
     Disclosed herein are a new and/or improved system and/or method for providing and/or utilizing an encrypted database. 
     INCORPORATION BY REFERENCE 
     The present specification incorporates by reference the U.S. Patent Application entitled “System and Architecture for Analytics on Encrypted Databases,” filed on Aug. 11, 2017, by inventors Shantanu Rane, et al., having U.S. patent application Ser. No. 16/674,935. 
     BRIEF DESCRIPTION 
     This Brief Description is provided to introduce concepts related to the present specification. It is not intended to identify essential features of the claimed subject matter nor is it intended for use in determining or limiting the scope of the claimed subject matter. The exemplary embodiments described below are not intended to be exhaustive or to limit the claims to the precise forms disclosed in the following Detailed Description. Rather, the embodiments are chosen and described so that others skilled in the art may appreciate and understand the principles and practices of the subject matter presented herein. 
     In accordance with one exemplary embodiment, there is provided a method for generating an encrypted database. The method includes: receiving a plaintext database having plaintext data entries in one or more columns; augmenting the received plaintext database to generate an augmented plaintext database, the augmenting including the addition of one or more columns to the received plaintext database, each added column corresponding to an attribute which is to be made available for conditional queries; and encrypting the augmented plaintext database to generate the encrypted database including encrypted data entries. The encrypted database supports at least one form of conditional query for those attributes corresponding to the added columns, the at least one form of conditional query being computed on the encrypted data entries without the decryption thereof to produce an encrypted result. 
     In accordance with another exemplary embodiment, there is provided a system for administering an encrypted database. The system includes: an Extract, Transfer and Load (ETL), implemented on one or more computers, wherein said ETL server is operative to (i) receive as input a plaintext database having unencrypted data entries therein in one or more columns, (ii) augment the received plaintext database to generate an augmented plaintext database, wherein said augmented plaintext database includes the addition of one or more columns to the input plaintext database, each said added column corresponding to an attribute which is to be made available for conditional queries, and (iii) encrypt the augmented plaintext database to generate the encrypted database including encrypted data entries; a database (DB), implemented on one or more computers, wherein said DB server is operative to (i) receive and maintain the encrypted database from the ETL server, and (ii) return encrypted data in response to queries submitted to the DB server; and a computation, implemented on one or more computers, wherein said computation server is operative to (i) submit queries to the DB server, and (ii) conduct computations on encrypted data returned from the DB server. Suitably, the computations are conducted on the encrypted data from the encrypted database without decryption of the encrypted data, and results obtained from said computations are encrypted. The encrypted database is suitably configured so as to support obtaining correct encrypted results in response to at least one form of conditional query without revealing samples of the unencrypted data underlying the encrypted data. 
     Numerous advantages and benefits of the subject matter disclosed herein will become apparent to those of ordinary skill in the art upon reading and understanding the present specification. It is to be understood, however, that the detailed description of the various embodiments and specific examples, while indicating preferred and/or other embodiments, are given by way of illustration and not limitation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following Detailed Description makes reference to the figures in the accompanying drawings. However, the inventive subject matter disclosed herein may take form in various components and arrangements of components, and in various steps and arrangements of steps. The drawings are only for purposes of illustrating exemplary and/or preferred embodiments and are not to be construed as limiting. Further, it is to be appreciated that the drawings may not be to scale. 
         FIG. 1  is a diagrammatic illustration showing an exemplary system and/or architecture in accordance with aspects of the present inventive subject matter. 
         FIG. 2  is a flow chart showing an exemplary process and/or method for pre-processing and encrypting a database in accordance with aspects of the present inventive subject matter. 
     
    
    
     DETAILED DESCRIPTION 
     For clarity and simplicity, the present specification shall refer to structural and/or functional elements, relevant standards, algorithms and/or protocols, and other components, methods and/or processes that are commonly known in the art without further detailed explanation as to their configuration or operation except to the extent they have been modified or altered in accordance with and/or to accommodate the preferred and/or other embodiment(s) presented herein. Moreover, the apparatuses and methods disclosed in the present specification are described in detail by way of examples and with reference to the figures. Unless otherwise specified, like numbers in the figures indicate references to the same, similar or corresponding elements throughout the figures. It will be appreciated that modifications to disclosed and described examples, arrangements, configurations, components, elements, apparatuses, methods, materials, etc. can be made and may be desired for a specific application. In this disclosure, any identification of specific materials, techniques, arrangements, etc. are either related to a specific example presented or are merely a general description of such a material, technique, arrangement, etc. Identifications of specific details or examples are not intended to be, and should not be, construed as mandatory or limiting unless specifically designated as such. Selected examples of apparatuses and methods are hereinafter disclosed and described in detail with reference made to the figures. 
     In accordance with aspects of the present inventive subject matter, the set of computations that can be performed on DBs secured with additively homomorphic cryptosystems is extended. One exemplary embodiment is concerned with relational DBs that can be queried using a language like SQL. Consider, for example, the following SQL query that adds up the number of children in a DB of a school:
         SELECT AVG(age) FROM hogwarts       

     If the number of children in each household is encrypted using a semantically secure additively homomorphic cryptosystem, then this query can be processed in the encrypted domain, returning an encrypted result. This result can then be decrypted by an analyst or other user with the appropriate privileges. 
     Consider now, a slightly more complicated query: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 SELECT AVG(age) FROM hogwarts 
               
               
                   
                 WHERE gender = “female”; 
               
               
                   
                   
               
            
           
         
       
     
     In this query, the encrypted-domain summation is performed only over those particular rows in the table that satisfy the specified condition, i.e., the gender attribute is “female”. Even with this small addition, executing the query is no longer straightforward. The reason is that, with semantically secure encryption, it is not readily feasible to tell which rows correspond to female children, just by examining the ciphertexts in the encrypted “gender” column of the table. 
     One could instead use deterministic encryption for the gender column. However, this will result in only two kinds of ciphertexts, one for male and one for female. This makes it easy to identify the rows corresponding to female and male children while still keeping the age of each student encrypted using the semantically secure additively homomorphic cryptosystem. A problem with the foregoing deterministic encryption approach is that it can leak information, not only to the DB server, but also to any computing node that is processing the query in the encrypted domain. In practice, the storage and computation could be based in the cloud or otherwise, and thus may be handled by an untrusted party. For example, a Chosen Plaintext Attack (CPA) on such a DB plainly reveals which entries in the database correspond to girls and which correspond to boys. In accordance with aspects of the present inventive subject matter, a system and/or method is proposed to avoid such privacy leakage. More specifically, a system and/or method is described which is capable of processing conditional queries like the above, with semantic security. 
     The present specification describes an architecture for performing analytics on privacy-sensitive data. Suitably, the architecture includes a DB server, e.g., an untrusted DB server. In practice, the DB server stores encrypted data and is backed by a relational database management system such as MySQL or the like. The architecture also includes a computation server (e.g., an untrusted computation server) that performs computations in the encrypted domain, and a web server or web service that queries the DB. Suitably, the computation server returns an encrypted result for every query submitted by the web server/service. In practice, only an authorized user is able to decrypt the returned results. In an exemplary embodiment, aggregate functions (e.g., including summations, linear combinations, basic classifiers, count queries and histograms) are computed without discovering the samples of the underlying data. Suitably, objectives of the present inventive subject matter (e.g., supporting a subset of SQL queries, while providing improved privacy assurances) are achieved using semantically secure homomorphic encryption techniques within the described system and/or architecture. 
     Generally, the system and/or architecture described herein enables privacy-preserving data analytics, whereby a dataset owner or curator grants to a user (e.g., such as an analyst or data scientist) the ability to run queries against an encrypted version of the dataset. More precisely, the disclosed system and/or architecture suitably provides the following functionality to the dataset owner and analyst:
         the dataset owner is provided the ability to generate cryptographic keys, pre-process and encrypt a dataset; and   the analyst is provided the ability to run queries against a dataset in its encrypted form, and obtain the necessary key(s) from the data owner to decrypt the query results.       

     Suitably, to provide the aforementioned functionality, the system is designed, for example, with a three-tiered architecture as illustrated in  FIG. 1 . More specifically, in practice, the system may include: (i) a so-called “Front-End,” e.g., implement via a web service and/or web server  10  or the like; (ii) a so-called “Back End” including a Computation Server (CS)  20 ; and (iii) a DBMS  30 , e.g., including a DB server implemented via MySQL or another relational or other suitable type of DB. 
     In practice, a basic embodiment includes the following elements: (1) a DB server that stores data in one or more of a plurality of encrypted formats (e.g., the DB server is a MySQL DB server or the like); (2) a CS that executes queries provided by a user/analyst using encrypted data served by the DB (e.g., via an appropriate privacy preserving protocol); and (3) a web service/server that supports queries made to the DB and receives encrypted results corresponding to the queries made. 
     In an expanded embodiment, a Key Authority (KA)  40  is included that provides key management functionality. In particular, the KA  40  provides public encryption keys to generate the encrypted DB that is stored in the DB server. Further, the KA  40  provides public encryption keys to the CS  20  for running privacy-preserving protocols. Finally, the KA  40  provides decryption keys to an authorized user of the web service/server that allows the user to decrypt the encrypted result of the query that is received from the CS  20 . 
     In a further expanded embodiment, an additional element and/or elements are provided to prepare the encrypted DB (denoted as D e  herein). In practice, preparation of D e  starts with an unencrypted DB (denoted as D p  herein) as input. That is to say, the data elements in D p  are initially stored and/or maintained in an unencrypted form or as plaintext. Prior to encryption, the schema of D p  is augmented in such a way that the augmented schema supports a desired subset of SQL queries. In the augmented DB (denoted herein as D a ), the data elements are also stored/maintained in an unencrypted form or as plaintext. D a  (having the augmented schema with the resulting data) is then encrypted using one or more encryption formats to achieve D e . Finally, D e  is transmitted to the DB server. 
     Suitably, the Front-End provides a specific view and/or user interface (UI) for a specific task or tasks. In practice, for example, an Analyst View  12  and/or suitable UI is provided in a first instance to be used by an analyst to write and run Structured Query Language (SQL) and/or SQL-like queries against an encrypted dataset  32   e , whereas in a second instance an Extract, Transfer and Load (ETL) View  14  and/or suitable UI is provided to be used by a data owner to pre-process and encrypt a plaintext dataset  32 . In practice, the Front-End may interact directly with the CS  20 , for the Analyst View  12 , and with an ETL server  50  for the ETL View  14 . In a suitable embodiment, the ETL server  50  may be a trusted “helper” under the control of the data owner. In contrast, the CS  20  may be an untrusted helper that functions as a separate entity. Suitably, the CS  20  is responsible for processing the analyst&#39;s queries it receives, and interacting with the DBMS  30 . Because the dataset  32   e  is encrypted in the DBMS  30 , the CS  20  performs the query on encrypted data and returns (encrypted) results to the analyst through the Front-End. The analyst, having previously obtained the necessary decryption keys, e.g., from the Key Authority (KA)  40 , can recover the queries&#39; results by decrypting the data received by the Front-End from the CS  20 . 
     In one exemplary embodiment, the DBMS  30  is implemented with a standard MySQL DB server, while both the CS  20  and ETL server  50  are implemented with Java-based programs (e.g., which use the same codebase). Suitably, the Front-End may be implemented as a combination of Javascript, HyperText MarkUp Language (HTML) and Cascading Style Sheets (CSS). That said, in practice, other implementations for the aforementioned components may be employed which are suitable for achieving the functions, objectives, operations and/or purposes described herein. 
     In accordance with exemplary embodiments described herein, one threat sought to be avoided is parties other than the data owner and analyst learning information about the dataset  32  imported into the system. This includes both accidental and intentional leaks at the CS  20  and DBMS  30 , both of which may be untrusted. Suitably, such leaks are prevented by design because the imported dataset  32  is encrypted under keys which neither the DBMS  30  nor the CS  20  have access to. Additionally, and depending on the context, the system&#39;s architecture may provide protection against additional threats, e.g., such as the following:
         (1) The analyst learning sensitive information about individuals whose records are in the imported dataset  32 ; and/or   (2) The CS  20 , DBMS  30  and/or data owner learning about the analyst&#39;s queries.       

     For example, guarding against item (1) above is referred to as preserving an individual&#39;s privacy, and may be accomplished using techniques such as Differential Privacy and, guarding against item (2) above is referred to as preserving query privacy, and may be accomplished using “special” queries which obfuscate the “real” query. 
     With additional reference now to  FIG. 2 , there is shown a process and/or method  100  by which a plaintext DB D p  is pre-processed and encrypted, e.g., via the ETL server  50 . In practice, a DB owner or the like may employ the Front-End web service/server  10 , e.g., using the ETL View  14  or other suitable UI to access the ETL server  50  in order to pre-process and encrypt the plaintext dataset  32 . 
     Suitably, the process or method  100  converts an input plaintext DB D p  to an encrypted DB D e , that supports conditional queries in the encrypted domain. Of course, one could construct D e  simply by encrypting each individual entry of D p  using an appropriate semantically secure homomorphic cryptosystem, but as explained above, this approach would not effectively support conditional queries as desired. Instead, as described herein, D a  is first constructed, which is an augmented plaintext version of D p , and then D a  is encrypt to obtain D e . 
     As shown, in step  110 , D p  (containing the plaintext dataset  32 ) is input into the ETL server  50 , e.g., using an ETL process. The data elements of D p  are suitably unencrypted and/or represented in a plaintext form. Suitably, along with D p  there is input a specification identifying those attributes which will be made available for use in connection with conditional queries and the like. For example, in the above-referenced scenario, the gender attribute may be such a specified conditional attribute that takes two distinct values, i.e., male or female. A conditional attribute is an attribute of the DB (e.g., which is specified and/or identified along with the input D p ) that will be made available for the execution of conditional queries and/or the like computed in the encrypted domain. 
     In step  120 , the schema of the input D p  is augmented to achieve D a , e.g., such that the augmented schema supports a desired set of queries after the DB is encrypted. 
     More specifically, the augmentation and/or generation of D a  may take place as follows. The resulting augmented plaintext DB D a  will contain a number of extra columns as compared to the input D p . The number of extra columns is  v =Π m=1   M v m , where there are M specified conditional attributes, and each of those attributes take v m  possible values, m=1, 2, . . . , M. In practice, some attributes may take only one value for a given DB entry. For instance, the aforementioned gender attribute may take a value of male or female. Other attributes can take more than one value for a given database entry. For instance, a hobbies attribute for a given student may take multiple values such as reading, cycling, herbology, etc. 
     In one suitable embodiment, to construct D a  from D p , the following sub-steps are applied to each of the M conditional attributes. In the following sub-steps consider a conditional attribute A m , m=1, 2, . . . , M that takes v m  distinct values. Then, for each attribute A m :
         1) Set D a =D p .   2) Create v m  extra columns in D a . For convenience, consider the additional v m ×n entries added to the database D a  as a result of the v m  extra columns as belonging to a matrix S. This notation will allow us to refer to the additional element in the i th  row and j th  column as S(i, j) where 1≤i≤n, and 1≤j≤v m .   3) For every row index i, set S(i, j) to be the binary indicator variable for the j th  possible value of A m . Thus, for a given row i∈{1, 2, . . . , n}, if the attribute value is b∈{1, 2, . . . , v m }, then S(i, b)=1 and S(i, j)=0 for all j≠b.       

     Having suitably obtained the augmented plaintext DB D a , at step  130 , D a  is encrypted to obtain D e , suitably using a public key (pk), e.g., obtained from the KA  40 . In practice, this encryption is suitably achieved by employing a combination of additive secret sharing and a semantically secure homomorphic cryptosystem. The following describes two suitable embodiments which may be employed depending upon the kind of homomorphic cryptosystem used to construct D e , although other variations may likewise be suitable and/or desired depending on the particular environment, computing, storage and/or other applicable considerations. 
     In a first variation or embodiment, the encryption procedure uses a cryptosystem that supports 2-DNF (Disjunctive Normal Form) operations, e.g., the BGN (Boneh, Goh, and Nissim) cryptosystem, which supports the encrypted-domain computations that involve a single multiplication followed by an unlimited number of additions. With the BGN cryptosystem, the database D a  (e.g., as obtained above) is encrypted, with the addition of a single encrypted column per queried attribute. The use of the BGN variant is particularly applicable when the computational power available for decrypting the encrypted result is relatively high, but the storage available at the DB server is relatively low. 
     In a second variant or embodiment, the encryption procedure uses an additively homomorphic cryptosystem, e.g., the Paillier cryptosystem, which supports only encrypted-domain additions. The two variants address a tradeoff between the capability of the cryptosystem and the storage overhead for D e . With the Paillier cryptosystem, the database D a  (e.g., as obtained above) is encrypted, with the addition of a single encrypted column per (queried attribute, conditional attribute) pair. The use of the Paillier variant is particularly applicable when the computational power available for decrypting the encrypted result is relatively low, but the storage available at the DB server can be relatively high. 
     Referring now to the aforementioned first variant, the input to the encryption process or step  130  includes: (1) the augmented plaintext database D a , which contains  v =Π j=i   m v i  extra columns; and (2) the public key pk of a 2-DNF homomorphic cryptosystem. The resulting output is the encrypted database D e , in which the entries in the  v  extra columns are encrypted using a 2-DNF homomorphic cryptosystem and attributes to be queried are additively blinded. 
     To describe the encryption protocol (including application of the below sub-steps), we focus here separately on the conditional attributes, i.e., the attributes following the WHERE clause and the query attributes, i.e., the attributes following the SELECT statement.
         1) As above, let the conditional attribute be A m , m=1, 2, . . . , M that takes v m  distinct values. Index these values using the variable j=1, 2, . . . , v m . Then, for each attribute A m , there is constructed binary indicator variables S(i, j) for the j th  possible value of A m  in the i th  row, where i∈{1, 2, . . . , n}. S(i, j) is then encrypted using a semantically secure 2-DNF homomorphic cryptosystem, to obtain E(pk, S(i, j)).   2) Let the queried attributes be Q k , k=1, 2, . . . , L. Then, instead of each plaintext value Q k (i) of attribute Q k  in row i∈{1, 2, . . . , n}, store E(pk, Q k (i)), which is the 2-DNF homomorphic encryption of the query attribute value under the public key pk of the data owner.       

     As a result of applying the above steps to the value of each of the M conditional attributes and L queried attributes in D a , the encrypted database D e  is obtained. 
     Referring now to the aforementioned second variant, the input to the encryption process or step  130  includes: (1) the augmented plaintext database D a , which contains  v =Π j=i   m v i  extra columns; and (2) the public key pk of an additively homomorphic cryptosystem. The resulting output is the encrypted database D e , in which the entries in the  v  extra columns are encrypted using an additively homomorphic cryptosystem and attributes to be queried are additively blinded. 
     To describe the encryption protocol (including application of the below sub-steps), we again focus here separately on the conditional attributes, i.e., the attributes following the WHERE clause and the query attributes, i.e., the attributes following the SELECT statement.
         1) As above, let the conditional attribute be A m , m=1, 2, . . . , M that takes v m  distinct values. As above, index these values using the variable j=1, 2, . . . , v m . Then, for each attribute A m , there is constructed binary indicator variables S(i, j) for the j th  possible value of A m  in the i th  row, where i∈{1, 2, . . . , n}. S(i, j) is then encrypted using a semantically secure additively homomorphic cryptosystem, to obtain E(pk, S(i, j)).   2) Let the queried attributes be Q k , k=1, 2, . . . , L. Then for the value Q k (i) of attribute Q k  in row i∈{1, 2, . . . , n}, choose an integer r k (i) uniformly at random from the interval ∈[−R k , R k ], where R k  is a positive integer, and the number of bits in R k , denoted by λ(R k ) is a security parameter. In place of the plaintext attribute value Q k (i), store the additively blinded value {tilde over (Q)} k (i)=Q k (i)+r k (i). Let the column containing these blinded values be considered as a new attribute {tilde over (Q)} k .   3) For each queried attribute Q k , and each of the v m  possible values of the conditional attribute A m , an extra column is introduced denoted by R k,m . The entry in the i th  row of this new column is given by R k,j (i)=E(pk, r k (i)·S(i, j)) for j=1, 2, . . . , v m .       

     As a result of applying the above steps to the value of each of the M conditional and L queried attributes in D a , we obtain the encrypted database D e . Unlike the 2-DNF homomorphic case considered above, the total number of columns added as a result of sub-step 3 above is L=Σ m=1   M v m , which makes this approach less storage-efficient. 
     In either case, having thus obtained the encrypted DB D e , at step  140 , the encrypted DB D e  is transmitted, loaded and/or otherwise sent to the DBMS  30 . In practice, in the DBMS  30 , all the table names are available in plaintext, and all the column attribute names are available in plaintext, but the entries in the tables are encrypted as explained above. That is to say, the only items available in plaintext at the DB server are the attribute names. For example, in a relational DB, the names of the tables and columns are known, but the data entries in those columns are encrypted. 
     Having thus loaded the encrypted DB D e  into the DBMS  30 , the same may be accessed by the CS  20  in response to queries submitted by a user/analyst via the Front-End web service/server  10 , e.g., using the Analyst View  12 . Suitably, the queries may be submitted in a plaintext form. The DB server of the DBMS  30  in turn provides data to the CS  20  and the computations executed by the CS  20  are suitably carried out in the encrypted-domain. In response to the submitted query, the results of the computations carried out by the CS  20  are returned in an encrypted form. Using a corresponding decryption key or private key (corresponding to the public key used to carry out the encryption), e.g., made available or otherwise obtained from the KA  40 , the analyst may decrypt the encrypted results that are received and view them in plaintext. In practice, such a decryption/private key is not made available to and/or otherwise kept from the CS  20  or DBMS  30  to limit the potential for information or data leakage thereat. 
     In accordance with one suitable embodiment, there are now described encrypted-domain computation protocols executed, for example, at the CS  20  and/or the DB server, in response to plaintext queries supplied by an analyst. Suitably, the analyst or other like user may submit the plaintext query via the Analyst View  12 . Recall that suitably, in the DB server of the DBMS  30 , the table names are available in plaintext, the column attribute names are available in plaintext, but the entries in the tables are encrypted as explained above. 
     Initially, there are considered herein simple aggregate queries, e.g., such as sum and average queries on single query attributes without WHERE clauses. In practice, to execute these queries, suitably the CS  20  simply exploits the additive homomorphic property of the cryptosystem used to encrypt the data. Through the summation protocol, there is now illustrated some of the operations that will be repeatedly used in the more involved conditional queries to follow. 
     For example, an analyst may provide as input, a plaintext query of the form:
         SELECT SUM(query_attribute) FROM table_name;       

     Suitably, the CS  20  parses this query, and immediately recognizes that it has to access encrypted data belonging to query_attribute. Following earlier notation, this attribute is denoted by Q, and the individual values in the ιth row as Q(i), i=1, 2, . . . , n. 
     In response to the aforementioned query, the CS  20  suitably returns to the analyst the encrypted summation given by: 
             E   ⁡     (     pk   ,       ∑     i   =   1     n     ⁢           ⁢     Q   ⁡     (   i   )           )           
where pk is the public key that was used to encrypt the DB D e . Presuming the analyst has received the proper authorization and/or key from the data owner and/or KA  40 , he can decrypt this result.
 
     More specifically, for example, the following protocol may be followed:
         1) The CS  20  retrieves the n entries in the table table_name, corresponding to the attribute Q.   2) It uses the additive homomorphic property to obtain the desired result as follows:       

     
       
         
           
             
               
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             3) The CS  20  returns the result to the analyst, e.g., via the Analyst View  12  of the web service/server  10 . 
           
         
       
    
     Recall that, based on the construction of the encrypted DB D e  the total number of rows in the DB is not a secret. Thus, for example, an analyst can also evaluate the queries of the following form:
         SELECT AVG(query_attribute) FROM table_name;       

     Notably, in practice, the CS  20  does not perform the averaging since it does not have access to the plaintext summation. Therefore, in response to this AVG query, it first runs the simple SUM protocol, e.g., as illustrated above, and additionally returns the number of rows n to the analyst. The analyst, e.g., via the Analyst View  12 , can then decrypt the summation and divide by n to obtain the answer to his query. 
     Next, the present specification address privacy-preserving WHERE queries, i.e., protocols involving queries utilizing a WHERE clause. Here, there will be utilized the extra columns that were introduced when the plaintext DB Dp was augmented to Da. The following will illustrate two exemplary protocols, one for the implementation based on 2-DNF homomorphic encryption, and one for the implementation based on Paillier homomorphic encryption. In either case, the dot product of the blinded values in the query attribute column and the encrypted values in a relevant indicator attribute column are securely computed, for example, as explained below. 
     For example, an analyst may provide as input, a plaintext query of the form: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 SELECT SUM(query_attribute) FROM table_name; 
               
            
           
           
               
               
            
               
                   
                 WHERE conditional_attribute = “some_value”; 
               
               
                   
                   
               
            
           
         
       
     
     Suitably, the CS  20  parses this query, and recognizes that it has to access blinded data belonging to query_attribute. Following earlier notation, this attribute is denoted by Q. Furthermore, it has to access encrypted data corresponding to the conditional_attribute. Following earlier notation, this attribute is denoted by A. Let the some_value be the j th  out of v possible values that can be taken by attribute A. Following earlier notation, the indicator variables are processed in the column S(⋅,j) of the matrix S that was used to augment the database, where each value in the matrix is encrypted using a semantically secure homomorphic encryption scheme. 
     In response to the aforementioned query, the CS  20  suitably returns to the analyst the encrypted summation given by: 
             E   ⁡     (     pk   ,       ∑     i   =   1     n     ⁢           ⁢       Q   ⁡     (   i   )       ⁢     𝕀     {       S   ⁡     (     i   ,   j     )       =   1     }             )           
where pk is the public key that was used to encrypt the DB D e . Presuming the analyst has received the proper authorization and/or key from the data owner and/or KA  40 , he can decrypt this result. By the construction described above, the indicator function denotes that the query picks up only those values for which conditional_attribute has value some_value.
 
     More specifically, for example, the following protocol may be followed in the case of the 2-DNF homomorphic scheme. In this case, the encryption function E(pk, ⋅) is the 2-DNF homomorphic encryption under the public key of the data owner. Suitably, the encrypted DB D e  is prepared according to the procedure described above.
         1) The CS  20  retrieves the n encrypted entries in the table table_name, corresponding to the attribute Q. These are represented as E(pk, Q(i)), i=1, 2, . . . , n.   2) The CS  20  retrieves the n encrypted indicator variables S(⋅, j), i.e., the jth column of the matrix S. These are represented as E(pk, S(i, j)), i=1, . . . , n.   3) The CS  20  uses the 2-DNF homomorphic properties to compute:       

     
       
         
           
             
               
                 
                   
                     
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             4) The CS  20  returns the result to the analyst, e.g., via the Analyst View  12  of the web service/server  10 . 
           
         
       
    
     More specifically, for example, the following protocol may be followed in the case of the Paillier homomorphic scheme. In this case, the encryption function E(pk, ⋅) is the additively homomorphic encryption under the public key of the data owner. Suitably, the encrypted DB D e  is prepared according to the procedure described above.
         1) The CS  20  retrieves the n blinded entries in the table table_name, corresponding to the attribute Q. These are represented as Q(i), i=1, 2, . . . , n.   2) The CS  20  retrieves the n encrypted indicator variables S(⋅, j), i.e., the jth column of the matrix S. These are represented as E(pk, S(i, j)), i=1, . . . , n.   3) Recall that, corresponding to each attribute Q k , and the j th  value of the conditional attribute A, the encrypted database D e  contains a column R k,j  of encrypted blinding entries. Dropping the first suffix k, let the column of blinding entries corresponding to the attribute {tilde over (Q)} be denoted by the attribute R j . The CS  20  also retrieves the n encrypted blinding terms from the column R j , represented as R l (i)=E(pk, r(i)·S(i, j)), i=1, . . . , n.   4) The CS  20  uses the additively homomorphic properties to compute:       

     
       
         
           
             
               
                 
                   
                     
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             5) The CS  20  returns the result to the analyst, e.g., via the Analyst View  12  of the web service/server  10 . 
           
         
       
    
     As desired for database privacy, the protocols do not reveal which rows were selected for the above summation calculations, even to the CS  20  which is performing the computation. These are the rows for which the value S(i, j)=1. Note that the analyst already knows the schema of the encrypted DB D e  along with the augmentations carried out. So, if he wants to find the number of rows for which conditional_attribute took the j th  possible value, he can send, for example, a query as follows:
         SELECT SUM (jth_value_of_conditional_attribute) FROM table_name;       

     This is essentially a count query, because the S(i, j) are indicator variables. In response to this count query, the CS  20  returns the encryption of the number of rows (for both the 2-DNF and the additively homomorphic schemes) using:
 
Number of Rows=Π i=1   n   E ( pk,S ( i,j ))
 
     The above argument also provides a way to execute average queries of the form: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 SELECT AVG(query_attribute) FROM table name; 
               
            
           
           
               
               
            
               
                   
                 WHERE conditional_attribute = “some_value”; 
               
               
                   
                   
               
            
           
         
       
     
     Essentially, when the CS  20  parses an average query of the above form, it internally generates two related queries on the encrypted database: the conditional sum query whose protocol is discussed above, followed by the count query discussed above. It returns to the analyst the results of both queries. By dividing the result of the conditional sum query with the result of the count query, the analyst obtains the result of the average query. 
     Next, the present specification addresses privacy-preserving GROUPBY queries, i.e., protocols involving queries utilizing a GROUPBY clause. These protocols will also utilize the extra columns that were introduced when the plaintext database D p  was augmented to D a . Essentially, the protocols achieve the GROUPBY functionality by executing multiple WHERE queries with an equality condition using the above protocols. 
     For example, an analyst may provide as input, a plaintext query of the form:
         SELECT SUM(query_attribute) FROM table_name   GROUPBY conditional_attribute;       

     Suitably, the CS  20  parses this query, and recognizes that it has to access blinded data belonging to query_attribute. Following earlier notation, this attribute is denoted by Q. Furthermore, it has to access encrypted data corresponding to the conditional_attribute. As before, the conditional attribute is denoted by A and it is assumed that it can take v possible values, which are denoted by value_1, value_2, . . . , value_v. The schema of the encrypted database D a  is assumed to be known to the CS  20 , the DB server and the analyst. 
     Suitably, the CS  20  returns to the analyst (e.g., via the Analyst View  12 ), an encrypted v-length vector, where the j th  element of the vector is given by:
 
 E ( pk,Σ   i=1   n   Q ( i )Π {S(i,j)=1} )  (1)
 
for j=1, 2, . . . , v. As before, pk is the public key that was used to encrypt the DB D e . Presuming the analyst has received the proper authorization and/or key from the data owner and/or KA  40 , he can decrypt this vector of encrypted values. Depending upon the encryption scheme used, E(pk,⋅) is a ciphertext for an additively homomorphic or a 2-DNF homomorphic cryptosystem respectively.
 
     More specifically, for each j=1, 2, . . . , v, the following steps may be executed:
         1) The compute server constructs a WHERE query given by:       

     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 SELECT SUM(query_attribute) FROM table_name; 
               
               
                   
                 WHERE conditional_attribute = value j; 
               
               
                   
                   
               
            
           
         
       
         
         
           
             2) Using the protocol described above, the CS  20  obtains an encrypted result given by equation (1). 
           
         
       
    
     Suitably, the CS  20  gathers the encrypted results obtain by repeatedly invoking WHERE protocols into a v-length vector and sends it to the analyst. 
     Clearly, the correctness of the privacy-preserving GROUPBY protocols follows from that of the WHERE protocols. By combining summation queries with count queries as before, the CS  20  can also execute average queries of the form: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 SELECT AVG(query_attribute) FROM table_name; 
               
               
                   
                 GROUPBY conditional_attribute; 
               
               
                   
                   
               
            
           
         
       
     
     In one suitable embodiment of the described privacy-preserving querying architecture, the plaintext database is read in the form of one or more text files. To facilitate the database preparation phase, an interface is suitably provided that displays to the data owner the data schema, the range of values for different attributes and the data types for each attribute. For example, the interface provides the data owner with the following capabilities:
         1) Import a database from a text file, such as a comma-separated values (*.csv) file.   2) Display the schema of the database.   3) For each attribute, choose whether to ignore it, import it in plaintext, or to import it in encrypted form.   4) For conditional attributes, choose whether or not to support encrypted-domain WHERE or GROUPBY queries.   5) For each attribute, choose whether or not to support queries on the statistical distributions on the attributes.   6) Load a key for Paillier homomorphic encryption, or generate a new key-pair.       

     In response to the commands provided from the data owner&#39;s interface, encryption is performed on the plaintext database D p  by an encryption server and the encrypted database D e  is stored on the DB server of the DBMS  30 . Suitably, the encrypted database is backed by MySQL. The data owner&#39;s interface may be implemented in Javascript in a browser, and it may communicate with the encryption server and database server via a RESTful interface. Suitably, the encryption routines executed by the encryption server are implemented in the Java programming language. 
     Similar to the case for the data owner, a querying interface is provided for a data analyst, also using Javascript in a browser. This may be a RESTful interface that can be accessed from a computer, tablet or smartphone, to transmit and receive data from the CS  20 . To facilitate querying, the data analyst may be provided with the following capabilities:
         1) Import an encrypted database from the MySQL database.   2) Load a key for decrypting the ciphertext results of the query returned by the CS  20 .   3) View the database schema and information about how the attributes have been encrypted.   4) View the suite of queries supported.   5) Enter a SQL-like query involving encrypted and/or plain-text attributes.   6) View the query results numerically (or graphically, if requested).       

     Since the database server may be backed by MySQL, any queries involving unencrypted attributes can be processed in the conventional way. Queries which involve processing of encrypted data suitably use the protocols that have been described herein. 
     The above methods, system, platforms, modules, processes, algorithms and/or apparatus have been described with respect to particular embodiments. It is to be appreciated, however, that certain modifications and/or alteration are also contemplated. 
     It is to be appreciated that in connection with the particular exemplary embodiment(s) presented herein certain structural and/or function features are described as being incorporated in defined elements and/or components. However, it is contemplated that these features may, to the same or similar benefit, also likewise be incorporated in other elements and/or components where appropriate. It is also to be appreciated that different aspects of the exemplary embodiments may be selectively employed as appropriate to achieve other alternate embodiments suited for desired applications, the other alternate embodiments thereby realizing the respective advantages of the aspects incorporated therein. 
     It is also to be appreciated that any one or more of the particular tasks, steps, processes, methods, functions, elements and/or components described herein may suitably be implemented via hardware, software, firmware or a combination thereof. In particular, various modules, components and/or elements may be embodied by processors, electrical circuits, computers and/or other electronic data processing devices that are configured and/or otherwise provisioned to perform one or more of the tasks, steps, processes, methods and/or functions described herein. For example, a processor, computer or other electronic data processing device embodying a particular element may be provided, supplied and/or programmed with a suitable listing of code (e.g., such as source code, interpretive code, object code, directly executable code, and so forth) or other like instructions or software or firmware, such that when run and/or executed by the computer or other electronic data processing device one or more of the tasks, steps, processes, methods and/or functions described herein are completed or otherwise performed. Suitably, the listing of code or other like instructions or software or firmware is implemented as and/or recorded, stored, contained or included in and/or on a non-transitory computer and/or machine readable storage medium or media so as to be providable to and/or executable by the computer or other electronic data processing device. For example, suitable storage mediums and/or media can include but are not limited to: floppy disks, flexible disks, hard disks, magnetic tape, or any other magnetic storage medium or media, CD-ROM, DVD, optical disks, or any other optical medium or media, a RAM, a ROM, a PROM, an EPROM, a FLASH-EPROM, or other memory or chip or cartridge, or any other tangible medium or media from which a computer or machine or electronic data processing device can read and use. In essence, as used herein, non-transitory computer-readable and/or machine-readable mediums and/or media comprise all computer-readable and/or machine-readable mediums and/or media except for a transitory, propagating signal. 
     Optionally, any one or more of the particular tasks, steps, processes, methods, functions, elements and/or components described herein may be implemented on and/or embodiment in one or more general purpose computers, special purpose computer(s), a programmed microprocessor or microcontroller and peripheral integrated circuit elements, an ASIC or other integrated circuit, a digital signal processor, a hardwired electronic or logic circuit such as a discrete element circuit, a programmable logic device such as a PLD, PLA, FPGA, Graphical card CPU (GPU), or PAL, or the like. In general, any device, capable of implementing a finite state machine that is in turn capable of implementing the respective tasks, steps, processes, methods and/or functions described herein can be used. 
     Additionally, it is to be appreciated that certain elements described herein as incorporated together may under suitable circumstances be stand-alone elements or otherwise divided. Similarly, a plurality of particular functions described as being carried out by one particular element may be carried out by a plurality of distinct elements acting independently to carry out individual functions, or certain individual functions may be split-up and carried out by a plurality of distinct elements acting in concert. Alternately, some elements or components otherwise described and/or shown herein as distinct from one another may be physically or functionally combined where appropriate. 
     In short, the present specification has been set forth with reference to preferred embodiments. Obviously, modifications and alterations will occur to others upon reading and understanding the present specification. It is intended that the inventive subject matter be construed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.