# Patent

## Title
Computer-implemented system and method for providing data privacy in a cloud using discrete homomorphic encryption

## Abstract

A homomorphic encryption algorithm is performed that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query including a cryptographically safe representation of one of the data items. The queries are transmitted to at least one discrete homomorphic encryption (DHE) server. An identifier is received from each query from the DHE server. The identifiers are transmitted to at least one computing server that maintains a database including data structures. The computing server is requested to requesting the computing server to insert the received identifiers into the database. At least one of the identifiers is processed: the computing server is requested to find the identifiers in the data structures that match the at least one identifiers and to perform at least one equality-based operation on the matching identifiers. A result of the at least one operation is received.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This non-provisional patent application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Ser. No. 61/615,835, filed Mar. 26, 2012, the disclosure of which is incorporated by reference.


FIELD
This application relates in general homomorphic encryption, and, in particular, to a computer-implemented system and method for providing data privacy in a cloud using discrete homomorphic encryption.
BACKGROUND
Homomorphic encryption is a form of encryption where a specific algebraic operation performed on the plaintext is equivalent to another (possibly different) algebraic operation performed on the ciphertext. Homomorphic encryption can be defined for both public-key (asymmetric) and private-key (symmetric) encryption. The original concept, called privacy homomorphism, was introduced by Rivest et al. in “On data banks and privacy homomorphisms,” Foundations of Secure Computation, pages 169-180 (1978), shortly after the invention of RSA, the public-key encryption algorithm. While encryption used in a number of industries, some unresolved difficulties in use of homomorphic encryption remain. In particular, the immediate downside aspect of encrypted data is that the data cannot be further processed (e.g. added, multiplied, searched), thus severely limiting any post-encryption computing of the ciphertext, especially by an external processing entity such as a cloud computing service.
Processing of this encrypted data has long been a problem without a practical and secure solution. While homomorphic encryption schemes are being developed to address this situation, aside from a few homomorphic encryption schemes involving almost exclusively asymmetric-key algorithms, there are no practical symmetric-key encryption solutions for the cloud today.
Gentry in “Fully homomorphic encryption using ideal lattices,” 41st ACM Symposium on Theory of Computing (STOC) (2009), used latticed-based cryptography to show the first fully homomorphic encryption (FHE) scheme for public-key cryptography. While this method creates an FHE scheme, the method remains impractical due to the complexity and large amount of computing involved. This complexity and the large amount of computing involved make the scheme's application, such as to a homomorphic search, not likely for the next 40 years, at least based on Moore's law. The scheme's applicability in the cloud storage and computing is also limited because the cloud uses prevalently private-key cryptography to store encrypted data.
Thus, existing technologies fail to provide an adequate solution to processing homomorphically-encrypted data in a cloud-computing environment, especially for data that is in motion. With the continual expansion of cloud computing, storing encrypted data using mostly symmetric-key encryption algorithms, having a practical homomorphic encryption method is critical in taking the cloud from a simple storage stage to having a real computing component that can process encrypted data and enable a series of cloud applications while retaining complete data privacy.
Therefore, there is a need for a way to provide data privacy in a cloud using homomorphic encryption while allowing the processing of such data.
SUMMARY
An application of homomorphic encryption, called discrete homomorphic encryption (DHE), allows querying, reading and writing encrypted data to and from any external data store without the data store ever decrypting the data.
The implementation of DHE can be used in conjunction with already established symmetric-key encryption algorithms, with intrinsic support for block ciphers. Data that is already encrypted with a key and stored in the cloud can also benefit from DHE. The use of DHE enables comparing two pieces of encrypted data and determine if they are the same, without decryption, thus enabling applications and services to find, retrieve and perform equality-based set and hierarchy operations on encrypted data located in the cloud without the cloud ever decrypting the data. Furthermore, using DHE can enable sharing of encrypted data between applications while having the encryption keys only on the client computing device and never in the cloud. The immediate practical implementation refers to applications in the cloud-computing environment where the external data source is a cloud web service. By using DHE, these applications can provide a series of cloud services (backup & restore, address books, database, collaboration & sharing) while having the data encrypted entirely.
A computer-implemented method for providing data privacy in a cloud using discrete homomorphic encryption is provided. A homomorphic encryption algorithm is performed that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query including a cryptographically safe representation of one of the data items. The queries are transmitted to at least one discrete homomorphic encryption (DHE) server in a cloud-computing environment. An identifier is received from each query from the DHE server. The received identifiers are transmitted to at least one computing server in the cloud-computing environment that maintains a database including data structures. The computing server is requested to insert the received identifiers into the database, which can include at least one of: requesting the computing server to substitute existing data in the data structures with the identifiers; and requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures. At least one of the identifiers is processed, including: the computing server is requested to find the identifiers in the data structures, both original and new, in the database that match the at least one identifiers; the computing server is requested to perform at least one equality-based operation on the matching identifiers; and a result of the at least one operation is received from the computing service.
In one embodiment, a computer-implemented method for providing data privacy in a cloud during data structure retrieval using discrete homomorphic encryption is provided. A homomorphic encryption algorithm is performed that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query including a cryptographically safe representation of one of the data items. The queries are transmitted to at least one discrete homomorphic encryption (DHE) server in a cloud-computing environment. An identifier is received from each query from the DHE server. The received identifiers are transmitted to at least one computing server in the cloud-computing environment that maintains a database including data structures. The computing server is requested to insert the received identifiers into the database, which can include at least one of: requesting the computing server to substitute existing data in the data structures with the identifiers; and requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures. Processing of at least one of the identifiers occurs, which includes: requesting the computing server to find the identifiers in the data structures that match the at least one identifier; requesting the computing server to perform at least one equality-based operation on the matching identifiers; receiving from computing server at least one of the data structures with one of the matching identifiers as a result of the equality-based operation. The plaintext data item from which was encrypted the query associated with at least one of the identifiers populating the received data structure is obtained.
In a further embodiment, a computer-implemented method for providing data privacy in a cloud during data processing using discrete homomorphic encryption is provided. A homomorphic encryption algorithm is performed that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query including a cryptographically safe representation of one of the data items. The queries are transmitted to at least one discrete homomorphic encryption (DHE) server in a cloud-computing environment. An identifier is received from each query from the DHE server. The received identifiers are transmitted to at least one computing server in the cloud-computing environment that maintains a database including data structures. The computing server is requested to insert the received identifiers into the database, which can include at least one of: requesting the computing server to substitute existing data in the data structures with the identifiers; and requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures. Processing at least one of the identifiers occurs, which includes: requesting the computing server to find the identifiers in the data structures that match the at least one identifier; requesting the computing server to perform at least one equality-based operation on the matching identifiers; and receiving from the computing server a result of the equality-based operation that includes a statistic associated with at least one of the identifiers in the data structures.
Still other embodiments of the present invention will become readily apparent to those skilled in the art from the following detailed description, wherein are described embodiments by way of illustrating the best mode contemplated for carrying out the invention. As will be realized, the invention is capable of other and different embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and the scope of the present invention. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not as restrictive.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram showing a high-level structural overview of a system for providing data privacy in a cloud using discrete homomorphic encryption in accordance with one embodiment.
FIG. 2 is a block diagram showing a functional architecture of the system of FIG. 1 in accordance with one embodiment.
FIG. 3 is a block diagram showing populating a data record with Ids in accordance with one embodiment.
FIG. 4 is a flow diagram illustrating a performance of the Cryptographically Secure Semantic Reduction Algorithm in accordance with one embodiment.
FIG. 5 is a flow diagram illustrating a method for providing data privacy in a cloud using discrete homomorphic encryption in accordance with one embodiment.
FIG. 6 is a flow diagram illustrating a routine for generating homomorphic queries for the method of FIG. 5 in accordance with one embodiment.
FIG. 7 is a flow diagram illustrating a routine for processing at least one identifier for the method of FIG. 5 in accordance with one embodiment.
FIG. 8 is a flow diagram illustrating a routine for obtaining plaintext data items from which queries associated with at least one of identifiers received from the computing service were generated.



DETAILED DESCRIPTION
The disclosed system and method define an application of the homomorphic encryption, called discrete homomorphic encryption (DHE) that enables applications and services to find, retrieve and perform equality-based set and hierarchy operations on encrypted data located in a cloud-computing environment without the cloud ever decrypting the data. Additionally, encrypted data can be shared across applications.
As discussed below, the disclosed system and method involve homomorphic encryption algorithm called cryptographically secure semantic reduction (CSSR). This algorithm creates cryptographically safe representations of data, called homomorphic queries that are answered by a service with a semantic-less identity (DHE Id), usually a number. This Id further enables a variety of equality-based set and hierarchy operations. These Ids are further used by cloud applications to replace all encrypted sensitive data that requires processing.
Structural Overview of the System for Providing Data Privacy Using Discrete Homomorphic Encryption
FIG. 1 is a block diagram showing a high-level structural overview of a system 10 for providing data privacy in a cloud using discrete homomorphic encryption in accordance with one embodiment. The system 10 includes at least one software application 11 running on a client computing device 12. While shown as a desktop computer, the computing device 12 can include any other computing devices capable of running software, including mobile phones, tablets, and laptops. The computing device 12 includes components commonly-present in computing devices such as a central processing unit (CPU), random access memory (RAM), non-volatile secondary storage, such as a hard drive or CD ROM drive, network interfaces, and peripheral devices, including user interfacing means, such as a keyboard and display. The device 12 is configured to execute code of the application 11, which can be implemented as modules.
The application 11 is connected over a network 13, such as the Internet or a cellular network, to components in a cloud-computing environment (not shown), and transmits encrypted data items into the cloud-computing environment. While the described embodiment refers to the application 11 as a single application, multiple applications on the client computing device 12 can interact with the cloud-computing environment as described below. As described below with reference to FIGS. 2, 4, and 6, the application 11 performs the CSSR homomorphic encryption algorithm to encrypt plaintext data items (not shown) present on the computing device 12 into homomorphic queries, with each query being a cryptographically safe representation of one of the plaintext data items. The application 11 transmits the queries to the cloud-computing environment.
The cloud-computing environment includes one or more servers 14, called DHE servers 14 for the purposes of this application, which receive the queries and implement a DHE service 15 that generates an identifier (not shown), known as “Id” or “DHE Id” below, for each query. The DHE servers 14, which can be dedicated or shared servers, provide the generated Ids to the application, as further described below with reference to FIG. 2. The Ids completely lack any semantic relationship to the queries for which they were created.
The cloud-computing environment further includes one or more computing servers 17 connected to a database 18. These computing servers 17 implement a computing service 19 capable of performing equality-based operations on data in data structures 20 stored in the database 18. In one embodiment, the service 19 can be the Amazon Elastic Compute Cloud (EC2®) offered by Amazon.com Inc. of Seattle, Wash. or Windows Azure service offered by Microsoft Corporation of Redmond, Wash. The servers 17 can further substitute data in the data structures 20 with the Ids generated by the DHE service 15 when requested by the application 11.
The application 11 further encrypts plaintext data items into ciphertext data items 21, and transmits the ciphertext data items 21 to be stored in a cloud-computing storage 22. The storage 22, which in one embodiment can be the S3 storage maintained by Amazon.com Inc. of Seattle, Wash., is connected to one or more storage servers 23. The storage servers 23 implement a storage service 24, which receives the ciphertext data items 21 from the application 11, stores the ciphertext data items 21 in a location in the storage 22, and returns a reference (not shown) to the location of a stored ciphertext data item 21 to the application 11. As described below with reference to FIG. 8, the application 11 can associate a reference with an Id corresponding to the query generated from the same plaintext data item as the ciphertext data item whose location is identified by the reference, and to provide the association to the DHE service 15. The application 11 can also retrieve the reference associated with one of the Ids from the DHE service 15. The application 11 can further retrieve the ciphertext data item 21 stored at the location identified by the reference, and decrypt the retrieved ciphertext data items 21 into plaintext.
In the system 10 described above, the data and the keys are always encrypted while in transit or processed by the services 15, 19, or 24 while these services never have access to the encryption keys. As described below, the application 11 includes a DHE Client Application Programming Interface (“API”), as well as other APIs to the other services 19, 24, which are implemented on the client computing device 12.
Functional Overview of the System for Providing Data Privacy Using Discrete Homomorphic Encryption
The operations called by the application 11 at the client computing device 12 drive the functionality of the system 10. FIG. 2 is a block diagram showing a functional architecture of the system of FIG. 1 in accordance with one embodiment. The system 10 is separated by a trust/no-trust line 31. The trust/no-trust line 31 conceptually divides the system 10 into two realms or zones: the trusted zone and the non-trusted zone. In FIG. 2, operations {0}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, and {10}, involve calling one of the services 15, 19, and 24, to request the services 15, 19, and 24 to perform at least a part of the operation.
In the trusted zone, data is available as plaintext 33 (unencrypted). This zone is usually a secure private client application space, not on the Internet, but connected to the Internet. Only the owner of the data has access to the data in both encrypted and unencrypted form through the trusted client application 11. In the non-trusted zone, data must be available as ciphertext 21 only (encrypted). This zone is the cloud-computing environment located on the Internet. The most important aspect of this zone is that the cloud-computing environment components never interact directly but only through the trusted client application 11.
Four entities interact in the system 10: the client application 11, the DHE service 15, the cloud computing service 19, and the cloud storage service 24. The application 11 includes the DHE Client API 32, as well as APIs to the other services (not shown). In one embodiment, the application 11 and the different services 11 have different ownership and are implemented by different entities, as described below with reference to Table 1. The ownership of implementation and operation (hosting) can belong to one of the following entities:
Customer: a user of the system, typically a company or user owning the data.
Cloud Provider: a provider of cloud services such as processing or storage.
DHE Provider: the provider of the DHE service 15.









TABLE 1





Category
Implementation
Operation







Client Application 11
Customer
Customer


DHE Client API 32 at client
DHE Provider
Customer


DHE Service 15
DHE Provider
DHE Provider


Object Model (sets, hierarchies)
Customer
Cloud Provider


Processing in computing service 19
Customer
Cloud Provider


Storage service 24
Cloud Provider
Cloud Provider









Returning to FIG. 2, the application 11 is main driver of the system 10, orchestrating all of the system's 10 operations. The application has access to and uses at least the following entities: plaintext data 33, an encryption key (K) 34 and an encryption algorithm (EK) 35. The plaintext data 33 needs to be encrypted, stored, and homomorphically processed in the cloud. When grouped together in data structures (e.g. sets, hierarchies), these form an object model. The encryption key (K) 34 is used to encrypt the plaintext data 33. The encryption algorithm (EK) 35 encrypts the plaintext data 33 with the encryption key (K) 34.
Operations Performed by DHE Client API
The DHE Client API 32 is the client-side API of the DHE service 15 and is responsible for following operations:
Identity and access: Operation {0} is an operation that ensures that all calls to the DHE service 15 are authenticated, authorized and audited (AAA protocol 36). A user name, which can be an e-mail address, and a hashed password are provided to the DHE service 15 that returns a user id enclosed securely in a security token (not shown). This function means that all secure calls to the service 15 must be accompanied by the security token. This requirement is assumed to be the case for all calls below. The implementation of the AAA protocol 36 is orthogonal to the DHE Client API.

    
    
        {0} Security Token (User)=AAA(email, password)
    
    


Initialization: Initialization ensures that the CSSR algorithm is properly initialized with the encryption key K 34 and encryption algorithm EK 35. If an encryption key is not available, a keyphrase, provided by the user or obtained from another source, can be used to generate the encryption key K 34. The operation {1} stores a portion of the internal state of the CSRR and associates a public key with the user when sharing-mode is used, as further described below with reference to FIG. 4. In one embodiment, the operation {1} transmits the encrypted CSSR algorithm to the DHE servers 14 for storage in the cloud-computing environment, as further described with reference to FIG. 4.

    
    
        CSSR=Init(K, EK) or
        CSSR=Init (keyphrase, EK)
        {1} Init (CSSR)
    
    


Query generation: using the CSSR algorithm a cryptographically safe representation of data called homomorphic query 37 is created.

    
    
        Query=CSSR(Plaintext)
    
    


Unique key generation: using the CSSR algorithm a unique encryption key (KH) is generated, when the sharing-mode is used.

    
    
        KH=CSSR(Plaintext)
    
    


Query: In operation {2}, the DHE service 15 is queried using the homomorphic query and it responds with an Id 38, which lacks any semantic relationship to the query 37. This Id 38 can be a sequential, random or global number based purely on the private internal state of the service DHE Service 15. Other Ids 38 are possible.

    
    
        {2} Id=Query
    
    


Set reference: Operation {3} associates an Uri (absolute or partial) with the Id. The Uri is a complete or partial reference 39 to the location of the encrypted data with the storage service 22.

    
    
        {3} Set(Id, Uri)
    
    


Get reference: Operation {4} retrieves the Uri associated with the Id 38. This function is also called a reverse query.

    
    
        {4} Uri=Get(Id)
    
    


Get info: Operation {5} retrieves all information and statistics associated with a specific DHE Id 38.

    
    
        {5} Info=Info(Id)
    
    


Unique key sharing: Operation {6} enables sharing of the unique encryption key (KH) between two users (U1, U2). The superscript notation in the command below refers to operation at user (U1) or (U2). The CSSR uses public-key encryption with the key-pair of (KP/KV) where the (KP) is the public key and (KV) is the private key.

    
    
        {6} Share=CSSR1(K1H, K2P)
        
            K1H=CSSR2(Share, K2V)
        
        
    
    


Other services: Operation {x} provides support for extra services such as signup, account management, key grouping, billing, expiration, deletion, status and troubleshooting.
Operations Performed by Computing and Storage Service APIs
The application 11 further includes a computing service API (not shown) and the storage service API (not shown). The computing service API makes application-specific calls to the application's 11 own object model stored in the cloud computing service 19. These calls are always implemented by the direct consumer of the DHE service 15, making the following operations possible:
Substitution: Operation {7} ensures that all encrypted sensitive data items that requires processing in the computing service 19 is replaced with Ids 38 produced by the Operation {2} call for the data items. In a further embodiment, the operation can create new data structures and insert the identifiers into the new data structures.

    
    
        {7} Id=Substitution(CSSR, Plaintext)
    
    


The operations {2} and {7} allow the client-side application 11 to substitute the fields in a data structure 20 with the corresponding Ids 38, as further described with reference to FIG. 3. Then the application 11 can find the data structure by secure queries by the DHE Ids 38 instead of the plaintext of its fields. When a data structure is retrieved from the computing service 19 and is available at the application 11, using operation {4} the Uri for each DHE Id 38 is retrieved; then the encrypted data is retrieved from the storage service 24 and decrypted locally, thus making the data structure available in the plaintext format to the application 11.
Equality-based operations: calls made to the object model exposed by the computing service 19, using the discrete homomorphic operations enabled by the Ids 38:

    
    
        {8} Set operations: query, enumerate, union, intersection, difference, subset and count
        {9} Hierarchy operations: enumerate, traverse, and count
    
    


Operations {8} and {9} are possible because the service 19 can find data organized in the data structures 20 by comparing and matching (an equality test) Ids 38 and then returning data structures (sets, hierarchies) 20 for these Ids.
Encrypt/Decrypt: encrypting of the plaintext 33 using the key (K) 34, an initialization vector described below with reference to FIG. 4, and encryption algorithm (EK) 35. The corresponding decryption algorithm is DK (not shown) is used to decrypt ciphertext 21 into plaintext. If sharing-mode is used the encryption key used is (KH).

    
    
        Ciphertext=EK(Plaintext, [K|KH, IV])
        Plaintext=DK(Ciphertext, [K|KH])
    
    


Read/Write: storing and retrieving of the ciphertext 21 to and from the storage 22 accessible to the storage service 24. The location of the ciphertext in the service 24 is used as the reference 39 for the DHE Client API 32 when associating the reference 39 with the DHE Id 38.

    
    
        {10} Reference=Write(Ciphertext)
        
            Ciphertext=Read(Reference)
        
        
    
    


The DHE, Computing, and Storage Services
As described above, three other entities interact in the system 10 in addition to the client application: the DHE service 15, the cloud computing service 19, and the cloud storage service 24.
The DHE service 15 is the server-side complement of the client-side DHE Client API 32, servicing the API's requests. The service's 15 critical responsibility and feature is the ability to answers the Query( ) operation {2}, calls with the Ids 38 in constant time, which in one implementation can be of O(1) complexity. The Id 38 can be a sequential, random or global number based purely on the private internal state of the DHE service 15, and thus have no semantic relationship to the client application (A) state. The operations for this service are grouped under {1-6} in FIG. 2.
The computing service 19 includes and exposes the application object model, as hosted in the database 18. The operations for this service are grouped under {7-9} in FIG. 2. The DHE Client API 32 never calls into this service 19 directly.
This storage service 24 stores the ciphertext data 21 into the storage 22, returning a reference (Uri) 39 that is associated with an Id 38. The operations for this service are grouped under {10} in the above diagram. The DHE Client API 32 never calls into this service 24 directly.
Example of Substituting Data Structures with Ids
As described above, the computing service 19 substitutes data structures 20 in the database with the identifiers 38 under the control of the application API. FIG. 3 is a block diagram showing substituting of data of in data in a record 41 with Ids 38 in accordance with one embodiment.
Client applications consume data that is stored in various data stores in the cloud. This data is usually organized in and accessed by various data structures 20, the simplest of them being a record 41, which is a row in a database table.
The application record 41 is typical of what is stored in the database 18 accessible to the computing service 19. The record 41 has the searchable fields 42 (F1 . . . Fn) and the data fields (D1 . . . Dm) 43. The searchable fields (F) 42 are usually indexed to be searchable, while the data fields (D) 43 may or may not be searchable depending of their size and data format. Examples of these records 42 are: customer/account information, file/directory metadata, order details etc.
The client-side application 11, substitutes the fields (F) and (D) with their corresponding Ids. Then the application 11 can find the record 41 by secure queries by the Ids 38 instead of the plaintext of the fields. Basically, each query for Id1 to Idn+m can return the application record 41.
CSSR Algorithm
As described above, the CSSR algorithm creates cryptographically safe representations of data, called homomorphic queries (Q) that are answered by a service with a sematic-less identifiers. The algorithm is based on a 3-phase polynomial-time transformation that is designed to gradually reduce the semantics of data until completely eliminated. The critical requirement of the algorithm is to ensure all of its internal operations are performed while maintaining a minimum of λ-bit security level.
FIG. 4 is a flow diagram illustrating a performance 40 of the CSSR algorithm in accordance with one embodiment. The algorithm includes three phases described below: initialization phase, semantic phase, and a closure phase.
Initialization Phase
During the initialization phase, the DHE Client API ensures that the CSSR algorithm is properly initialized with the encryption key (K) and encryption algorithm (EK). If an encryption key is not available, a keyphrase can be used to generate the encryption key. The size of the key depends on the lambda security level.

    
    
        {1} CSSR=Init(K, EK) or
        
            CSSR=Init(keyphrase, EK)
        
        
    
    


The initialization creates the internal state (stream of bytes) needed for the algorithm plus additional keys using a secure key derivation algorithm:
KO—the key that encrypts the algorithm state itself, hence used only once;
KS—the semantic key used in operation {3} described below;
KC—the closure key used in operation {4} described below;
KP/KV—a public-private key pair used in the sharing mode;
The internal state is encrypted with the key (KO) in order to be persisted locally or with the DHE service for later re-creation or recovery. The public key (KP) is stored with the DHE service and is associated with a user account (U).
Semantic Phase
Using a cryptographically secure one-way compression function (FS) with the key (KS) the plaintext on the client computing device is transformed into a vector (V). Using a one-way compression function (FV) the vector (V) is transformed into the initialization vector (IV) later used for the encryption of the plaintext, as described with reference to FIG. 2.
{3} Vector=CSSR(FS, KS, Plaintext)
{8} IV=CSSR (FV, Vector)
The function (FS) can be any secure Merkle-Damgård construction and thus must operate at a 2λ-bit security level due to collision caused by the birthday paradox. An example of acceptable algorithm is the HMAC-SHA256. The function (Fv) can also be a Merkle-Damgård construction. Other suitable algorithms can be used.
The transition at operation {2} from the initialization phase to semantic phase is one-way. The operation {8} is also one-way.
Closure Phase
Using a length-preserving encryption algorithm (EC) with the key (KC) the vector (V) is transformed into the query (Q). An example of acceptable algorithm is the AES algorithm in FFX or BPS modes.
{5} Query=EC(KC, Vector)
The transition {4} from the Semantic to Closure is reversible.
The client application using the DHE Client API can query {6} the DHE service for the Id or store and retrieve {9} the encrypted data from the storage service.
Sharing Mode
As mentioned above, the client application can also share data with DHE service by running the CSSR algorithm in the sharing-mode. In this mode the plaintext is encrypted with a unique key (KH) that is derived by a one-way operation from the encryption key (EK) and the vector (V), described above with reference to FIG. 3. Then a system user (U1) can give access to another user (U2) to specific DHE Ids.
The user (U2) retrieves the encrypted data for these DHE Ids via operations {4} and {10} described with reference to FIG. 2, and the associated unique encryption keys (KH) encrypted with the user (U2) public key (KP) from the DHE service. The user (U2) can decrypt these keys with the private key (PV), thus recovering the keys (KH) and finally decrypting the ciphertext associated with each DHE Id. During this process the data or the keys were always encrypted while in transit or processed by the DHE service, computing service, or the storage service.
Method for Providing Data Privacy Using Discrete Homomorphic Encryption
The simplicity of how DHE allows equality-based operations on encrypted data located in the cloud is also a powerful foundation that enables applications built on a DHE service to deliver very interesting scenarios of processing encrypted data with 100% privacy. FIG. 5 is a flow diagram illustrating a method 60 for providing data privacy in a cloud using discrete homomorphic encryption in accordance with one embodiment.
Initially, the DHE Client API performs an initialization step (step 61), as described above in reference to FIGS. 2 and 4, creating an internal state and obtaining the keys necessary for performance of the CSSR algorithm. Once the initialization (step 61) is complete, the DHE Client API generates homomorphic queries from plaintext data items maintained at a client computing device (step 62), as further described with reference to FIG. 6. The homomorphic queries are transmitted to the DHE service (step 62), which generates an Id for each query, and transmits the Id to the application at the client computing device, which receives the Ids (step 64). The Id for a query lacks a semantic relationship to that query.
Upon receiving the Ids, the client application transmits the Ids to the computing service (step 65) and requests the computing service to substitute data in data structures in the database accessible to the computing service with the Ids (step 66). Subsequently, the application processes at least one of the Ids using the computing service, as further described with reference to FIG. 7 (step 67). The application can then obtain the plaintext data item from which was generated the query corresponding to an Id delivered from the computing service as a result of the processing in step 61 (step 68), as further described with reference to FIG. 8. Optionally, if the CSSR algorithm is used in sharing mode, the client application can provide to the DHE service a public encryption key that can be used to obtain plaintext corresponding to a query identified by a specific Id, and requesting the DHE service to provide the key to a computing device of a user different than the user of client application, as described above with reference to FIGS. 2 and 4 (step 69), terminating the method 50.
As described above, the homomorphic queries are cryptographically safe representations of plaintext data items. FIG. 6 is a flow diagram illustrating a routine 70 for generating homomorphic queries for the method 60 of FIG. 5 in accordance with one embodiment. First, a plaintext data items is converted into a vector using a cryptographically secure one-way compression function, which can be a Merkle-Damgård construction, and a semantic key described above with reference to FIG. 4 (step 71). The vector is further encrypted by a length-preserving encryption algorithm using the closure key described above with reference to FIG. 4 to generate a homomorphic query (step 72), terminating the routine 70.
Processing Ids corresponding to homomorphic queries allows processing data in a cloud computing environment while maintaining the encryption of the data. In a further embodiment, the operation can create new data structures and insert the identifiers into the new data structures. FIG. 7 is a flow diagram illustrating a routine 80 for processing at least one identifier for the method 60 of FIG. 5 in accordance with one embodiment. First, the client-side application requests the computing service to find, in the database accessible to the computing service and whose data structures include the Ids received from the application, the Ids matching a particular Id being processed (step 81). The computing service compares the at least one identifier to the identifiers in the data structures, and after the matching identifiers are found based on the comparison, the application requests the computing service to perform at least one equality-based operation on the matching identifiers, or on the data structures, in which one of the matching identifiers is present (step 82). As described above, the equality-based operations can vary depending on the type of data structure involve, and in one embodiment, can be hierarchy-based operations for hierarchy data structures and set operations for set data structures. Some of the equality-based operations involve processing more than one identifier. The hierarchy-based operations include enumerate, traverse, and count; the set operations query, enumerate, union, intersection, difference, subset and count. Other operations are possible. Depending on the operation used, the computing service can simply retrieve data structures that include one of the matching identifiers; retrieve the data structures and perform further processing on the data structures before the data structures are transmitted to the application as a result of the operation; and provide a statistic regarding the identifiers in the data structures, such as how many matching identifiers are in the data structures when the count operation is performed. The results of at least one of the equality-based operations performed are received by the client application, terminating the routine 80. Multiple identifiers can be processed using the routine 80.
Once either the data structures or the statistic regarding the matching Id are received, the client application can obtain plaintext for either at least some of the identifiers in the returned data structures, or the Ids regarding which the statistic is received. FIG. 8 is a flow diagram illustrating a routine 90 for the method 50 of FIG. 5 for obtaining plaintext data items from which queries associated with at least one of identifiers received from the computing service were generated. Initially, the client application API converts the same plaintext data items that were used to generate the homomorphic queries into ciphertext data items (step 91). The client application transmits the ciphertext data items into the storage service (step 92). After the storage service stores the ciphertext data items into a location in the cloud-computing storage, the client application receives a Uri, a reference, to the location from the storage service (step 93).
The application associates the Uri with an Id identifying a query generated from the same plaintext data item as the ciphertext data item stored at the location identified by the Uri, and provides the association to the DHE service (step 94). Upon request, the application receives the Uri for a particular Id from the client (step 95). This step can be used to retrieve the Uri for Ids included in the results of the equality-based operation described above (step 95). The application then retrieves the ciphertext data item stored at the location by requesting the data item from the storage service (step 96). Upon receiving the data item, still encrypted as ciphertext, the application decrypts the data item into plaintext by performing a decryption algorithm (step 97), terminating the routine 90. Thus, the client application can process data items in the cloud without the data items being decrypted for the processing.
Examples of Certain Embodiments of the System and Method
The following examples are presented for the purposes of illustration and not limitation.
Customer Management System in the Cloud
Table 2 presents various structures typical for several records that can be used in one embodiment of the described system and method. Left side is the name of the record name; the right side is the fields of the record.










TABLE 2





Record
Fields
Structure
Parent







Customer
Account Number (Cid), 
database
n/a



First Name, Last Name 
row




Address, City, State, Zip, Country




Product
ProductId (Pid), Name, Price, 
row
n/a



Quantity, Description, Date




Order
OrderId (Oid), Cid, Date
Row
Customer


OrderDetail
DetailId (Did), Oid, Pid, Price, 
Row
Order



Quantity









The client application ensures that all sensitive fields is substituted by with the DHE Ids, and thus enabling encrypted queries (in pseudo-SQL code below) based on equality-based operations on the DHE Ids.

a. Get all customers from “Seattle”:

    
    
        Unencrypted: select * from Customers where City=‘Seattle’
        Encrypted: Id1=Query(“Seattle”)
        
            select * from Customers where City=Id1 

b. Get all orders for customer “John Smith”:

        
        
        Unencrypted: select Cid from Customers where First Name=‘John’ and Last Name=‘Smith’
        
            Select * from Orders where Cid=Cid
        
        
        Encrypted: Id1=Query(“John”)
        
            Id2=Query(“Smith”)
            select Cid from Customers where First Name=Id1 and Last Name=Id2 
            Select * from Orders where Cid=Cid

c. Get a count of all orders for product “P”:

        
        
        Unencrypted: select Pid from Products where Name=‘P’
        
            Select count(*) from OrderDetails where Pid=Pid
        
        
        Encrypted: Id1=Query(“P”)
        
            select Pid from Products where Name=Id1 
            Select count(*) from OrderDetails where Pid=Pid
        
        
    
    


Sharing of a Document
Using the DHE service, a user (U1) can share a document (D) with another user (U2). The document typically consists of fields (F) of metadata: Name, Extension, Created, Modified and the data populating the fields. Other types of documents are possible.
When the user (U1) stores the document in the computing service in the sharing-mode, each piece of information (F) (metadata and data) will be encrypted with a unique encryption key (KH) and substituted with their corresponding DHE Id. Finally a document identifier (D1) will be returned to the application 11.
The user (U2) is given access to the document (D1), so that user (U2) can retrieve the composing fields as DHE Ids that can be further “decrypted” through the DHE service reverse queries in conjunction with their corresponding unique encryption key (KH), as further described with reference to FIGS. 2 and 8.
While the invention has been particularly shown and described as referenced to the embodiments thereof, those skilled in the art will understand that the foregoing and other changes in form and detail may be made therein without departing from the spirit and scope.

## Claims

1. A computer-implemented method for providing data privacy in a cloud using discrete homomorphic encryption, comprising the steps of:
performing a homomorphic encryption algorithm that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query comprising a cryptographically safe representation of one of the data items;
transmitting the queries to at least one discrete homomorphic encryption (DHE) server and receiving from the DHE server an identifier associated with each query;
transmitting the received identifiers to at least one computing server in a cloud-computing environment that maintains a database comprising data structures;
requesting the computing server to insert the received identifiers into the database comprising at least one of:
requesting the computing server to substitute existing data in the data structures with the identifiers; and
requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures;

processing at least one of the identifiers, comprising:
requesting the computing server to find the identifiers in the data structures in the database that match the at least one identifier;
requesting the computing server to perform at least one equality-based operation on the matching identifiers; and
receiving from the computing server a result of the at least one operation;

performing the homomorphic encryption algorithm to encrypt at least the portion of the plaintext data items into ciphertext data items;
transmitting the ciphertext data items to at least one storage server in the cloud-computing environment and requesting the storage server to store the ciphertext data items in the storage in the cloud-computing environment;
receiving a reference from the storage server to a location of each ciphertext data item in the storage;
obtaining an association between the at least one identifier comprised in the result and one of the references for the location of the ciphertext data item generated from the same plaintext data item as the query identified by the at least one identifier;
retrieving the ciphertext data item from the storage using the one reference; and
decrypting the retrieved ciphertext data item into the corresponding plaintext data item.

2. A method according to claim 1, further comprising:
transmitting to the DHE server the association between the at least one identifier and the one reference;
requesting the reference associated with the at least one identifier comprised in the result from the DHE server; and
receiving the associated reference from the DHE server.

3. A method according to claim 1, further comprising:
encrypting at least one encryption key for use in a sharing mode of the homomorphic encryption algorithm;
transmitting at least one encrypted encryption key to the DHE server; and
requesting the DHE server to transmit the at least one encrypted encryption key to a computing device associated with a different user than the user of the client computing device.

4. A method according to claim 1, wherein the identifier for each query lacks a semantic relationship to the query.

5. A method according to claim 1, wherein the at least one equality-based operation comprises at least one of:
equality-based set operations comprising at least one of query, enumerate, union, intersection, difference, subset, and count; and
equality-based hierarchy operations comprising at least one of enumerate, traverse, and count.

6. A method according to claim 1, further comprising at least one of:
creating a stream of bytes sufficient for an operation of the homomorphic encryption algorithm; and
generating one or more encryption keys for the homomorphic encryption algorithm.

7. A method according to claim 6, wherein at least one of the encryption keys is generated using a key phrase.

8. A method according to claim 6, further comprising:
transforming at least the portion of the plaintext data items into vectors using a cryptographically secure one-way compression function;
transforming the vectors into queries using a length-preserving encryption algorithm; and
transforming the vectors into initialization vectors using a one-way compression function.

9. A method according to claim 8, wherein the cryptographically secure one-way compression function is a Merkle-Damgård construction.

10. A method according to claim 1, further comprising:
encrypting the homomorphic encryption algorithm; and
preserving the encrypted algorithm comprising at least one of:
storing the encrypted algorithm at the client computing device; and
transmitting the encrypted algorithm to the DHE server.

11. A computer-implemented method for providing data privacy in a cloud during data structure retrieval using discrete homomorphic encryption, comprising the steps of:
performing a homomorphic encryption algorithm that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query comprising a cryptographically safe representation of one of the data items;
transmitting the queries to at least one discrete homomorphic encryption (DHE) server in a cloud-computing environment and receiving from the DHE server an identifier associated with each query;
transmitting the received identifiers to at least one computing server in the cloud-computing environment and that maintains a database that comprises data structures;
requesting the computing server to insert the received identifiers into the database comprising at least one of:
requesting the computing server to substitute existing data in the data structures with the identifiers; and
requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures;

processing at least one of the identifiers, comprising:
requesting the computing server to find the identifiers in the data structures in the database that match the at least one identifier;
requesting the computing server to perform at least one equality-based operation on the matching identifiers; and
receiving from computing server at least one of the data structures with one of the matching identifiers as a result of the equality-based operation; and

obtaining the plaintext data item from which the query associated with at least one of the identifiers in the received data structure was generated, comprising:
performing the homomorphic encryption algorithm to encrypt at least the portion of the plaintext data items into ciphertext data items;
transmitting the ciphertext data items to at least one storage server in the cloud-computing environment and requesting the storage server to store the ciphertext data items in a storage in the cloud-computing environment;
receiving a reference from the storage server to a location of each ciphertext data item in the storage;
obtaining an association between the at least one identifier in the received data structure and the reference for the location of the ciphertext data item generated from the same plaintext data item as the query identified by the at least one identifier;
retrieving the ciphertext data item from the storage using the one reference; and
decrypting the retrieved ciphertext data item into the corresponding plaintext data item.

12. A method according to claim 11, further comprising:
transmitting to the DHE server the association between the at least one identifier and the one reference;
requesting the one reference associated with the at least one identifier; and
receiving the associated reference from the DHE server.

13. A computer-implemented method for providing data privacy in a cloud during data processing using discrete homomorphic encryption, comprising the steps of:
performing a homomorphic encryption algorithm that encrypts at least a portion of a plurality of plaintext data items at a client computing device into homomorphic queries, each query comprising a cryptographically safe representation of one of the data items;
transmitting the queries to at least one discrete homomorphic encryption (DHE) server in a cloud-computing environment and receiving from the DHE server an identifier associated with each query;
transmitting the received identifiers to at least one computing server in the cloud-computing environment and that maintains a database that comprises data structures;
requesting the computing server to insert the received identifiers into the database comprising at least one of:
requesting the computing server to substitute existing data in the data structures with the identifiers; and
requesting the computing server to create one or more additional data structures in the database and inserting the identifiers into the additional data structures;

processing at least one of the identifiers, comprising:
requesting the computing server to find the identifiers in the data structures in the database that match the at least one identifier;
requesting the computing server to perform at least one equality-based operation on the matching identifiers; and
receiving from the computing server a result of the equality-based operation comprising a statistic associated with at least one of the identifiers populating the data structures;

performing the homomorphic encryption algorithm to encrypt at least the portion of the plaintext data items into ciphertext data items;
transmitting the ciphertext data items to at least one storage server in the cloud-computing environment and requesting the storage server to store the ciphertext data items in a storage in the cloud-computing environment;
receiving a reference from the storage server to a location of each ciphertext data item in the storage;
obtaining an association between the at least one identifier associated with the statistic and the reference for the location of the ciphertext data item generated from the same plaintext data item as the query identified by the at least one identifier;
retrieving the ciphertext data item from the storage using the one reference; and
decrypting the retrieved ciphertext data item into the corresponding plaintext data item.

14. A method according to claim 13, further comprising at least one of:
creating a stream of bytes sufficient for an operation of the homomorphic encryption algorithm; and
generating one or more encryption keys for the homomorphic encryption algorithm.

15. A method according to claim 14, wherein at least one of the encryption keys is generated using a key phrase.

16. A method according to claim 14, further comprising:
transforming at least the portion of the plaintext data items into vectors using a cryptographically secure one-way compression function;
transforming the vectors into queries using a length-preserving encryption algorithm; and
transforming the vectors into initialization vectors using a one-way compression function.

17. A method according to claim 16, wherein the cryptographically secure one-way compression function is a Merkle-Damgård construction.