Abstract: A method for outsourcing exponentiation in a private group includes executing a query instruction to retrieve a query element stored on an untrusted server by selecting a prime factorization of two or more prime numbers of a modulus associated with the query element stored on the server, obtaining a group element configured to generate a respective one of the prime numbers, generating a series of base values using the prime factorization and the group element, and transmitting the series of base values from the client device to the server. The server is configured to determine an exponentiation of the group element with an exponent stored on the server using the series of base values. The method also includes receiving a result from the server based on the exponentiation of the group element with the exponent.

Abstract: A method includes obtaining, from a server, a filter including a set of encrypted identifiers each encrypted with a server key controlled by the server. The method includes obtaining a request that requests determination of whether a query identifier is a member of a set of identifiers corresponding to the set of encrypted identifiers. The method also includes transmitting an encryption request to the server that requests the server to encrypt the query identifier. The method includes receiving, from the server, an encrypted query identifier including the query identifier encrypted by the server key and determining, using the filter, whether the encrypted query identifier is not a member of the set of encrypted identifiers. When the encrypted query identifier is not a member of the set of encrypted identifiers, the method includes reporting that the query identifier is not a member of the set of identifiers.

Abstract: A method for searchable encryption with a public key includes receiving an operation request from a user device associated with a user requesting that encryption of data associated with the user. The data includes a corpus of documents stored on a remote storage device. The method also includes receiving a public key associated with the user. The public key includes an asymmetric cryptographic public key. The method also includes generating a random data key. The data key includes a symmetric cryptographic key. The method also includes encrypting, using the data key, a search index for the corpus of documents based on keywords within the corpus of documents. The method also includes encrypting, using the public key, the data key and sending the encrypted data key to a user device associated with the user.

Abstract: A method for providing response-hiding searchable encryption includes receiving a search query for a keyword from a user device associated with a user. The keyword appears in one or more encrypted documents within a corpus of encrypted documents stored on an untrusted storage device. The method also includes accessing a document oblivious key-value storage (OKVS) to obtain a list of document identifiers associated with the keyword. Each document identifier in the list of document identifiers associated with a respective keyword identifier is concatenated with the keyword and uniquely identifies a respective one of the one or more encrypted documents that the keyword appears in. The method also includes returning the list of document identifiers obtained from the document OKVS to the user device.

Abstract: A method executing an instruction (300) to execute a query (q) for a data block (102) and determining whether the data block is stored in a block stash (370). When the data block is stored in the block stash during a download phase, the method includes removing the data block from the block stash, sending a fake query (304) to a distributed system (140) to retrieve a random data block stored in memory (114) of a distributed system (140), and discarding the random data block. When a current version of the data block is stored in the block stash during an overwrite phase, the method includes sending a fake query to the distributed system to retrieve another random data block stored in the memory of the distributed system, decrypting and re-encrypting the random data block with fresh randomness, and re-uploading the re-encrypted random data block onto the distributed system.

Abstract: A method for searchable encryption with a public key includes receiving an operation request from a user device associated with a user requesting that encryption of data associated with the user. The data includes a corpus of documents stored on a remote storage device. The method also includes receiving a public key associated with the user. The public key includes an asymmetric cryptographic public key. The method also includes generating a random data key. The data key includes a symmetric cryptographic key. The method also includes encrypting, using the data key, a search index for the corpus of documents based on keywords within the corpus of documents. The method also includes encrypting, using the public key, the data key and sending the encrypted data key to a user device associated with the user.

Abstract: A method includes obtaining, from a server, a filter including a set of encrypted identifiers each encrypted with a server key controlled by the server. The method includes obtaining a request that requests determination of whether a query identifier is a member of a set of identifiers corresponding to the set of encrypted identifiers. The method also includes transmitting an encryption request to the server that requests the server to encrypt the query identifier. The method includes receiving, from the server, an encrypted query identifier including the query identifier encrypted by the server key and determining, using the filter, whether the encrypted query identifier is not a member of the set of encrypted identifiers. When the encrypted query identifier is not a member of the set of encrypted identifiers, the method includes reporting that the query identifier is not a member of the set of identifiers.

Abstract: A method includes initializing a client state on a client device be executing a private batched sum retrieval instruction to compute c sums O of data blocks from an untrusted storage device. Each computed sum O stored on memory hardware of the client device and including a sum of a corresponding subset S of exactly k data blocks. The method also includes a query instruction to retrieve a query block Bq stored on the untrusted storage device by iterating through each of the c sums O of data blocks to identify one of the c sums O that does not include the query block Bq, instructing a service to pseudorandomly partition the untrusted storage device into partitions and sum the data blocks in each partition to determine a corresponding encrypted data block sum.

Abstract: A method for providing response-hiding searchable encryption includes receiving a search query for a keyword from a user device associated with a user. The keyword appears in one or more encrypted documents within a corpus of encrypted documents stored on an untrusted storage device. The method also includes accessing a document oblivious key-value storage (OKVS) to obtain a list of document identifiers associated with the keyword. Each document identifier in the list of document identifiers associated with a respective keyword identifier is concatenated with the keyword and uniquely identifies a respective one of the one or more encrypted documents that the keyword appears in. The method also includes returning the list of document identifiers obtained from the document OKVS to the user device.

Abstract: A method for sharing read access to a document stored on memory hardware. The method includes receiving a shared read access command from a sharor sharing read access to a sharee for a document stored on memory hardware in communication with the data processing hardware, and receiving a shared read access request from the sharee. The shared read access command includes an encrypted value and a first cryptographic share value based on a write key, a read key, a document identifier, and a sharee identifier. The method also includes multiplying the first and second cryptographic share values to determine a cryptographic read access value. The cryptographic read access value authorizes read access to the sharee for the document. The method also includes storing a read access token for the sharee including the cryptographic read access value and the encrypted value in a user read set of the memory hardware.

Abstract: A method for providing encrypted search includes receiving, at a user device associated with a user, a search query for a keyword that appears in one or more encrypted documents stored on an untrusted storage device and accessing a count table to obtain a count of documents that include the keyword. The method also includes generating a delegatable pseudorandom function (DPRF) based on the keyword, a private cryptographic key, and the count of documents. The method also includes evaluating a first portion of the DPRF and delegating a remaining second portion of the DPRF to the untrusted storage device which causes the untrusted storage device to evaluate the DPRF and access an encrypted search index associated with the documents. The untrusted storage device determines one or more encrypted documents associated with DPRF and returns, to the user device, an identifier for each encrypted document associated with the DPRF.

Abstract: A method includes executing an instruction to execute a query for a data block, the data block associated with a corresponding memory level of a logarithmic number of memory levels (li) of memory, each memory level (li) including physical memory (RAMi) residing on memory hardware of a distributed system. The method also includes retrieving a value associated with the data block from an oblivious hash table using a corresponding key, and extracting un-queried key value pairs from the oblivious hash table associated with un-queried data blocks after executing a threshold number of queries for data blocks. The method also includes a multi-array shuffle routine on the extracted key value pairs from the oblivious hash table to generate an output array containing the un-queried key value pairs.

Abstract: A method includes obtaining, from a server, a filter including a set of encrypted identifiers each encrypted with a server key controlled by the server. The method includes obtaining a request that requests determination of whether a query identifier is a member of a set of identifiers corresponding to the set of encrypted identifiers. The method also includes transmitting an encryption request to the server that requests the server to encrypt the query identifier. The method includes receiving, from the server, an encrypted query identifier including the query identifier encrypted by the server key and determining, using the filter, whether the encrypted query identifier is not a member of the set of encrypted identifiers. When the encrypted query identifier is not a member of the set of encrypted identifiers, the method includes reporting that the query identifier is not a member of the set of identifiers.

Abstract: A method includes obtaining, from a server, a filter including a set of encrypted identifiers each encrypted with a server key controlled by the server. The method includes obtaining a request that requests determination of whether a query identifier is a member of a set of identifiers corresponding to the set of encrypted identifiers. The method also includes transmitting an encryption request to the server that requests the server to encrypt the query identifier. The method includes receiving, from the server, an encrypted query identifier including the query identifier encrypted by the server key and determining, using the filter, whether the encrypted query identifier is not a member of the set of encrypted identifiers. When the encrypted query identifier is not a member of the set of encrypted identifiers, the method includes reporting that the query identifier is not a member of the set of identifiers.

Abstract: A method (500) includes initializing a client state (250) on a client device (120) be executing a private batched sum retrieval instruction (200) to compute c sums O of data blocks (102) from an untrusted storage device (150). Each computed sum O stored on memory hardware (122) of the client device and including a sum of a corresponding subset S of exactly k data blocks. The method also includes a query instruction (300) to retrieve a query block Bq stored on the untrusted storage device by iterating through each of the c sums O of data blocks to identify one of the c sums O that does not include the query block Bq, instructing a service to pseudorandomly partition the untrusted storage device into partitions and sum the data blocks in each partition to determine a corresponding encrypted data block sum (302).

Abstract: A method for sharing read access to a document stored on memory hardware. The method includes receiving a shared read access command from a sharor sharing read access to a sharee for a document stored on memory hardware in communication with the data processing hardware, and receiving a shared read access request from the sharee. The shared read access command includes an encrypted value and a first cryptographic share value based on a write key, a read key, a document identifier, and a sharee identifier. The method also includes multiplying the first and second cryptographic share values to determine a cryptographic read access value. The cryptographic read access value authorizes read access to the sharee for the document. The method also includes storing a read access token for the sharee including the cryptographic read access value and the encrypted value in a user read set of the memory hardware.

Abstract: A method includes executing an instruction to execute a query for a data block, the data block associated with a corresponding memory level of a logarithmic number of memory levels (li) of memory, each memory level (li) including physical memory (RAMi) residing on memory hardware of a distributed system. The method also includes retrieving a value associated with the data block from an oblivious hash table using a corresponding key, and extracting un-queried key value pairs from the oblivious hash table associated with un-queried data blocks after executing a threshold number of queries for data blocks. The method also includes a multi-array shuffle routine on the extracted key value pairs from the oblivious hash table to generate an output array containing the un-queried key value pairs.

Abstract: A method for providing an encrypted search system includes receiving a search query for a keyword that appears in one or more encrypted emails stored on an untrusted storage device and accessing, a count table to obtain a count of unique emails within the emails that include the keyword. The method also includes generating a delegatable pseudorandom function (DPRF) based on the keyword, a private cryptographic key, and the count of unique emails that include the keyword and delegating at least a portion of the DPRF to the untrusted storage device that causes the storage device to evaluate the delegated DPRF, access an encrypted search index associated with the emails, and determine one or more encrypted emails associated with the delegated DPRF based on the encrypted search index. The storage device also returns, to the user device, an identifier for each encrypted email associated with the delegated DPRF.

Abstract: A method includes obtaining a plaintext query that includes a sequence of plaintext integers and generating a polynomial having coefficients that include the sequence of plaintext integers of the plaintext query. The method also includes encrypting the polynomial using a secret encryption key and transmitting the encrypted polynomial to a server. The secret encryption key is randomly sampled from a ciphertext space and the server is configured to expand the encrypted polynomial using a public encryption key to obtain a sequence of encrypted integers corresponding to the sequence of plaintext integers. The method also includes receiving an encrypted result from the server. The encrypted result is based on the sequence of encrypted integers.

Abstract: A method for providing encrypted search includes receiving, at a user device associated with a user, a search query for a keyword that appears in one or more encrypted documents stored on an untrusted storage device and accessing a count table to obtain a count of documents that include the keyword. The method also includes generating a delegatable pseudorandom function (DPRF) based on the keyword, a private cryptographic key, and the count of documents. The method also includes evaluating a first portion of the DPRF and delegating a remaining second portion of the DPRF to the untrusted storage device which causes the untrusted storage device to evaluate the DPRF and access an encrypted search index associated with the documents. The untrusted storage device determines one or more encrypted documents associated with DPRF and returns, to the user device, an identifier for each encrypted document associated with the DPRF.