Abstract: A computer-implemented system and method for providing secure data processing in a cloud using discrete homomorphic encryption is provided. Plaintext data items are homomorphically encrypted into queries, which are transmitted to a discrete homomorphic encryption server. From the server are received identifiers associated with the queries. The identifiers are transmitted to a computing server in a cloud-computing environment, where at least one of the identifiers is processed. The plaintext data items are encrypted into ciphertext data items and transmitted to a storage server in the environment requested to store the items in a storage. References for storage locations of the ciphertext data items are received and associated with identifiers for the queries encrypted from the same plaintext data item as the ciphertext data items at the locations. The ciphertext data item whose location is identified by the reference associated with the identifier in the processing result is retrieved and decrypted.

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.