The processing of queries to an encrypted database without its decryption has been actively investigated recently by both cryptographers and database researchers. Such a work is allowed by various types of so-called Processable encryption (PE), as well as special architectures of database management systems (DBMS) which use these types of encryption. The most known types of PEs are order-preserving encryption, homomorphic encryption, functional encryption, searchable encryption, and property-preserving encryption. Based on these types of encryption, various DBMSs are built, the most famous of which are CryptDB, Mo- nomi, Arx and DBMS by researchers from Novosibirsk. These DBMSs are built on the basis of various types of PEs, for example order-preserving encryption, homomorphic encryption and traditional block encryption. However, this approach can cause privacy problems. The best approach from the security viewpoint is to build a cryptographic database using only homomorphic encryption. An obstacle to this is insufficient efficiency of the existing homomorphic encryption schemes and incomplete solution of a set of issues related to ensuring the confidentiality of decisions making in an untrusted environment. In this paper, we propose the techniques for solving these problems, in particular for organization of execution arbitrary secure query to the encrypted relational database using fully homomorphic encryption. Also we propose a model of query condition that splits query into atomic predicates and linking condition. One of roposed technique is aimed at ensuring the security of linking condition of queries, others keep security of atomic predicates. The parameters of the proposed techniques make it possible to implement them using the already existing homomorphic encryption schemes. The proposed techniques can be a basis for building secure cryptographic cloud databases.
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