Provable and Practical Security for Database Outsourcing

Provable security is one of the greatest achievements of modern cryptography. When proving the security of a cryptographic scheme, its security properties are reduced to problems known or assumed to be hard to solve. Therefore, breaking the security of such a scheme in its security model involves solving the corresponding problem which is deemed infeasible for su ciently large instances. Provable security has many bene ts. For example, it allows to design schemes that provide security against attacks that have not yet been conceived. Furthermore, formal security guarantees allow to compare the security of schemes without comparing the schemes itself which can be a tedious task. A central focus of cryptographic research is to conceive more and more stronger security notions and to nd schemes that ful l such notions. For example, the gold standard for encryption schemes is the notion of semantic security, where an adversary is not allowed to learn even one bit about the plaintext. For many complex applications such as database outsourcing classical, strong security requirements imply methods with large overheads. On the other hand, there are more practical data outsourcing schemes that intuitively provide some security but do not have any proven security properties at all. Relaxing the classical security requirements potentially allows for more e cient schemes while maintaining provable security properties. This implies a trade-o : The resulting security notion should be meaningful in the context of the application while at the same time it should allow for e cient schemes. A eld where such weak security notions play an essential role is database privacy. While the intention of security notions for encryption schemes is to hide all information of the plain text from the adversary, so-called privacy notions describe a trade-o between the con dentiality of the original database and the usefulness of the disclosed database. Database privacy is closely related to data outsourcing. E cient data outsourcing schemes imply leakage of information about the data to the server. Therefore, a security notion for e cient data outsourcing schemes also describes a trade-o , here, between the con dentiality of data and queries and the e ciency of schemes ful lling this notion. The goal of this thesis is to bridge the gap between practical methods for data outsourcing and the eld of cryptographic research that is concerned with formal security notions. Starting in the eld of data privacy, we provide a framework for de ning and reasoning about privacy notions. In contrast to existing notions and frameworks, our framework allows for an intuitive de nition of privacy notions by allowing to de ne sensitive predicates and explicitly limiting what an adversary is allowed to learn about them from a release. Furthermore, we provide meta notions for di erent privacy goals of data outsourcing and establish their relations. As a main contribution of this thesis, we provide a meaningful security notion for database outsourcing and a practical scheme ful lling this notion as well as implementations that demonstrate the viability. Therefore, we capture database outsourcing in a formal model and de ne our scheme with the means of this model. We prove the security of our scheme by a reduction to the security of an internally used encryption scheme. Additionally, we examine the design space for this scheme by discussing extensions and optimisations of this scheme for performance as well as for security.