A Note for the Ideal Order-Preserving Encryption Object and Generalized Order-Preserving Encryption

Order-preserving encryption (OPE) preserves the order of data in their ciphertexts and, hence, allows range search on the encrypted data without needing to decrypt them. Security analysis of OPE schemes is very important because OPE is not a perfect encryption algorithm (the ciphertexts leak the ordering information of the plaintexts). Most of the existing security analysis for the OPE schemes are informal: they are either based on author-defined attacks or experiments. The authors in \cite{Bol09} initiate the cryptographic study of the OPE scheme. They define the security notion POPF-CCA to qualify the security of OPE. In POPF-CCA, the ``ideal OPE object is defined where the encryption function is uniformly randomly selected from all order-preserving functions (generally the ``ideal OPE object is not computationally feasible), and a (constructed) ``real OPE scheme is secure under POPF-CCA if it is computationally indistinguishable from the ideal object. In other words, although the ``ideal OPE object is not computationally feasible, it is used as the security goal, and a (constructed) ``real OPE scheme is secure if it is as secure as the ``ideal OPE object. Such approach conceives the assumption (but not clearly stated and proved) that the ``ideal OPE object is the most secure OPE. But the correctness of the assumption is an easily ignored problem. In this paper, we investigate the security of the OPE in more depth. We first give example to show that the ``ideal OPE object may not always be the most secure OPE. It indicates that we need to use the ``ideal encryption object more cautiously in the security analysis of OPE. Additionally we extend the concept of OPE to generalized OPE (GOPE). Unlike OPE, the ciphertexts of GOPE may not be numbers, but GOPE still enables the comparisons on the encrypted data without needing to decrypt them. We present two GOPEs in polynomial-sized and superpolynomial-sized domains that satisfy stronger notions of security than that of the ideal OPE object, respectively

A Practical and Secure Stateless Order Preserving Encryption for Outsourced Databases

Order-preserving encryption (OPE) plays an important role in securing outsourced databases. OPE schemes can be either Stateless or Stateful. Stateful schemes can achieve the ideal security of order-preserving encryption, i.e., “reveal no information about the plaintexts besides order.” However, comparing to stateless schemes, stateful schemes require maintaining some state information locally besides encryption keys and the ciphertexts are mutable. On the other hand, stateless schemes only require remembering encryption keys and thus is more efficient. It is a common belief that stateless schemes cannot provide the same level of security as stateful ones because stateless schemes reveal the relative distance among their corresponding plaintext. In real world applications, such security defects may lead to the leakage of statistical and sensitive information, e.g., the data distribution, or even negates the whole encryption. In this paper, we propose a practical and secure stateless order-preserving encryption scheme. With prior knowledge of the data to be encrypted, our scheme can achieve IND-CCPA (INDistinguishability under Committed ordered Chosen Plaintext Attacks) security for static data set. Though the IND-CCPA security can\u27t be met for dynamic data set, our new scheme can still significantly improve the security in real world applications. Along with the encryption scheme, in this paper we also provide methods to eliminate access pattern leakage in communications and thus prevents some common attacks to OPE schemes in practice

Privacy-preserving queries on encrypted databases

In today's Internet, with the advent of cloud computing, there is a natural desire for enterprises, organizations, and end users to outsource increasingly large amounts of data to a cloud provider. Therefore, ensuring security and privacy is becoming a significant challenge for cloud computing, especially for users with sensitive and valuable data. Recently, many efficient and scalable query processing methods over encrypted data have been proposed. Despite that, numerous challenges remain to be addressed due to the high complexity of many important queries on encrypted large-scale datasets. This thesis studies the problem of privacy-preserving database query processing on structured data (e.g., relational and graph databases). In particular, this thesis proposes several practical and provable secure structured encryption schemes that allow the data owner to encrypt data without losing the ability to query and retrieve it efficiently for authorized clients. This thesis includes two parts. The first part investigates graph encryption schemes. This thesis proposes a graph encryption scheme for approximate shortest distance queries. Such scheme allows the client to query the shortest distance between two nodes in an encrypted graph securely and efficiently. Moreover, this thesis also explores how the techniques can be applied to other graph queries. The second part of this thesis proposes secure top-k query processing schemes on encrypted relational databases. Furthermore, the thesis develops a scheme for the top-k join queries over multiple encrypted relations. Finally, this thesis demonstrates the practicality of the proposed encryption schemes by prototyping the encryption systems to perform queries on real-world encrypted datasets

Communication Complexity and Secure Function Evaluation

We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". The second methodology uses the circuit computing f, enhanced with look-up tables as its underlying computational model. It is possible to simulate any RAM machine in this model with polylogarithmic blowup. Hence it is possible to start with a computation of f on a RAM machine and transform it into a secure protocol. We show many applications of these new methodologies resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation