Steven D. Galbraith⋆

Muhammad Rizwan Asghar, Steven Galbraith, Andrea Lanzi et al.

Most recent theoretical literature on program obfuscation is based on notions like Virtual Black Box (VBB) obfuscation and indistinguishability Obfuscation (iO). These notions are very strong and are hard to satisfy. Further, they offer far more protection than is typically required in practical applications. On the other hand, the security notions introduced by software security researchers are suitable for practical designs but are not formal or precise enough to enable researchers to provide a quantitative security assurance. Hence, in this paper, we introduce a new formalism for practical program obfuscation that still allows rigorous security proofs. We believe our formalism will make it easier to analyse the security of obfuscation schemes. To show the flexibility and power of our formalism, we give a number of examples. Moreover, we explain the close relationship between our formalism and the task of providing obfuscation challenges. This is the full version of the paper. In this version, we also give a new rigorous analysis of several obfuscation techniques and we provide directions for future research.

Shujie Cui, Xiangfu Song, Muhammad Rizwan Asghar et al.

Searchable Encryption (SE) is a technique that allows Cloud Service Providers (CSPs) to search over encrypted datasets without learning the content of queries and records. In recent years, many SE schemes have been proposed to protect outsourced data from CSPs. Unfortunately, most of them leak sensitive information, from which the CSPs could still infer the content of queries and records by mounting leakage-based inference attacks, such as the count attack and file injection attack. In this work, first we define the leakage in searchable encrypted databases and analyse how the leakage is leveraged in existing leakage-based attacks. Second, we propose a Privacy-preserving Multi-cloud based dynamic symmetric SE (SSE) scheme for relational Database (P-McDb). P-McDb has minimal leakage, which not only ensures confidentiality of queries and records, but also protects the search, access, and size patterns from CSPs. Moreover, P-McDb ensures both forward and backward privacy of the database. Thus, P-McDb could resist existing leakage-based attacks, e.g., active file/record-injection attacks. We give security definition and analysis to show how P-McDb hides the aforementioned patterns. Finally, we implemented a prototype of P-McDb and test it using the TPC-H benchmark dataset. Our evaluation results show the feasibility and practical efficiency of P-McDb.

Steven Galbraith, Lorenz Panny, Benjamin Smith et al.

In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) to the parallelization problem (CDHP) for group actions. Combined with the trivial reduction from par-allelization to vectorization, we thus prove the quantum equivalence of both problems.

Steven D. Galbraith, Joel Laity, Barak Shani

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any finite abelian group. Their algorithm stimulated a lot of interest in the cryptography community, especially in the context of `bit security'. This manuscript attempts to be a friendly and comprehensive guide to the tools and results in this field. The intended readership is cryptographers who have heard about these tools and seek an understanding of their mechanics and their usefulness and limitations. A compact overview of the algorithm is presented with emphasis on the ideas behind it. We show how these ideas can be extended to a `modulus-switching' variant of the algorithm. We survey some applications of this algorithm, and explain that several results should be taken in the right context. In particular, we point out that some of the most important bit security problems are still open. Our original contributions include: a discussion of the limitations on the usefulness of these tools; an answer to an open question about the modular inversion hidden number problem.