A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

Achieving Secure and Efficient Cloud Search Services: Cross-Lingual Multi-Keyword Rank Search over Encrypted Cloud Data

Multi-user multi-keyword ranked search scheme in arbitrary language is a novel multi-keyword rank searchable encryption (MRSE) framework based on Paillier Cryptosystem with Threshold Decryption (PCTD). Compared to previous MRSE schemes constructed based on the k-nearest neighbor searcha-ble encryption (KNN-SE) algorithm, it can mitigate some draw-backs and achieve better performance in terms of functionality and efficiency. Additionally, it does not require a predefined keyword set and support keywords in arbitrary languages. However, due to the pattern of exact matching of keywords in the new MRSE scheme, multilingual search is limited to each language and cannot be searched across languages. In this pa-per, we propose a cross-lingual multi-keyword rank search (CLRSE) scheme which eliminates the barrier of languages and achieves semantic extension with using the Open Multilingual Wordnet. Our CLRSE scheme also realizes intelligent and per-sonalized search through flexible keyword and language prefer-ence settings. We evaluate the performance of our scheme in terms of security, functionality, precision and efficiency, via extensive experiments