On the Impossibility of Basing Identity Based Encryption on Trapdoor Permutations

We ask whether an Identity Based Encryption (IBE) sys-tem can be built from simpler public-key primitives. We show that there is no black-box construction of IBE from Trapdoor Permutations (TDP) or even from Chosen Ci-phertext Secure Public Key Encryption (CCA-PKE). These black-box separation results are based on an essential prop-erty of IBE, namely that an IBE system is able to compress exponentially many public-keys into a short public parame-ters string. 1

POPE: Partial Order Preserving Encoding

Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. In this paper, we propose an alternative approach to range queries over encrypted data that is optimized to support insert-heavy workloads as are common in "big data" applications while still maintaining search functionality and achieving stronger security. Specifically, we propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Using only O(1) persistent and $O(n^\epsilon)$ non-persistent client storage for $0<\epsilon<1$, our POPE scheme provides extremely fast batch insertion consisting of a single round, and efficient search with O(1) amortized cost for up to $O(n^{1-\epsilon})$ search queries. This improved security and performance makes our scheme better suited for today's insert-heavy databases.Comment: Appears in ACM CCS 2016 Proceeding

Conditionals in Homomorphic Encryption and Machine Learning Applications

Homomorphic encryption aims at allowing computations on encrypted data without decryption other than that of the final result. This could provide an elegant solution to the issue of privacy preservation in data-based applications, such as those using machine learning, but several open issues hamper this plan. In this work we assess the possibility for homomorphic encryption to fully implement its program without relying on other techniques, such as multiparty computation (SMPC), which may be impossible in many use cases (for instance due to the high level of communication required). We proceed in two steps: i) on the basis of the structured program theorem (Bohm-Jacopini theorem) we identify the relevant minimal set of operations homomorphic encryption must be able to perform to implement any algorithm; and ii) we analyse the possibility to solve -- and propose an implementation for -- the most fundamentally relevant issue as it emerges from our analysis, that is, the implementation of conditionals (requiring comparison and selection/jump operations). We show how this issue clashes with the fundamental requirements of homomorphic encryption and could represent a drawback for its use as a complete solution for privacy preservation in data-based applications, in particular machine learning ones. Our approach for comparisons is novel and entirely embedded in homomorphic encryption, while previous studies relied on other techniques, such as SMPC, demanding high level of communication among parties, and decryption of intermediate results from data-owners. Our protocol is also provably safe (sharing the same safety as the homomorphic encryption schemes), differently from other techniques such as Order-Preserving/Revealing-Encryption (OPE/ORE).Comment: 14 pages, 1 figure, corrected typos, added introductory pedagogical section on polynomial approximatio

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

Order-Revealing Encryption and the Hardness of Private Learning

An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning from efficient $(\epsilon, \delta)$-differentially private PAC learning. That is, we construct a concept class that is efficiently PAC learnable, but for which every efficient learner fails to be differentially private. This answers a question of Kasiviswanathan et al. (FOCS '08, SIAM J. Comput. '11). To prove our result, we give a generic transformation from an order-revealing encryption scheme into one with strongly correct comparison, which enables the consistent comparison of ciphertexts that are not obtained as the valid encryption of any message. We believe this construction may be of independent interest.Comment: 28 page

Format and Order Revealing Encryption

As more and more cloud services emerge so does the need for new methods for securing the data these services consume, especially since data leaks have become the norm rather than the exception. Since most cloud services require some kind of access to our private data in order to perform searches and provide services, new ways of securing our data in the cloud is needed. This dissertation examines the current state of the cryptographic world in order to try to and understand and resume what solutions currently exist for this particular type of problem. This work is motivated by a particular problem of data delegation to a cloud infrastructure. This problem involves the protection of sensitive data whilst it’s analysed by a third party. While there is no simple approach to solve this particular problem, this dissertation discusses three main approaches to tackle this problem. One approach attempts to define a new cryptographic scheme with a leakage profile that would allow a third party to only have access to some information of the plaintext but, at the same time, keep the plaintext safe from attackers. Another approach attempts to use already existing cryptographic schemes, such as, Format Preserving Encryption and Order Revealing Encryption to solve this particular problem. A final approach tries to solve this problem by utilising cryptographic tools, such as hash-functions and hash-based message authentication codes. An extended study was also conducted in many cryptographic schemes, both current and old cryptographic schemes. This study allowed for a better view of the cryptographic world and how these schemes could help us achieve a solution. For this dissertation, a prototype was also implemented of some recent cryptographic schemes. These prototype implementations allowed for a deeper understanding of how these schemes work and also allowed us to conduct some experiments while trying to combine two cryptographic schemes. The results of this dissertation show that that trying to solve a problem via creating a new cryptographic scheme is not an easy feat especially when one wants to define correctly the strict security requirements and also the work needed to understand the mathematical workings of similar schemes. Lastly we conclude that solving the problem with the help of already existing tools may be the easiest solution, but, it may also only work for a specific scenario and hence is of no use in other similar situations. A solution to the particular problem studied in this thesis is also presented at the end of this dissertation, although, it only applies to this specific problem and does not solve the more general problem of privacy of data delegation to the cloud.Com a explosão de serviços baseados na nuvem que ocorre nos dias de hoje, torna-se imperativo que os dados que são consumidos por este tipo de serviços sejam de alguma forma protegidos contra ataques ou roubos[Cen18]. O principal problema com este tipo de serviços é que, normalmente, estes serviços precisam de acesso aos dados para conseguirem fazer pesquisas e correlacionar dados de forma a que seja possível fornecer diversos serviços. Esta dissertação tem como objetivo estudar o mundo da criptografia de forma a perceber que tipo de garantias são oferecidas pelos esquemas criptográficos existentes nos dias de hoje para serviços baseados na nuvem. Este trabalho é motivado por um problema real de delegação de dados para a nuvem. Este problema envolve a proteção de dados sensíveis que precisam de ser analisados por entidades externas. Embora não haja uma abordagem simples para resolver este tipo de problemas, nesta dissertação iremos discutir três abordagens que, potencialmente, poderão resolver este problema. Uma abordagem tenta definir o que poderia ser a estrutura geral de um novo esquema criptográfico que pudesse lidar com o problema específico em análise. Numa outra abordagem iremos utilizar ferramentas existentes para tentar resolver o problema em questão. Iremos também tentar unir dois esquemas criptográficos existentes, de forma a tentar combater este problema em específico. Foi também realizado um estudo a vários esquemas criptográficos de forma a perceber quais as soluções que existem hoje em dia para problemas relacionados com a delegação de dados para entidades externas, como também, tentar perceber que esquemas criptográficos que ainda são resultados meramente teóricos mas que possam vir, no futuro, a ser úteis para combater esta problemática. Os resultados desta dissertação mostram que resolver um problema relacionado com criptografia nem sempre é fácil, uma vez que, a má utilização destes esquemas poderá levar a uma falha grave de segurança. Por fim, concluímos que, resolver um problema desta natureza através de ferramentas existentes é bastante mais fácil do que tentar desenvolver esquemas criptográficos novos, mas que irá perder o poder de poder ser aplicado a outros problemas semelhantes