Attacks on the Search-RLWE problem with small errors

The Ring Learning-With-Errors (RLWE) problem shows great promise for post-quantum cryptography and homomorphic encryption. We describe a new attack on the non-dual search RLWE problem with small error widths, using ring homomorphisms to finite fields and the chi-squared statistical test. In particular, we identify a "subfield vulnerability" (Section 5.2) and give a new attack which finds this vulnerability by mapping to a finite field extension and detecting non-uniformity with respect to the number of elements in the subfield. We use this attack to give examples of vulnerable RLWE instances in Galois number fields. We also extend the well-known search-to-decision reduction result to Galois fields with any unramified prime modulus q, regardless of the residue degree f of q, and we use this in our attacks. The time complexity of our attack is O(nq2f), where n is the degree of K and f is the residue degree of q in K. We also show an attack on the non-dual (resp. dual) RLWE problem with narrow error distributions in prime cyclotomic rings when the modulus is a ramified prime (resp. any integer). We demonstrate the attacks in practice by finding many vulnerable instances and successfully attacking them. We include the code for all attacks

Confidential Boosting with Random Linear Classifiers for Outsourced User-generated Data

User-generated data is crucial to predictive modeling in many applications. With a web/mobile/wearable interface, a data owner can continuously record data generated by distributed users and build various predictive models from the data to improve their operations, services, and revenue. Due to the large size and evolving nature of users data, data owners may rely on public cloud service providers (Cloud) for storage and computation scalability. Exposing sensitive user-generated data and advanced analytic models to Cloud raises privacy concerns. We present a confidential learning framework, SecureBoost, for data owners that want to learn predictive models from aggregated user-generated data but offload the storage and computational burden to Cloud without having to worry about protecting the sensitive data. SecureBoost allows users to submit encrypted or randomly masked data to designated Cloud directly. Our framework utilizes random linear classifiers (RLCs) as the base classifiers in the boosting framework to dramatically simplify the design of the proposed confidential boosting protocols, yet still preserve the model quality. A Cryptographic Service Provider (CSP) is used to assist the Cloud's processing, reducing the complexity of the protocol constructions. We present two constructions of SecureBoost: HE+GC and SecSh+GC, using combinations of homomorphic encryption, garbled circuits, and random masking to achieve both security and efficiency. For a boosted model, Cloud learns only the RLCs and the CSP learns only the weights of the RLCs. Finally, the data owner collects the two parts to get the complete model. We conduct extensive experiments to understand the quality of the RLC-based boosting and the cost distribution of the constructions. Our results show that SecureBoost can efficiently learn high-quality boosting models from protected user-generated data

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

Security considerations for Galois non-dual RLWE families

We explore further the hardness of the non-dual discrete variant of the Ring-LWE problem for various number rings, give improved attacks for certain rings satisfying some additional assumptions, construct a new family of vulnerable Galois number fields, and apply some number theoretic results on Gauss sums to deduce the likely failure of these attacks for 2-power cyclotomic rings and unramified moduli

Privately Connecting Mobility to Infectious Diseases via Applied Cryptography

Human mobility is undisputedly one of the critical factors in infectious disease dynamics. Until a few years ago, researchers had to rely on static data to model human mobility, which was then combined with a transmission model of a particular disease resulting in an epidemiological model. Recent works have consistently been showing that substituting the static mobility data with mobile phone data leads to significantly more accurate models. While prior studies have exclusively relied on a mobile network operator's subscribers' aggregated data, it may be preferable to contemplate aggregated mobility data of infected individuals only. Clearly, naively linking mobile phone data with infected individuals would massively intrude privacy. This research aims to develop a solution that reports the aggregated mobile phone location data of infected individuals while still maintaining compliance with privacy expectations. To achieve privacy, we use homomorphic encryption, zero-knowledge proof techniques, and differential privacy. Our protocol's open-source implementation can process eight million subscribers in one and a half hours. Additionally, we provide a legal analysis of our solution with regards to the EU General Data Protection Regulation.Comment: Added differentlial privacy experiments and new benchmark

Homomorphic Encryption and Cryptanalysis of Lattice Cryptography

The vast amount of personal data being collected and analyzed through internet connected devices is vulnerable to theft and misuse. Modern cryptography presents several powerful techniques that can help to solve the puzzle of how to harness data for use while at the same time protecting it---one such technique is homomorphic encryption that allows computations to be done on data while it is still encrypted. The question of security for homomorphic encryption relates to the broader field of lattice cryptography. Lattice cryptography is one of the main areas of cryptography that promises to be secure even against quantum computing. In this dissertation, we will touch on several aspects of homomorphic encryption and its security based on lattice cryptography. Our main contributions are: 1. proving some heuristics that are used in major results in the literature for controlling the error size in bootstrapping for fully homomorphic encryption, 2. presenting a new fully homomorphic encryption scheme that supports k-bit arbitrary operations and achieves an asymptotic ciphertext expansion of one, 3. thoroughly studying certain attacks against the Ring Learning with Errors problem, 4. precisely characterizing the performance of an algorithm for solving the Approximate Common Divisor problem

Confidential Machine Learning on Untrusted Platforms: a Survey

With the ever-growing data and the need for developing powerful machine learning models, data owners increasingly depend on various untrusted platforms (e.g., public clouds, edges, and machine learning service providers) for scalable processing or collaborative learning. Thus, sensitive data and models are in danger of unauthorized access, misuse, and privacy compromises. A relatively new body of research confidentially trains machine learning models on protected data to address these concerns. In this survey, we summarize notable studies in this emerging area of research. With a unified framework, we highlight the critical challenges and innovations in outsourcing machine learning confidentially. We focus on the cryptographic approaches for confidential machine learning (CML), primarily on model training, while also covering other directions such as perturbation-based approaches and CML in the hardware-assisted computing environment. The discussion will take a holistic way to consider a rich context of the related threat models, security assumptions, design principles, and associated trade-offs amongst data utility, cost, and confidentiality