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

Distributed and Deep Vertical Federated Learning with Big Data

In recent years, data are typically distributed in multiple organizations while the data security is becoming increasingly important. Federated Learning (FL), which enables multiple parties to collaboratively train a model without exchanging the raw data, has attracted more and more attention. Based on the distribution of data, FL can be realized in three scenarios, i.e., horizontal, vertical, and hybrid. In this paper, we propose to combine distributed machine learning techniques with Vertical FL and propose a Distributed Vertical Federated Learning (DVFL) approach. The DVFL approach exploits a fully distributed architecture within each party in order to accelerate the training process. In addition, we exploit Homomorphic Encryption (HE) to protect the data against honest-but-curious participants. We conduct extensive experimentation in a large-scale cluster environment and a cloud environment in order to show the efficiency and scalability of our proposed approach. The experiments demonstrate the good scalability of our approach and the significant efficiency advantage (up to 6.8 times with a single server and 15.1 times with multiple servers in terms of the training time) compared with baseline frameworks.Comment: To appear in CCPE (Concurrency and Computation: Practice and Experience

High-Precision Arithmetic in Homomorphic Encryption

In most RLWE-based homomorphic encryption schemes the native plaintext elements are polynomials in a ring $\mathbb{Z}_t[x]/(x^n+1)$, where $n$ is a power of $2$, and $t$ an integer modulus. For performing integer or rational number arithmetic one typically uses an encoding scheme, which converts the inputs to polynomials, and allows the result of the homomorphic computation to be decoded to recover the result as an integer or rational number respectively. The problem is that the modulus $t$ often needs to be extremely large to prevent the plaintext polynomial coefficients from being reduced modulo~$t$ during the computation, which is a requirement for the decoding operation to work correctly. This results in larger noise growth, and prevents the evaluation of deep circuits, unless the encryption parameters are significantly increased. We combine a trick of Hoffstein and Silverman, where the modulus $t$ is replaced by a polynomial $x-b$, with the Fan-Vercauteren homomorphic encryption scheme. This yields a new scheme with a very convenient plaintext space $\mathbb{Z}/(b^n+1)\mathbb{Z}$. We then show how rational numbers can be encoded as elements of this plaintext space, enabling homomorphic evaluation of deep circuits with high-precision rational number inputs. We perform a fair and detailed comparison to the Fan-Vercauteren scheme with the Non-Adjacent Form encoder, and find that the new scheme significantly outperforms this approach. For example, when the new scheme allows us to evaluate circuits of depth $9$ with $32$-bit integer inputs, in the same parameter setting the Fan-Vercauteren scheme only allows us to go up to depth $2$. We conclude by discussing how known applications can benefit from the new scheme

Privacy-preserving biometric matching using homomorphic encryption

Biometric matching involves storing and processing sensitive user information. Maintaining the privacy of this data is thus a major challenge, and homomorphic encryption offers a possible solution. We propose a privacy-preserving biometrics-based authentication protocol based on fully homomorphic encryption, where the biometric sample for a user is gathered by a local device but matched against a biometric template by a remote server operating solely on encrypted data. The design ensures that 1) the user's sensitive biometric data remains private, and 2) the user and client device are securely authenticated to the server. A proof-of-concept implementation building on the TFHE library is also presented, which includes the underlying basic operations needed to execute the biometric matching. Performance results from the implementation show how complex it is to make FHE practical in this context, but it appears that, with implementation optimisations and improvements, the protocol could be used for real-world applications

Privacy-preserving data sharing infrastructures for medical research: systematization and comparison

Background: Data sharing is considered a crucial part of modern medical research. Unfortunately, despite its advantages, it often faces obstacles, especially data privacy challenges. As a result, various approaches and infrastructures have been developed that aim to ensure that patients and research participants remain anonymous when data is shared. However, privacy protection typically comes at a cost, e.g. restrictions regarding the types of analyses that can be performed on shared data. What is lacking is a systematization making the trade-offs taken by different approaches transparent. The aim of the work described in this paper was to develop a systematization for the degree of privacy protection provided and the trade-offs taken by different data sharing methods. Based on this contribution, we categorized popular data sharing approaches and identified research gaps by analyzing combinations of promising properties and features that are not yet supported by existing approaches. Methods: The systematization consists of different axes. Three axes relate to privacy protection aspects and were adopted from the popular Five Safes Framework: (1) safe data, addressing privacy at the input level, (2) safe settings, addressing privacy during shared processing, and (3) safe outputs, addressing privacy protection of analysis results. Three additional axes address the usefulness of approaches: (4) support for de-duplication, to enable the reconciliation of data belonging to the same individuals, (5) flexibility, to be able to adapt to different data analysis requirements, and (6) scalability, to maintain performance with increasing complexity of shared data or common analysis processes. Results: Using the systematization, we identified three different categories of approaches: distributed data analyses, which exchange anonymous aggregated data, secure multi-party computation protocols, which exchange encrypted data, and data enclaves, which store pooled individual-level data in secure environments for access for analysis purposes. We identified important research gaps, including a lack of approaches enabling the de-duplication of horizontally distributed data or providing a high degree of flexibility. Conclusions: There are fundamental differences between different data sharing approaches and several gaps in their functionality that may be interesting to investigate in future work. Our systematization can make the properties of privacy-preserving data sharing infrastructures more transparent and support decision makers and regulatory authorities with a better understanding of the trade-offs taken

A HYBRIDIZED ENCRYPTION SCHEME BASED ON ELLIPTIC CURVE CRYPTOGRAPHY FOR SECURING DATA IN SMART HEALTHCARE

Recent developments in smart healthcare have brought us a great deal of convenience. Connecting common objects to the Internet is made possible by the Internet of Things (IoT). These connected gadgets have sensors and actuators for data collection and transfer. However, if users' private health information is compromised or exposed, it will seriously harm their privacy and may endanger their lives. In order to encrypt data and establish perfectly alright access control for such sensitive information, attribute-based encryption (ABE) has typically been used. Traditional ABE, however, has a high processing overhead. As a result, an effective security system algorithm based on ABE and Fully Homomorphic Encryption (FHE) is developed to protect health-related data. ABE is a workable option for one-to-many communication and perfectly alright access management of encrypting data in a cloud environment. Without needing to decode the encrypted data, cloud servers can use the FHE algorithm to take valid actions on it. Because of its potential to provide excellent security with a tiny key size, elliptic curve cryptography (ECC) algorithm is also used. As a result, when compared to related existing methods in the literature, the suggested hybridized algorithm (ABE-FHE-ECC) has reduced computation and storage overheads. A comprehensive safety evidence clearly shows that the suggested method is protected by the Decisional Bilinear Diffie-Hellman postulate. The experimental results demonstrate that this system is more effective for devices with limited resources than the conventional ABE when the system’s performance is assessed by utilizing standard model

Public Health Surveillance using Decentralized Technologies

This article describes how blockchain technologies can be used in the context of Public Health Surveillance through decentralized sharing of genomic data. A brief analysis of why blockchain technologies are needed in public health is presented together with a distinction between public and private blockchains. Finally, a proposal for a network of blockchains, using the Cosmos framework, together with decentralized storage systems like IPFS and BigchainDB, is included to address the issues of interoperability in the health sector.&#x0D; Keywords: Blockchain, Cosmos Framework, Decentralized Technology, PublicHealth Surveillance</jats:p