Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.Comment: Improved numerical exampl

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

Toward Lossless Homomorphic Encryption for Scientific Computation

This paper presents a comprehensive investigation into encrypted computations using the CKKS (Cheon-Kim-Kim-Song) scheme, with a focus on multi-dimensional vector operations and real-world applications. Through two meticulously designed experiments, the study explores the potential of the CKKS scheme in Super Computing and its implications for data privacy and computational efficiency. The first experiment reveals the promising applicability of CKKS to matrix multiplication, indicating marginal differences in Euclidean distance and near-to-zero mean square error across various matrix sizes. The second experiment, applied to a wildfire dataset, illustrates the feasibility of using encrypted machine learning models without significant loss in accuracy. The insights gleaned from the research set a robust foundation for future innovations, including the potential for GPU acceleration in CKKS computations within TenSEAL. Challenges such as noise budget computation, accuracy loss in multiplication, and the distinct characteristics of arithmetic operations in the context of CKKS are also discussed. The paper serves as a vital step towards understanding the complexities and potentials of encrypted computations, with broad implications for secure data processing and privacy preservation in various scientific domains

Exploring the Application of Homomorphic Encryption to a Cross Domain Solution

A Cross Domain Solution (CDS) is a means of secure information exchange that provides the ability to access or transfer digital data between varying security domains. Most existing CDS methods focus on risk management policies that rely on using protected or trusted parties to process the information in order to solve this problem. A CDS that is able to function in the presence of untrusted parties is a challenge. We apply the concepts of homomorphic encryption (HE) to explore a new solution to the CDS problem. We built a practical software case study application using the Yet Another Somewhat Homomorphic Encryption Scheme (YASHE) around the specific challenge of evaluating the gateway bypass condition on encrypted data. We assess the feasibility of such an application through performance and memory profiling in order to find a parameter selection that ensures proper homomorphic evaluation. The correctness of the application was assured for 64-, 72-, 96-, and 128-bit security parameter selections of YASHE resulting in high latency performance. The computing time required by our proof-of-concept implementation may be high but this approach allows the manual process employed in current systems to be eliminated

On the relationship between functional encryption, obfuscation, and fully homomorphic encryption

We investigate the relationship between Functional Encryption (FE) and Fully Homomorphic Encryption (FHE), demonstrating that, under certain assumptions, a Functional Encryption scheme supporting evaluation on two ciphertexts implies Fully Homomorphic Encryption. We first introduce the notion of Randomized Functional Encryption (RFE), a generalization of Functional Encryption dealing with randomized functionalities of interest in its own right, and show how to construct an RFE from a (standard) semantically secure FE. For this we define the notion of entropically secure FE and use it as an intermediary step in the construction. Finally we show that RFEs constructed in this way can be used to construct FHE schemes thereby establishing a relation between the FHE and FE primitives. We conclude the paper by recasting the construction of RFE schemes in the context of obfuscation.NSF -National Science Foundatio

Homomorphic Proximity Computation in Geosocial Networks

With the growing popularity of mobile devices that have sophisticated localization capability, it becomes more convenient and tempting to give away location data in exchange for recognition and status in the social networks. Geosocial networks, as an example, offer the ability to notify a user or trigger a service when a friend is within geographical proximity. In this paper, we present two methods to support secure distance computation on encrypted location data; that is, computing distance functions without knowing the actual coordinates of users. The underlying security is ensured by the homomorphic encryption scheme which supports computation on encrypted data. We demonstrate feasibility of the proposed approaches by conducting various performance evaluations on platforms with different specifications. We argue that the novelty of this work enables a new breed of pervasive and mobile computing concepts, which was previously not possible due to the lack of feasible mechanisms that support computation on encrypted location data