Circuit-Private Multi-Key FHE

Multi-key fully homomorphic encryption (MFHE) schemes allow polynomially many users without trusted setup assumptions to send their data (encrypted under different FHE keys chosen by users independently of each other) to an honest-but-curious server that can compute the output of an arbitrary polynomial-time computable function on this joint data and issue it back to all participating users for decryption. One of the main open problems left in MFHE was dealing with malicious users without trusted setup assumptions. We show how this can be done, generalizing previous results of circuit-private FHE. Just like standard circuit-private FHE, our security model shows that even if both ciphertexts and public keys of individual users are not well-formed, no information is revealed regarding the server computation--- other than that gained from the output on some well-formed inputs of all users. MFHE schemes have direct applications to server-assisted multiparty computation (MPC), called on-the-fly MPC, introduced by López-Alt et al. (STOC \u2712), where the number of users is not known in advance. In this setting, a poly-time server wants to evaluate a circuit $C$ on data uploaded by multiple clients and encrypted under different keys. Circuit privacy requires that users\u27 work is independent of $|C|$ held by the server, while each client learns nothing about $C$ other than its output. We present a framework for transforming MFHE schemes with no circuit privacy into maliciously circuit-private schemes. We then construct 3-round on-the-fly MPC with circuit privacy against malicious clients in the plain model

Multi-key Fully-Homomorphic Encryption in the Plain Model

The notion of multi-key fully homomorphic encryption (multi-key FHE) [Löpez-Alt, Tromer, Vaikuntanathan, STOC\u2712] was proposed as a generalization of fully homomorphic encryption to the multiparty setting. In a multi-key FHE scheme for $n$ parties, each party can individually choose a key pair and use it to encrypt its own private input. Given $n$ ciphertexts computed in this manner, the parties can homomorphically evaluate a circuit $C$ over them to obtain a new ciphertext containing the output of $C$, which can then be decrypted via a decryption protocol. The key efficiency property is that the size of the (evaluated) ciphertext is independent of the size of the circuit. Multi-key FHE with one-round decryption [Mukherjee and Wichs, Eurocrypt\u2716], has found several powerful applications in cryptography over the past few years. However, an important drawback of all such known schemes is that they require a trusted setup. In this work, we address the problem of constructing multi-key FHE in the plain model. We obtain the following results: - A multi-key FHE scheme with one-round decryption based on the hardness of learning with errors (LWE), ring LWE, and decisional small polynomial ratio (DSPR) problems. - A variant of multi-key FHE where we relax the decryption algorithm to be non-compact -- i.e., where the decryption complexity can depend on the size of $C$ -- based on the hardness of LWE. We call this variant multi-homomorphic encryption (MHE). We observe that MHE is already sufficient for some applications of multi-key FHE

Multiparty Homomorphic Encryption (or: On Removing Setup in Multi-Key FHE)

The notion of threshold multi-key fully homomorphic encryption (TMK-FHE) [Lopez-Alt, Tromer, Vaikuntanathan, STOC\u2712] was proposed as a generalization of fully homomorphic encryption to the multiparty setting. In a TMK-FHE scheme for $n$ parties, each party can individually choose a key pair and use it to encrypt its own private input. Given $n$ ciphertexts computed in this manner, the parties can homomorphically evaluate a circuit $C$ over them to obtain a new ciphertext containing the output of $C$, which can then be decrypted via a threshold decryption protocol. The key efficiency property is that the size of the (evaluated) ciphertext is independent of the size of the circuit. TMK-FHE with one-round threshold decryption, first constructed by Mukherjee and Wichs [Eurocrypt\u2716], has found several powerful applications in cryptography over the past few years. However, an important drawback of all such TMK-FHE schemes is that they require a common setup which results in applications in the common random string model. To address this concern, we propose a notion of multiparty homomorphic encryption (MHE) that retains the communication efficiency property of TMK-FHE, but sacrifices on the efficiency of final decryption. Specifically, MHE is defined in a similar manner as TMK-FHE, except that the final output computation process performed locally by each party is ``non-compact\u27\u27 in that we allow its computational complexity to depend on the size of the circuit. We observe that this relaxation does not have a significant bearing in many important applications of TMK-FHE. Our main contribution is a construction of MHE from the learning with errors assumption in the plain model. Our scheme can be used to remove the setup in many applications of TMK-FHE. For example, it yields the first construction of low-communication reusable non-interactive MPC in the plain model. To obtain our result, we devise a recursive self-synthesis procedure to transform any ``delayed-function\u27\u27 two-round MPC protocol into an MHE scheme

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

Towards the AlexNet Moment for Homomorphic Encryption: HCNN, theFirst Homomorphic CNN on Encrypted Data with GPUs

Deep Learning as a Service (DLaaS) stands as a promising solution for cloud-based inference applications. In this setting, the cloud has a pre-learned model whereas the user has samples on which she wants to run the model. The biggest concern with DLaaS is user privacy if the input samples are sensitive data. We provide here an efficient privacy-preserving system by employing high-end technologies such as Fully Homomorphic Encryption (FHE), Convolutional Neural Networks (CNNs) and Graphics Processing Units (GPUs). FHE, with its widely-known feature of computing on encrypted data, empowers a wide range of privacy-concerned applications. This comes at high cost as it requires enormous computing power. In this paper, we show how to accelerate the performance of running CNNs on encrypted data with GPUs. We evaluated two CNNs to classify homomorphically the MNIST and CIFAR-10 datasets. Our solution achieved a sufficient security level (> 80 bit) and reasonable classification accuracy (99%) and (77.55%) for MNIST and CIFAR-10, respectively. In terms of latency, we could classify an image in 5.16 seconds and 304.43 seconds for MNIST and CIFAR-10, respectively. Our system can also classify a batch of images (> 8,000) without extra overhead

A comprehensive meta-analysis of cryptographic security mechanisms for cloud computing

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The concept of cloud computing offers measurable computational or information resources as a service over the Internet. The major motivation behind the cloud setup is economic benefits, because it assures the reduction in expenditure for operational and infrastructural purposes. To transform it into a reality there are some impediments and hurdles which are required to be tackled, most profound of which are security, privacy and reliability issues. As the user data is revealed to the cloud, it departs the protection-sphere of the data owner. However, this brings partly new security and privacy concerns. This work focuses on these issues related to various cloud services and deployment models by spotlighting their major challenges. While the classical cryptography is an ancient discipline, modern cryptography, which has been mostly developed in the last few decades, is the subject of study which needs to be implemented so as to ensure strong security and privacy mechanisms in today’s real-world scenarios. The technological solutions, short and long term research goals of the cloud security will be described and addressed using various classical cryptographic mechanisms as well as modern ones. This work explores the new directions in cloud computing security, while highlighting the correct selection of these fundamental technologies from cryptographic point of view

SHE based Non Interactive Privacy Preserving Biometric Authentication Protocols

Being unique and immutable for each person, biometric signals are widely used in access control systems. While biometric recognition appeases concerns about password's theft or loss, at the same time it raises concerns about individual privacy. Central servers store several enrolled biometrics, hence security against theft must be provided during biometric transmission and against those who have access to the database. If a server's database is compromised, other systems using the same biometric templates could also be compromised as well. One solution is to encrypt the stored templates. Nonetheless, when using traditional cryptosystem, data must be decrypted before executing the protocol, leaving the database vulnerable. To overcame this problem and protect both the server and the client, biometrics should be processed while encrypted. This is possible by using secure two-party computation protocols, mainly based on Garbled Circuits (GC) and additive Homomorphic Encryption (HE). Both GC and HE based solutions are efficient yet interactive, meaning that the client takes part in the computation. Instead in this paper we propose a non-interactive protocol for privacy preserving biometric authentication based on a Somewhat Homomorphic Encryption (SHE) scheme, modified to handle integer values, and also suggest a blinding method to protect the system from spoofing attacks. Although our solution is not as efficient as the ones based on GC or HE, the protocol needs no interaction, moving the computation entirely on the server side and leaving only inputs encryption and outputs decryption to the client