Ring Packing and Amortized FHEW Bootstrapping

The FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) offers very fast homomorphic NAND-gate computations (on encrypted data) and a relatively fast refreshing procedure that allows to homomorphically evaluate arbitrary NAND boolean circuits. Unfortunately, the refreshing procedure needs to be executed after every single NAND computation, and each refreshing operates on a single encrypted bit, greatly decreasing the overall throughput of the scheme. We give a new refreshing procedure that simultaneously refreshes n FHEW ciphertexts, at a cost comparable to a single-bit FHEW refreshing operation. As a result, the cost of each refreshing is amortized over n encrypted bits, improving the throughput for the homomorphic evaluation of boolean circuits roughly by a factor n

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

Encrypted Dynamic Control exploiting Limited Number of Multiplications and a Method using Ring-LWE based Cryptosystem

In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output of the given controller as a linear combination of a fixed number of previous inputs and outputs. As a result, the encrypted controller involves only a limited number of homomorphic multiplications on every encrypted data, assuming that the output is re-encrypted and transmitted back from the actuator. A guidance for parameter choice is also provided, ensuring that the encrypted controller achieves predefined performance for an infinite time horizon. Furthermore, we propose a customization of the method for Ring-Learning With Errors (Ring-LWE) based cryptosystems, where a vector of messages can be encrypted into a single ciphertext and operated simultaneously, thus reducing computation and communication loads. Unlike previous results, the proposed customization does not require extra algorithms such as rotation, other than basic addition and multiplication. Simulation results demonstrate the effectiveness of the proposed method.Comment: 11 pages, 4 figures, submitted to IEEE Transactions on Systems, Man, and Cybernetics: System

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

Homomorphic Evaluation of Lattice-Based Symmetric Encryption Schemes

Optimizing performance of Fully Homomorphic Encryption (FHE) is nowadays an active trend of research in cryptography. One way of improvement is to use a hybrid construction with a classical symmetric encryption scheme to transfer encrypted data to the Cloud. This allows to reduce the bandwidth since the expansion factor of symmetric schemes (the ratio between the ciphertext and the plaintext length) is close to one, whereas for FHE schemes it is in the order of 1,000 to 1,000,000. However, such a construction requires the decryption circuit of the symmetric scheme to be easy to evaluate homomorphically. Several works have studied the cost of homomorphically evaluating classical block ciphers, and some recent works have suggested new homomorphic oriented constructions of block ciphers or stream ciphers. Since the multiplication gate of FHE schemes significantly increases the noise of the ciphertext, we cannot afford too many multiplication stages in the decryption circuit. Consequently, FHE-friendly symmetric encryption schemes have a decryption circuit with small multiplication depth. We aim at minimizing the cost of the homomorphic evaluation of the decryption of symmetric encryption schemes. To do so, we focus on schemes based on learning problems: Learning With Errors (LWE), Learning Parity with Noise (LPN) and Learning With Rounding (LWR). We show that they have lower multiplicative depth than usual block ciphers, and hence allow more FHE operations before a heavy bootstrapping becomes necessary. Moreover, some of them come with a security proof. Finally, we implement our schemes in HElib. Experimental evidence shows that they achieve lower amortized and total running time than previous performance from the literature: our schemes are from 10 to 10,000 more efficient for the time per bit and the total running time is also reduced by a factor between 20 to 10,000. Of independent interest, the security of our LWR-based scheme is related to LWE and we provide an efficient security proof that allows to take smaller parameters