This work describes a fast fully homomorphic encryption scheme over the torus (TFHE), that revisits, generalizes and improves the fully homomorphic encryption (FHE) based on GSW and its ring variants. The simplest FHE schemes consist in bootstrapped binary gates. In this gate bootstrapping mode, we show that the scheme FHEW of [29] can be expressed only in terms of external product between a GSW and a LWE ciphertext. As a consequence of this result and of other optimizations, we decrease the running time of their bootstrapping from 690ms to 13ms single core, using 16MB bootstrapping key instead of 1GB, and preserving the security parameter. In leveled homomorphic mode, we propose two methods to manipulate packed data, in order to decrease the ciphertext expansion and to optimize the evaluation of look-up tables and arbitrary functions in RingGSW based homomorphic schemes. We also extend the automata logic, introduced in [31], to the efficient leveled evaluation of weighted automata, and present a new homomorphic counter called TBSR, that supports all the elementary operations that occur in a multiplication. These improvements speed-up the evaluation of most arithmetic functions in a packed leveled mode, with a noise overhead that remains additive. We finally present a new circuit bootstrapping that converts LWE ciphertexts into low-noise RingGSW ciphertexts in just 137ms, which makes the leveled mode of TFHE composable, and which is fast enough to speed-up arithmetic functions, compared to the gate bootstrapping approach. Finally, we provide an alternative practical analysis of LWE based schemes, which directly relates the security parameter to the error rate This work was done while I. Chillotti was a PhD student in the Laboratoire de Mathématiques de Versailles, UVSQ (Versailles, France) and while M. Georgieva worked in Gemalto (Meudon, France). of LWE and the entropy of the LWE secret key, and we propose concrete parameter sets and timing comparison for all our constructions.

No abstract

No abstract

This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN. This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by applying efficient switching algorithms. This approach has many practical applications. First and foremost, it becomes an integral tool for the recent standardization initiatives of homomorphic schemes and common APIs. Then, it can be used in many real-life scenarios where operations of different nature and not achievable within a single FHE scheme have to be performed and where it is important to efficiently switch from one scheme to another. Finally, as a byproduct of our analysis we introduce the notion of a FHE module structure, that generalizes the notion of the external product, but can certainly be of independent interest in future research in FHE.