Abstract
AbstractThis 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.
Highlights
Homomorphic encryption enables computations on encrypted data without decrypting it
This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based fully homomorphic encryption (FHE) schemes: TFHE, B/FV and HEAAN
Several constructions based on the Ring-LWE problem [26] are today among the most promising FHE candidates, each of them having particular advantages that depend on the type of the target homomorphic operations and arithmetic
Summary
Homomorphic encryption enables computations on encrypted data without decrypting it. Shortly after the development of the first fully homomorphic encryption (FHE) scheme by Gentry [23], extensive research has been carried out on the design, implementation and cryptanalysis of various other FHE schemes. 2) B/FV [6, 13, 21] allowing to perform large vectorial arithmetic operations as long as the multiplicative depth of the evaluated circuit remains small; 3) HEAAN [15, 16] - a mixed encryption scheme shown to be very efficient for floating-point computations We achieve such a hybrid solution by first mapping the different plaintext spaces of the different schemes to a common algebraic structure using certain natural algebraic homomorphisms. Various financial systems need to perform small computations on an encrypted database with a potentially very large multiplicative depth over a long period of time and at the end of the period provide statistics on the current dataset In this case, it is essential to operate in bootstrapped mode as in TFHE and perform the low-depth statistical calculations in B/FV or HEAAN. It permits to express the relinearization in the internal products of HEAAN and B/FV in terms of the FHE module structure for TFHE and this without loss as it is the same algorithm
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