Paper 2018/622

New techniques for multi-value homomorphic evaluation and applications

Sergiu Carpov and Malika Izabachène and Victor Mollimard

Abstract

In this paper, we propose a new technique to perform several homomorphic operations in one bootstrapping call over a multi-value plaintext space. Our construction relies on the FHEW-based gate bootstrapping: we analyze its structure and propose a strategy we call multi-value bootstrapping which allows to bootstrap an arbitrary function in an efficient way. The security of our scheme relies on the LWE assumption over the torus. We give three applications: the first one is the efficient evaluation of an arbitrary boolean function (LUT), the second one is the optimization of the circuit bootstrapping from (Asiacrypt'2017) which allows to compose circuits in a leveled mode, the third one is the homomorphic evaluation of a neural network where the linear part is evaluated using a generalization of the key-switching procedure and the non-linear part is evaluated with our multi-value bootstrapping. We have implemented the proposed method and were able to evaluate arbitrary 6-to-6 LUTs under 1.2 seconds. Our implementation is based on the TFHE library but can be easily integrated into other homomorphic libraries based on the same structure, such as FHEW (Eurocrypt'2015). The number of LUT outputs does not influence the execution time by a lot, e.g. evaluation of additional 128 outputs on the same 6 input bits takes only 0.05 more seconds.