Integerwise Functional Bootstrapping on TFHE

Abstract

We propose a new technique for implementing an arbitrary 1-variable function during a bootstrapping procedure based on an integerwise variant of the fully homomorphic encryption scheme TFHE. The integerwise TFHE was implicit in the original TFHE paper (Asiacrypt’ 2016), and Bourse et al. provided an explicit form (CRYPTO’ 2018). However, the modified integerwise TFHE scheme can perform only the homomorphic evaluations of the integer addition and the sign function, and thus, the application of the scheme is restricted. Our scheme has diverse functionalities of the integerwise TFHE scheme. Based on our bootstrapping procedure, we propose several useful basic functions: homomorphic equality testing, multiplication by a binary number and a division algorithm. We also derive empirical results that show that our division algorithm is approximately 3.4 x faster than the fastest division algorithm in the literature based on fully homomorphic encryption schemes, with a runtime less than 1 s for each 4-bit integer division task.