Integer-Wise Functional Bootstrapping on TFHE: Applications in Secure Integer Arithmetics

TFHE is a fast fully homomorphic encryption scheme proposed by Chillotti et al. in Asiacrypt’ 2018. Integer-wise TFHE is a generalized version of TFHE that can encrypt the plaintext of an integer that was implicitly presented by Chillotti et al., and Bourse et al. presented the actual form of the scheme in CRYPTO’ 2018. However, Bourse et al.’s scheme provides only homomorphic integer additions and homomorphic evaluations of a sign function. In this paper, we construct a technique for operating any 1-variable function in only one bootstrapping of the integer-wise TFHE. For applications of the scheme, we also construct a useful homomorphic evaluation of several integer arithmetics: division, equality test, and multiplication between integer and binary numbers. Our implementation results show that our homomorphic division is approximately 3.4 times faster than any existing work and that its run time is less than 1 second for 4-bit integer inputs.