An Efficient Integer-Wise ReLU on TFHE

Yi Huang, Junping Wan, Zoe L. Jiang, Jun Zhou, Junbin Fang, Zhenfu Cao

Abstract: Fully homomorphic encryption (FHE) enables users to process encrypted data, while preserving data privacy throughout the data computation process. It develops ways to privately execute neural networks. Although bit-wise FHE over the torus (TFHE) was originally proposed to support non-linear functions, such as ReLU operation which is often used in neural networks, the computational complexity of the homomorphic ReLU operation is linearly to data precision. Integer-wise TFHE enables integer bootstrapping with homomorphic addition. However, it leaves an open problem to support homomorphic multiplication and ReLU due to negacyclicity limitation. In this paper, we first propose the ExMultbyBin(x) algorithm for integer-wise multiplication by extending the data range from \(\{0,\cdots ,B/2-1\}\) to \(\{-B,\cdots ,B-1\}\). Then, we propose the idea of function transformation by equivalently transform the ReLU(x) function to a new function \(ExMultbyBin(x, f_{id}(x), sign(x)-B/2)\). Finally, we achieve a privacy-preserving ReLU function IntReLU with integer-wise TFHE, resulting in computational complexity independent of data precision. That is, when the data precision is n-bit, IntReLU has a computational complexity of \(\mathcal {O}(1)\). Experimental results in the TFHE library indicate that, the operation time of our intReLU is reduced by \(17\%\) when the data precision is 6-bit compared to the bit-wise TFHE scheme.