Efficient Software Implementation of Homomorphic Encryption for Addition and Multiplication Operations.

Fully homomorphic encryption enables any type of calculation on encrypted data. There are several crypto libraries that provide such fully homomorphic encryption. However, since most libraries only support single level binary circuit operations, it is required for developers to efficiently implement basic arithmetic algorithms such as addition, subtraction, multiplication, and division for their own applications. In this paper, we propose fast binary addition and multiplication algorithms to support various bit-wise operations. To show the feasibility of the proposed algorithms, we implemented the proposed algorithms for 16, 32, 48, and 64 bits integers using the TFHE library. Our experiment results demonstrate that the proposed addition operation decreases the running time by 11 to 12%, and our multiplication implementation is about 3 to 4 times faster than the non-threaded method for 16, 32, 48 and 64 bits integers.