Efficiently Processing Complex-Valued Data in Homomorphic Encryption

Abstract

We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan-Vercauteren scheme by replacing the integral plaintext modulus t by a linear polynomial X - b. Our generalization studies plaintext moduli of the form Xm + b. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed.