High-Precision Leveled Homomorphic Encryption for Rational Numbers

Abstract

In most homomorphic encryption schemes based on RLWE, native plaintexts are represented as polynomials in a ring (Formula presented.), where t is a plaintext modulus and (Formula presented.) is a cyclotomic polynomial with a degree power of two. An encoding scheme should be used to transform some natural data types (such as integers and rational numbers) into polynomials in the ring. After homomorphic computations on the polynomial aare finished, the decoding procedure is invoked to obtain the results. We employ the Hensel code for encoding rational numbers and construct a high-precision leveled homomorphic encryption scheme with double-CRT. The advantage of our scheme is that the limitations of previous works are avoided, such as unexpected decoding results and loss of precision. Moreover, the plaintext space can be adjusted simply by changing a hyper-parameter to adapt to different computation tasks.