Paper 2022/1267
High-precision Leveled Homomorphic Encryption with Batching
Long Nie, National Pilot School of software, Yunnan University
ShaoWen Yao, National Pilot School of software, Yunnan University
Jing Liu, National Pilot School of software, Yunnan University
Abstract
In most homomorphic encryption schemes based on the RLWE, the native plaintexts are represented as polynomials in a ring where is a plaintext modulus and is a cyclotomic polynomial with 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 a homomorphic computation on the polynomial is finished, the decoding procedure is invoked to obtain the result. However, conditions for decoding correctly are strict in a way. For example, the overflows of computation modulo both the plaintext modulus and the cyclotomic polynomial will result in a unexpected result for decoding. The reason is that decoding the part which is discarded by modular reduction is not 0.
We combine number theory transformation with Hensel Codes to construct a scheme. Intuitively, decoding the discarded part will yield 0 so the limitations are overcome naturally in our scheme. On the other hand, rational numbers can be handled with high precision in parallel.