密码学报（中英文）2026，Vol.13Issue(2)：325-337,13.DOI:10.13868/j.cnki.jcr.000853
一种小数精确加法同态方案的研究
Precise Homomorphic Addition Scheme for Decimal Numbers
摘要
Abstract
In previous work,Cheon et al.proposed a method for constructing approximate arithmetic homomorphic encryption schemes(CKKS).Nevertheless,the approximate nature of these computa-tions sometimes fails to meet the requirements for precise calculations.In response to this limitation,this paper presents a rational number encoding method in the complex plane,combined with complex canonical embedding techniques,to construct a fractional exact addition homomorphic scheme based on RLWE.The scheme can perform precise encryption,decryption,and homomorphic operations with predetermined accuracy.Both theoretical analysis and experimental validation demonstrate that the proposed scheme can correctly perform encryption,decryption,and homomorphic addition while en-suring semantic security.With appropriately chosen parameters,the proposed scheme achieves smaller polynomial norms compared to CKKS,allowing for higher precision inputs and supporting more rounds of homomorphic additions.Finally,experiments show that the proposed scheme incurs no efficiency loss compared to the CKKS scheme under the same precision requirements.关键词
同态加密/明文编码/小数同态运算Key words
homomorphic encryption/plaintext encoding/decimal homomorphic operations分类
信息技术与安全科学引用本文复制引用
马培超,梁碧滢,张娟,赵德,张克君,李子臣..一种小数精确加法同态方案的研究[J].密码学报（中英文）,2026,13(2):325-337,13.基金项目
国家自然科学基金(62472040)National Natural Science Foundation of China(62472040) （62472040）
