基于商密SM9算法同态加密方案  

Homomorphic Encryption Scheme Based on Commercial Cryptography SM9

作　　者：秦体红 汪宗斌 刘洋 马姚 刘金华 Qin Tihong;Wang Zongbin;Liu Yang;Ma Yao;Liu Jinhua(Beijing Infosec Technologies Co.,Ltd.,Beijing 100096)

机构地区：[1]北京信安世纪科技股份有限公司,北京100096

出　　处：《信息安全研究》2024年第6期513-518,共6页Journal of Information Security Research

摘　　要：同态加密(homomorphic encryption,HE)被认为是隐私保护应用中最重要的密码技术之一.SM9算法是我国发布的商用密码算法标准,但SM9算法并不满足同态的属性.以SM9的算法为基础,设计一种基于PKI体制且具有同态性质的加密方案,使得新设计的算法同时具备加法和乘法同态性质,即满足任意次密文加法运算和1次密文乘法运算,且密文经过乘法运算后仍然满足加法同态性质以及标量乘,适合2次多项式的隐私计算.该方案具备选择明文攻击(IND-CPA)安全性.Homomorphic encryption(HE)is considered to be one of the most important cryptographic techniques in privacy protection applications.The SM9 algorithm is a commercial cryptographic algorithm standard published in China,but it does not has the homomorphic property.In this paper,based on the algorithm of SM9,we designs a cryptographic scheme with homomorphic properties based on PKI system.The newly designed algorithm simultaneously possesses the homomorphic properties of addition and multiplication.It satisfy the addition homomorphic property of arbitrary ciphertext and a ciphertext multiplication operation,Additionally,the ciphertext still satisfies the addition homomorphic property and scalar multiplication after multiplication operations.This scheme is suitable for privacy calculation:such asquadratic polynomials and provides selective plaintext attack(IND-CPA)security.

关 键 词：同态加密 椭圆曲线 双线性对 SM9 隐私计算 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]