基于A-GCDP困难性的矩阵同态加密方案  

Matrix Homomorphic Encryption Scheme Based on Hardness of Approximate Greatest Integer Common Divisors Problems

作　　者：朱艳琴[1] 靳方元[1] 张娟[1] 罗喜召[1] 

机构地区：[1]苏州大学计算机科学与技术学院,苏州215006

出　　处：《系统仿真学报》2013年第4期699-703,708,共6页Journal of System Simulation

基　　金：国家自然科学基金(61070170);江苏省高校自然科学研究项目(11KJB520017);苏州市应用基础研究计划项目(SYG201238)

摘　　要：安全有效的矩阵同态加密方案在云计算环境中有着重要的应用。已有的矩阵同态加密方案密钥生成过程繁琐且加解密机制不够灵活,使得其应用范围受到很大限制。针对这些问题,在A-GCDP困难性假设的基础上,构造了一个新的矩阵同态加密方案,并通过将方案的安全性归约为求A-GCDP问题,来证明方案是安全的。与同类方案相比,新方案的密钥生成过程简单,密钥长度短,加解密速度快且加密机制较为灵活,不仅满足矩阵同态,还满足矩阵内部元素运算的同态,同时一对密钥可以对任意维数的矩阵进行加密。仿真实验进一步验证了新方案具有较好的加解密性能,是一个实用的矩阵同态加密方案。An efficient and secure matrix homomorphic encryption scheme has a number of important applications. The existed matrix homomophic encryption schemes have defects such as complex keygeneration process, unflexible encryption mechanism. To solve these problems, based on the hardness of A-GCDP problems, a new matrix homomorphic encryption scheme was proposed. Its security was proved by reducing it to solve A-GCDP problems. Compared with the existing matrix homomorphic encryption scheme, the new scheme enjoys easy key generation process, shorter keys, simple encryption/decryption process and more flexible encryption mechanism. The computation among inner elements satisfies homomorphism, and a pair of keys can be applied in any dimension of matrix. Experiment results show that the new scheme has good performance in encryption and decryption. It＇s a practical matrix homomorphic encryption scheme.

关 键 词：同态加密 矩阵同态加密 近似最大整数公因子 CPA安全 

分 类 号：TP309.2[自动化与计算机技术—计算机系统结构]