具有循环安全性的同态加密方案的设计  

Application of a Circular Secure Variant of LWE in the Homomorphic Encryption

作　　者：杨晓元[1,2] 周潭平 张薇[1,2] 吴立强[1,2] 

机构地区：[1]武警工程大学网络与信息安全武警部队重点实验室,西安710086 [2]武警工程大学电子技术系,西安710086

出　　处：《计算机研究与发展》2015年第6期1389-1393,共5页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(61272492;61103230;61103231;61202492)

摘　　要：同态加密在云计算等领域具有重要的应用价值,针对现有同态加密方案中私钥个数多和需要预设乘法同态次数的缺陷,基于一个具有特殊b的误差学习问题(learning with errors problem,LWE)变种bLWE(the"special b"variant of the learning with errors problem),得到具有循环安全性的重线性化过程,据此构造了一个较高效的同态加密方案.与Brakerski等人的方案相比,方案的构造者不需要事先知道服务器中乘法同态次数,且私钥个数由原来的L+1个大幅度地缩小为1个.最后,在标准模型下对重线性化过程的循环安全性和方案的CPA安全性进行了严格证明.Homomorphic encryption scheme is a powerful＂ cryptographic system which allows for a variety of applications. Fully homomorphie eneryption （FHE） permits arbitrary computations on encrypted data. The recent breakthrough work in 2009 by Craig Gentry has shown the possibility of FHE sehemes, and has provided the first construction. Consequently, during the past five years, numerous FHE involving novel mathematical techniques and a number of application schemes have appeared. Indeed, the construction and applieation of homomorphic encryption schemes have great theoretic and practical meaning. Homomorphic eneryption has important applications in cloud computing. However, that the multiplication almost all of the homomorphic encryption schemes share two common flaws depth must be set in advance and they all use secret keys of large scales. We construct a circularly secure re-linearization process based on the ＂special b＂ variant of the earning with errors problem （bLWE）. Then, we present an efficient homomorphic encryption scheme. Compared with Brakerski et al＇s scheme, our scheme reduces the L＋I secret keys to one and doesn＇t need to know the multiplication depth in advance. Finally, we prove the chosen-plaintext attack （CPA） security of the homomorphic scheme and the circular security of the re-linearization process in standard model by reducing them into learning with errors problem（LWE） assumption.

关 键 词：循环安全 同态加密 LWE问题 格 标准模型 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]