摘要
全同态加密无疑是当前国际密码学界的前沿热点课题之一,自从Gentry发表第一个全同态加密方案以来,已经有不少全同态加密方案被提出:或基于不同的平台给出新的实现,或进行效率方面的改进,等等.纵观这些全同态加密方案,不难发现大多数均是基于"噪声"技术的:一方面,噪声在相关方案的底层密码学困难问题之所以困难方面扮演了很重要的角色;另一方面,对噪声累积的抑制往往也是方案构造的核心技术之一.噪声这把双刃剑似乎成为构造全同态绕不开的一个工具,噪声的引入和对噪声累积的抑制也往往成为制约全同态加密方案性能进一步提升的固有障碍.能否设计出无噪声的全同态加密呢?尽管有许多人认为无噪声的全同态加密均是不安全的,然而在没有严格证明这样的否定性结论之前,对于无噪声全同态加密方案的探索始终是一个有意义的课题.事实上,人们确实已经提出了不少无噪声的全同态加密方案,但目前仍没有一个可以在可证明安全框架下严格做到安全可行的方案.本文主要围绕我们已知的无噪声全同态加密体制的设计思想和方案的安全性展开讨论.
Fully homomorphic encryption is undoubtedly one of the forefront of the hot topics in the current international cryptographic community. Since Gentry published the first FHE scheme, many other FHE schemes have been proposed. Some are new implementations based on different platforms,and some are focused on efficiency improvements. Throughout those FHE schemes, it is not difficult to find that most are based on the "noise" technology. On one hand, noise plays a very important role in ensuring the hardness of the underlying intractability assumptions of the corresponding schemes.On the other hand, the suppression of the noise accumulation is often one of the core technics of the related constructions. Noise seems to be a double-edge and inevitable sword in building FHEs:the introduction of noise and the suppression of noise accumulation are also inherent barriers to the improvement of the performance. One important problem is the existence and construction of noiseless FHE schemes. Although many people think that noiseless FHEs are insecure, the exploration of the noiseless FHEs is always a significant topic before the negative conclusions of such proofs are strictly demonstrated. In fact, several noiseless FHEs have already been proposed, but none can be proved strictly secure and feasible in the framework of provable security. This survey mainly discusses the design idea and the security of known noiseless FHEs.
出处
《密码学报》
CSCD
2017年第6期579-595,共17页
Journal of Cryptologic Research
基金
国家重点研发计划(2016YFB0800602)
国家自然科学基金项目(61370194
61502048)
关键词
无噪声
全同态
加密
noiseless
fully homomorphic
encryption
