安全高效的全同态加密方案的构造

Promoted by the demand for data privacy in cloud computing environments, the project focuses on the constructions of secure and efficient fully homomorphic encryption schemes, which are able to support any efficiently calculable computation on encrypted data without using the secret key and still assure the data privacy, in conjunction with the theory of computational geometry, algebra and cryptography. We intend to study the specific contents as follows: efficient constructions of fully homomorphic encryption schemes; efficient designs of bootstrapping algorithms; constructions of circularly secure fully homomorphic encryption schemes; constructions of fully homomorphic encryption schemes with access control; constructions of fully homomorphic encryption schemes secure against chosen-ciphertext attacks; constructions of fully homomorphic encryption schemes resistant to side-channel attacks; constructions of noiseless fully homomorphic encryption schemes and so on. The research of this project will not only enrich the theory and technology of fully homomorphic encryption, but also can be widely used in many fields including cloud computing, secure data mining and so on. Therefore it will promote greatly the study of the information security of our country.

本项目以云计算环境中对数据私密性的需求为研究背景，结合计算几何、代数学和密码学等相关理论，拟重点研究如何构造安全高效的全同态加密方案，即在保证数据私密性的前提下仍能够对加密数据进行任意高效计算的加密方案。具体研究如下内容：高效的全同态加密方案的构造；高效的自举算法的设计；循环安全的全同态加密方案的构造；具有访问控制功能的全同态加密方案的构造；抵抗选择密文攻击的全同态加密方案的构造；抵抗侧信道攻击的全同态加密方案的构造和无噪音全同态加密方案的构造等。本项目的研究成果不但可以丰富全同态加密的理论与技术，而且可以广泛应用于云计算、安全数据挖掘等领域，将极大地促进我国的信息安全研究。

目前，由于云计算的快速发展，人们通常会借助云服务器强大的计算能力来处理一些庞大的数据。然而，这一类数据通常是一些涉及到医疗、金融、军事等敏感信息的数据。如何在进行数据的外包计算的过程中保护数据的隐私，成为隐私保护领域亟待解决的问题。同态加密以其独特的优势，成为应用最广泛的隐私保护技术之一。. 在理论方面，本项目深入分析全同态加密方案基于的底层困难问题、全同态加密方案与具有访问控制功能的加密方案之间的内在联系以及全同态加密中自举方案的设计，提出了基于LWR困难问题的高效全同态加密方案、具有访问控制功能的全同态加密方案以及紧致编码下的自举方案；在实际应用方面，本项目探索了同态加密在神经网络隐私保护领域的应用，提出了基于同态加密的 BP 神经网络的训练模型。