抗恶意敌手攻击的信息论意义下安全多方计算

Secure multi-party computation is fundamental to the cryptography and distributed computing. This project focuses on the theory and practice of secure multi-party computation and consists of the following several programs. We study the verifiable secret sharing over non-abelian groups and in multicast network via using the algebraic method and the combinatorial method, and study the information theoretically secure multi-party computation against malicious adversary over non-abelian groups and in multicast network. We also study some non-homomorphic cryptography and the secure outsoucred computation in the cloud computing. The aim of this project is to discover the principle and essential property of designing new multi-party computation, and to clarify the relationship between verifiable secret sharing and the proposed multi-party computation against malicious adversary attack. We also try to explore some new applications of the multi-party computation. The outcomes of this project will not only enrich the research results in the theory of cryptography but also get some new applications in the threshold cryptography and secure outsourced computation. Our works will propose some new methods and ideas to support the current research on information security and cloud computing.

安全多方计算协议是密码学和分布式计算的基石。本项目以安全多方计算协议的理论与应用为研究对象，采用代数方法和组合方法研究非交换群上和多播通信网络中的可验证秘密共享体制，研究非交换群和多播通信网络等计算域中抗恶意敌手攻击的信息论意义下安全多方计算协议，探索它们在非同态的门限密码和云计算中的安全外包计算中的应用。本项目预期揭示新型安全多方计算协议设计的原理与本质，阐明可验证秘密共享体制与抗恶意敌手攻击的安全多方计算协议的机制，挖掘安全多方计算协议新的应用领域。研究成果不仅在理论上丰富了密码学的理论成果，而且在应用上拓展了门限密码和安全外包计算的研究，为信息安全及云计算的研究与应用提供新的理论工具和思路。

在本项目执行期间，区块链技术得到了前所未有的发展并受到了学术界和各行各业共同的关注。安全多方计算作为区块链最重要的密码技术之一，它也获得了较快速的发展并愈显重要。本项目以此为研究契机，利用有限域上多项式理论、椭圆曲线、格等代数工具，研究了一些特殊性质的多方计算协议并探索了在区块链这一新领域中的应用。主要的研究成果概况为如下四部分：1）研究了高效的可验证秘密分享以及新型的信息论意义下安全的函数秘密分享；2）研究了可用于设计安全多方计算的全同态加密与外包数据的认证机制；3）研究了云环境下外包数据的完整性检测问题；4）研究了安全多方计算协议在区块链与电子投票领域中的应用。这些理论研究进一步丰富了多方计算协议及其相关应用的研究成果。