基于高效全同态加密的安全多方计算协议  

Secure Multi-party Computing Protocol Based on Efficient Fully Homomorphic Encryption

作　　者：朱宗武 黄汝维[1] ZHU Zong-wu;HUANG Ru-wei(School of Computer and Electronic Information,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学计算机与电子信息学院,南宁530004

出　　处：《计算机科学》2022年第11期345-350,共6页Computer Science

基　　金：国家自然科学基金(62062009);广西科技重大专项资助项目(AA17204058-17,AA18118047-7)。

摘　　要：针对目前基于全同态加密的安全多方计算协议存在的密文尺寸大、效率较低的问题,文中证明了Chen等提出的支持多比特加密的全同态加密方案满足密钥同态性,基于该方案和门限解密设计了一个在公共随机串模型下的3轮交互的高效安全多方计算协议。该协议由非交互的零知识证明可以得出协议在恶意模型下是安全的,其安全性可归结为容错学习问题的变种问题Some-are-errorless LWE。与现有的在CRS模型下的协议相比,该协议支持多比特加密,能有效降低与非门复杂度;同时密文尺寸较小,减少了运算量,从而提高了时间与空间效率。In view of the problem of large ciphertext size and low efficiency of the current secure multi-party computation protocol based on fully homomorphic encryption,this paper proves that the fully homomorphic encryption scheme that supports multi-bit encryption proposed by Chen et al.satisfies the key homomorphism.Based on this scheme and threshold decryption,an efficient and secure multi-party computation protocol with three rounds of interaction under the common random string(CRS)model is designed.The protocol can be concluded from the non-interactive zero knowledge proof that the protocol is safe under the malicious model,and its security can be boiled down to the variants of the learning with errors problem(LWE).Compared with the existing protocol of the CRS model,the protocol supports multi-bit encryption,which can effectively reduce the complexity of the NAND gate.At the same time,the size of the ciphertext is smaller,the amount of calculation is reduced,and the time and space efficiency are improved.

关 键 词：全同态加密 安全多方计算 多比特加密 门限解密 容错学习问题 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]