基于多密钥全同态加密方案的无CRS模型安全多方计算

Three Round Secure Multiparty Computation Based on Multi-Key Full-Homomorphic Encryption Without CRS

利用多密钥全同态加密方案(multi-key fully homomorphic encryption scheme,MFHE)可以设计一个安全多方计算协议.在公共随机串(common random string,CRS)模型中构造的安全多方计算协议,每一个参与方在生成公钥阶段要用到一个公共随机矩阵,这削弱了每个人独立生成公钥的能力.本文首先设计一个无CRS的基于GSW的安全多方计算协议,与已有的同类协议相比,由于我们的方案利用了编码操作,从而把单密钥密文扩展成多密钥密文,提高了效率,并将解密噪音从2(m4+m)mNBχ降低到(2+m)mNBχ.我们也以LWE假设为依据构造了一个无CRS模型的3轮安全多方计算协议,并证明其在半恶意敌手的情形下是安全的.

Multi-key fully homomorphic encryption scheme(MFHE)can be used to design a secure multi-party computing protocol.In the common random string(CRS)model,each participant needs to use a public random matrix in the generation of public keys,which weakens the ability of each participant to generate public keys independently.This study designs a secure multi-party computation protocol based on GSW without CRS.Compared with some existing similar protocols,the proposed scheme makes use of encoding operation to expand the single-key ciphertext into multi-key ciphertext,which improves the efficiency and reduces the decryption noise from 2(m4+m)mNBχto(2+m)mNBχ.Finally,a three-round secure multi-party computation protocol without CRS is constructed based on LWE assumption,and the protocol is proved to be secure against a semi-malicious adversary.