BFV-MKFHE:基于BFV的多密钥全同态加密方案设计

BFV-MKFHE:Design of Multi-Key Fully Homomorphic Encryption Scheme Based on BFV

传统的全同态加密方案仅支持对单一密钥加密的数据计算,无法适应多用户场景下的应用需求,多密钥全同态加密可以对不同密钥(用户)下的密文进行运算,最终密文由所有相关用户联合解密.目前在多密钥全同态加密领域针对BFV加密系统的研究较少,为了将BFV同态加密体制拓展到多密钥应用领域,本文设计了一种基于BFV的多密钥全同态加密方案BFV-MKFHE.本方案以CZW17中基于BGV的MKFHE方案为基础,首先将BGV加密系统的结构修改为BFV的结构,减去了每一层的模数转换环节,简化了算法运算过程;其次在重线性化过程中,构造用户私钥的组合密文来生成计算密钥,并利用模数提高技术来优化重线性化过程,降低了同态运算过程中产生的噪声,提高了计算密钥生成效率;最后通过修改加密过程的取整方式,减少了计算冗余.本方案中完成一次同态乘法解密时产生的噪声值减小为CDKS19方案的1/p,生成计算密钥的密文尺寸与CDKS19方案相同,较CZW17方案和LZY+19方案约减小1/4,且无需对用户私钥的密文进行扩展,运算效率更高.

The traditional fully homomorphic encryption scheme only supports data computations for single-key encryption,which cannot be adapted to the applications with multiple users.Multi-key fully homomorphic encryption can compute ciphertexts under different keys(for different users),and the final ciphertext is jointly decrypted by all relevant users.In order to extend the BFV homomorphic encryption system to multi-key applications,a multi-key fully homomorphic encryption scheme BFV-MKFHE based on BFV is designed.This scheme is based on the BGV-based MKFHE scheme in CZW17.Firstly,the structure of the BGV encryption system is modified to that of BFV,where the modulus-switching in each layer is removed,which simplifies the algorithm operation process.Secondly,in the relinearization process,the combined ciphertext of the user’s private key is constructed to generate the evaluation key,and the modulus enhancement technique is used to optimize the relinearization process,which reduces the noise generated in the homomorphic operation process and improves the evaluation key generation efficiency;Finally,the computational redundancy is reduced by modifying the rounding method of the encryption process.In the proposed scheme,the noise value generated when completing one homomorphic multiplication decryption is reduced to 1/p of that in the CDKS19 scheme,and the ciphertext size of the generated evaluation key is the same as that of the CDKS19 scheme,which is about 1/4 times smaller than that of the CZW17 scheme and that of the LZY+19 scheme,and there is no need to extend the ciphertext of the user’s private key,which makes the computation more efficient.