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利用高效的格陷门生成算法构造了身份基加密方案。方案的安全性可归约到标准LWE问题,大大降低了格安全维数,同时降低了密钥规模和计算复杂度。将该方案转化为单身份的全同态加密方案,利用近似奇异向量消除同态运算密钥,运用原象矩阵进行加密,使用子高斯随机变量分析参数,同时将方案的噪声膨胀率由O(n)降为O(n~(0.5))。最后进一步利用扩展密文方法和掩藏方案构造了高效的支持多身份的全同态加密方案。
The identity-based encryption scheme is constructed by using efficient trapdoor generation algorithm. The security of the scheme can be reduced to the standard LWE problem, which greatly reduces the lattice safety dimension and reduces the key size and computational complexity. The scheme is transformed into a single identity homomorphic encryption scheme, the homomorphic vector is used to eliminate the homomorphic operation key, the original matrix is used to encrypt, the parameter is analyzed using Gaussian random variables, and the noise expansion rate of the scheme is given by O ( n) to O (n ~ (0.5)). In the end, we further utilize the extended ciphertext method and the concealment scheme to construct an efficient multi-identity fully homomorphic encryption scheme.