标准模型下可证安全的无证书全同态加密体制

针对现有全同态加密体制普遍存在的公钥尺寸大的缺陷,结合无证书公钥加密的思想,提出一种无证书全同态加密体制设计方案,无需对公钥进行身份认证,因而有效提高密码系统的整体应用效率。体制利用满秩差分矩阵实现身份信息的嵌入,摆脱了对于哈希函数的依赖,因而在安全性证明中无需引入随机谕示假设;借助一对彼此对偶的正态分布采样函数实现部分私钥的提取,进而结合容错学习问题实例生成体制私钥;通过双重加密使服务器失去对用户密文进行解密的能力,从而杜绝密钥托管问题。体制的安全性在标准模型下归约到容错学习问题的难解性。

Provable secure certificateless fully homomorphic encryption scheme in standard model

Focused on the flaw of large-scale public keys which is shared by the existing fully homomorphic encryption schemes, the idea of certificateless public-key encryption was introduced into the design of fully homomorphic encryption schemes, and an certificateless fully homomorphic encryption scheme was proposed. The overall efficiency of the cryptosystem would be improved since the public keys of the scheme no longer need identity authentication. The full-rank differencing matrix was used to embed the identities into the scheme, and the random oracles were no longer needed in the security proof because of the absence of hash function. The partial private keys were abstracted by a pair of dual normal distribution sampling functions, and were transformed to the private keys by the instance of learning with errors problem. The scheme employed double encryption to deprive the servers of the capability of decryption and thus avoided key escrow. The security of the scheme reduces to the hardness of learning with errors problem.