中文摘要：

前全同态加密的效率圣待提高，为了提高全同态加密的效率，提出一个LWE(learningwitherrors)上的短公钥多位全同态加密方案.方案中从离散高斯分布上选取LWE样例，并且将高斯噪音与之相加，导致LWE样例从2nlogg下降到n+1，使得方案的公钥长度变短.详细给出了该方案的噪音增长分析与安全性证明；此外，对目前密钥交换技术进行了优化，并且针对多位全同态加密，给出了密钥交换优化版本的形式化描述；最后，针对目前全同态加密的实践应用，给出了分析全同态加密具体安全参数的方法.分析了该方案与BGH13方案的具体安全参数，数据显示该方案的具体参数长度要优于BGH13方案.

英文摘要：

The efficiency of fully homomorphic encryption is a big question at present. To improve the efficiency of fully homomorphic encryption, we use the technique of packed ciphertexts to construct a multi-bit fully homomorphic encryption based on learning with errors (LWE) problem. Our scheme has a short public key. Since our fully homomorphic encryption scheme builds on the basic encryption scheme that chooses learning with errors samples from Gaussian distribution and add Gaussian error toit , which results in that the number of learning with errors samples decrease from 2n\ogqton + 1. Weprove that our fully homomorphic encryption scheme is feasible and its security relies on the hardnessof learning with errors problem. In addition, we adapt the optimization for the process of keyswitching from BGH13 and formal this new process of key switching for multi-bit fully homomorphic encryption. At last, we analyze the concert parameters and compare these parameters between our scheme and BGH13 scheme. The data show that our scheme has smaller public key by a factor of about logg than the one in BGH13 scheme.