中文摘要：

基于容错学习问题构造的一类全同态加密体制在云计算安全领域具有重要的潜在应用价值，但同时普遍存在着公钥尺寸较大的缺陷，严重影响其身份认证与密钥管理的效率。将基于身份加密的思想与基于容错学习问题的全同态加密相结合，提出一种基于身份的全同态加密体制，能够有效克服公钥尺寸对于全同态加密应用效率的影响。在随机喻示模型下，体制的安全性归约到容错学习问题难解性和陷门单向函数单向性，并包含严格的安全性证明。

英文摘要：

The fully homomorphic encryption schemes based on learning with errors problem own a great potential value in the cloud computing security. However, the existing schemes share a common flaw of large sized public keys, which may cause inefftciency of such schemes in the key and identity management. An identity-based fuUy homomorphic en- cryption scheme was presented. The scheme compromises the merits of both identity-based and fully homomorphic en- cryption schemes, and it overcomes the above mentioned flaw. The security of the proposed scheme reduces to the hard- ness of learning with errors problem and the one-wayness of trapdoor function in the random oracle model.