FHE-CF:基于密文展缩的全同态密码体制设计

FHE-CF: designing of fully homomorphic encryption scheme based on ciphertext flattening technique

为了解决云环境下密文处理的问题,构造了一个基于LWE问题的全同态加密体制FHE-CF。该体制没有采用传统的基于LWE问题的全同态密码体制设计中的重线性化技术,而是利用一种新的密文展缩技术来实现噪声的有效控制。在不引入新的未经论证的安全假设的前提下,可以获得KDM安全的自举加密体制,其安全性有了突破性提高。由于其KDM安全性,可以构造循环的密钥链,实现从分层全同态到全同态的过渡。还证明了所构造的全同态密码体制是RO模型下IND-CPA安全的。除了安全性上的优势外,该密码体制效率与当前最好的全同态密码体制相当。

In order to solve the problem of ciphertext operation in the cloud, this paper presented a new fully homomorphie encryption scheme based on LWE problem. It applied a novel ciphertext flattening technique in this scheme to control the noise efficiently instead of relinearization technique which was applied by other traditional LWE-based fully homomorphic eneryption schemes. Without introducing new assumptions whose security had not been confirmed, it constructed a KDM secure bootstrappable encryption scheme, which leaded to a breakthough in the security of FHE-CF. Because of its KDM secuity, a cyclic keychain could be designed properly to transform a leveled fully homomorphic eneryption scheme into a fully homomorphic encryption scheme. This paper has also been proved the FHE-CF scheme＇ s IND-CPA security under the random oracle model. Besides,the FHE-CF scheme has the same efficiency with these previous fully homomorphie encryption schemes.