基于LWE的BGN类CPA安全加密方案设计与应用

Design and Application of BGN-type CPA Secure Encryption Scheme Based on LWE

针对GHV方案对二元明文矩阵加密导致密文扩展率较高的缺陷,提出一种针对p元明文矩阵的BGN类公钥加密方案。给出不可区分性选择明文攻击的安全性证明和Somewhat同态性分析,并应用于隐私信息检索协议的构造。分析结果表明,与原始GHV方案相比,该方案不但具有多次加法同态和一次乘法同态性质,而且在明文空间上做出了一定的编码修改,将密文扩展率从logq降低至logq/logp。

Aiming at the awful encryption expansion rate while encrypting a binary plaintext matrix in GHV scheme,a BGN-type public cryptosystem is proposed for p plaintext matrix. It gives the security proof and analyzes the Somewhat homomorphism of Indistinguishability under Chosen Plaintext Attack （ IND-CPA）, and the new scheme is applied to the construction of privacy information retrieval protocol. Compared with the original GHV scheme, analysis results show that the proposed scheme not only supports multiple homomorphic addition and a single homomorphic multiplication,but also makes some encoding modification in the plaintext space from logq. The ciphertext extension rate is reduced to logq/logp