基于LWR问题的无证书全同态加密方案

Certificateless Fully Homomorphic Encryption Scheme Based on the LWR Problem

无证书全同态加密(CLFHE)把全同态加密和无证书加密两者的优势结合了起来,它吸引了人们关注的目光。目前人们基于带误差学习(LWE)问题提出了几个CLFHE方案。带舍入学习(LWR)问题是LWE问题的变形。它免除了LWE问题中计算代价高昂的高斯噪声抽样。迄今为止人们尚未提出基于LWR问题的CLFHE方案。本文利用Gentry、Sahai和Waters提出的近似特征向量技术,基于LWR问题设计了一个CLFHE方案,并在随机预言机模型下证明了它满足INDr-CPA安全性。与已有的基于LWE问题的CLFHE方案相比,所设计的方案免除了耗时的高斯噪声抽样而具有更高的计算效率。

Certificateless fully homomorphic encryption (CLFHE) combines the advantages of fully homomor-phic encryption and certificateless encryption. Itcatches the attention of researchers. Several CLFHE schemes have been proposed based on the learning with errors (LWE) problem. The learning with rounding (LWR) problem is a variant of the LWE problem. It dispenses withthe costly Gaussian noise sampling required in the LWE problem. So far, no CLFHE scheme based on the LWR problem has been proposed. This paper designs a CLFHE scheme based on the LWR problem using Gentry, Sahai, and Waters’s approximate eigenvector technique and proves that the designed scheme satisfies INDr-CPA securityin the random oracle model. Compared with existing CLFHE schemes based on the LWE problem, the proposedschemedispenses with the costly Gaussian noise sampling and en-joys higher computational efficiency.