摘 要：基于身份的全同态加密体制因能够克服同态加密时公钥尺寸带来的影响而受到广泛关注。传统的身份基全同态加密方案只能满足单一身份下的同态运算，且在加密阶段普遍存在高斯采样频繁问题。针对以上问题，文章基于 LWR 假设提出了一个无高斯采样的层级多身份全同态加密方案，利用舍入函数去除了加密阶段的高斯采样过程，并提出了一种新型 LWR-Mask系统，将单一身份设置扩展至多身份设置。将同类方案的主私钥缩减至原方案的 1/4，具有更小的密文扩展率。
关键词：多身份；层级身份；全同态加密；LWR 问题
DOI:10.19850/j.cnki.2096-4706.2022.19.031
基金项目：国家自然基金项目（62062009）
中图分类号：TP309 文献标识码：A 文章编号：2096-4706（2022）19-0128-05
Hierarchical Multi-Identity Fully Homomorphic Encryption Scheme without Gaussian Sampling
HOU Lingyun
(School of Computer and Electronic Information, Guangxi University, Nanning 530004, China)
Abstract: Identity-based fully homomorphic encryption system has received extensive attention because of the capability to overcome the impact of public key size in homomorphic encryption. The traditional identity-based Fully Homomorphic Encryption scheme can only satisfy the homomorphic operation under a single identity, and there are existing frequent Gaussian sampling problems in the encryption phase. To solve the above problems, this paper proposes a hierarchical multi-identity Fully Homomorphic Encryption scheme without Gaussian sampling based on the LWR assumption. The Gaussian sampling process in the encryption phase is removed by using the rounding function, and a new LWR-Mask system is proposed, which extends the single identity setting to the multi-identity setting. The master private key of the same type of scheme is reduced to 1/4 of original scheme, and it has a smaller ciphertext expansion rate.
Keywords: multi-identity; hierarchical identity; Fully Homomorphic Encryption; LWR problem
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作者简介：侯凌云（1997—），女，汉族，湖北十堰人，硕士研究生在读，主要研究方向：密码学、同态加密。