无高斯噪声的全同态加密方案

doi:10.11772/j.issn.1001-9081.2017.12.3430

计算机应用 ›› 2017, Vol. 37 ›› Issue (12): 3430-3434.DOI: 10.11772/j.issn.1001-9081.2017.12.3430

无高斯噪声的全同态加密方案

李明祥^1,2, 刘照^1,3, 张明艳^1,3

1. 河北金融学院金融研究所, 河北保定 071051;
2. 河北省科技金融重点实验室, 河北保定 071051;
3. 河北省科技金融协同创新中心, 河北保定 071051

收稿日期:2017-06-23 修回日期:2017-08-27 出版日期:2017-12-10 发布日期:2017-12-18
通讯作者: 李明祥
作者简介:李明祥(1968-),男,山东济宁人,副教授,博士,主要研究方向:全同态加密方案;刘照(1989-),女,河北保定人,助教,硕士,主要研究方向:云计算安全;张明艳(1983-),女,湖北荆州人,副研究员,硕士,主要研究方向:互联网金融。
基金资助:
河北省重点研发计划项目（16210701）；河北省高等学校科学技术研究项目（ZD2017228）。

Fully homomorphic encryption scheme without Gaussian noise

LI Mingxiang^1,2, LIU Zhao^1,3, ZHANG Mingyan^1,3

1. Institute of Finance, Hebei Finance University, Baoding Hebei 071051, China;
2. Science and Technology Finance Key Laboratory of Hebei Province, Baoding Hebei 071051, China;
3. Financial Synergy Innovation of Science and Technology Center in Hebei Province, Baoding Hebei 071051, China

Received:2017-06-23 Revised:2017-08-27 Online:2017-12-10 Published:2017-12-18
Supported by:
This work is partially supported by the Key Research and Development Program of Hebei Province (16210701), the Scientific and Technological Research Project of Higher Education of Hebei Province (ZD2017228).

摘要/Abstract

摘要： 基于带舍入学习（LWR）问题，一个分级全同态加密方案最近被提出。LWR问题是带误差学习（LWE）问题的变型，但它省掉了代价高昂的高斯噪声抽样，因此与现有基于LWE问题的全同态加密方案相比，该基于LWR问题的全同态加密方案具有更高的计算效率。然而，该基于LWR问题的全同态加密方案在同态运算时需要输入用户的运算密钥。因此，基于LWR问题构造了一个新的分级全同态加密方案，该方案在同态运算时不需要输入用户的运算密钥。鉴于所提方案可应用于构造基于身份的全同态加密方案、基于属性的全同态加密方案等，它具有比最近所提出的基于LWR问题的全同态加密方案更广泛的应用场景。

关键词: 全同态加密, 分级全同态加密, 带舍入学习问题, 带误差学习问题, 高斯噪声抽样

Abstract: Much lately, a leveled fully homomorphic encryption scheme was proposed based on the Learning With Rounding (LWR) problem. The LWR problem is a variant of the Learning With Errors (LWE) problem, but it dispenses with the costly Gaussian noise sampling. Thus, compared with the existing LWE-based fully homomorphic encryption schemes, the proposed LWR-based fully homomorphic encryption scheme has much higher efficiency. But then, the user's evaluation key was needed to be obtained in the homomorphic evaluator of the proposed LWR-based fully homomorphic encryption scheme. Accordingly, a new leveled fully homomorphic encryption scheme was constructed based on the LWR problem, and the user's evaluation key was not needed to be obtained in the homomorphic evaluator of the new fully homomorphic encryption scheme. Since the new proposed fully homomorphic encryption scheme can be used to construct the schemes such as identity-based fully homomorphic encryption schemes, and attribute-based fully homomorphic encryption schemes, the new proposed scheme has wider application than the lately proposed LWR-based fully homomorphic encryption scheme.

Key words: Fully Homomorphic Encryption (FHE), leveled Fully Homomorphic Encryption (FHE), Learning With Rounding (LWR) problem, Learning With Errors (LWE) problem, Gaussian noise sampling

中图分类号:

TP309.7

李明祥, 刘照, 张明艳. 无高斯噪声的全同态加密方案[J]. 计算机应用, 2017, 37(12): 3430-3434.

LI Mingxiang, LIU Zhao, ZHANG Mingyan. Fully homomorphic encryption scheme without Gaussian noise[J]. Journal of Computer Applications, 2017, 37(12): 3430-3434.

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无高斯噪声的全同态加密方案

Fully homomorphic encryption scheme without Gaussian noise

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