基于NTRU的多密钥同态代理重加密方案及其应用

李瑞琪; 贾春福; 王雅飞

doi:10.11959/j.issn.1000-436x.2021023

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基于NTRU的多密钥同态代理重加密方案及其应用

学术论文 | 更新时间：2024-06-05

- 基于NTRU的多密钥同态代理重加密方案及其应用
- Multi-key homomorphic proxy re-encryption scheme based on NTRU and its application
- 通信学报 2021年42卷第3期页码：11-22
- 作者机构：
  
  1. 南开大学网络空间安全学院，天津 300350
  2. 天津市网络与数据安全技术重点实验室，天津 300350
- 作者简介：
  
  [ "李瑞琪（1993- ），男，黑龙江尚志人，南开大学博士生，主要研究方向为同态加密、格密码学等。" ]
  [ "贾春福（1967- ），男，河北文安人，博士，南开大学教授、博士生导师，主要研究方向为网络与信息安全、可信计算、恶意代码分析、密码技术应用等。" ]
  [ "王雅飞（1995- ），女，天津人，南开大学硕士生，主要研究方向为同态加密应用、隐私保护等。" ]
- 基金信息：
  
  国家重点研发计划基金资助项目(2018YFA0704703);国家自然科学基金资助项目(61972215);国家自然科学基金资助项目(61702399);国家自然科学基金资助项目(61972073);天津市自然科学基金资助项目(20JCZDJC00640)
- DOI：10.11959/j.issn.1000-436x.2021023
  中图分类号： TP309.7
- 网络出版日期：2021-03，
  
  纸质出版日期：2021-03-25
- 稿件说明：
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李瑞琪, 贾春福, 王雅飞. 基于NTRU的多密钥同态代理重加密方案及其应用[J]. 通信学报, 2021,42(3):11-22.

Ruiqi LI, Chunfu JIA, Yafei WANG. Multi-key homomorphic proxy re-encryption scheme based on NTRU and its application[J]. Journal on communications, 2021, 42(3): 11-22.
李瑞琪, 贾春福, 王雅飞. 基于NTRU的多密钥同态代理重加密方案及其应用[J]. 通信学报, 2021,42(3):11-22. DOI： 10.11959/j.issn.1000-436x.2021023.

Ruiqi LI, Chunfu JIA, Yafei WANG. Multi-key homomorphic proxy re-encryption scheme based on NTRU and its application[J]. Journal on communications, 2021, 42(3): 11-22. DOI： 10.11959/j.issn.1000-436x.2021023.

摘要

为了提高同态加密算法在多用户云计算场景下的实用性，构造了一个基于NTRU的多密钥同态代理重加密方案。首先利用密文扩张思想提出了一种新的NTRU型多密钥同态密文形式，并基于此设计了相应的同态运算和重线性化过程，从而形成一个支持分布式解密的NTRU型多密钥同态加密方案；然后借助于密钥交换思想设计了重加密密钥和重加密过程，将代理重加密功能集成到该NTRU型多密钥同态加密方案中。所提方案保留了多密钥同态加密和代理重加密的特性，而且在用户端的计算开销较低。将所提方案应用于联邦学习中的隐私保护问题并进行了实验，结果表明，所提方案基本不影响联邦训练的准确率，加解密、同态运算和重加密等过程的计算开销也可接受。

Abstract

To improve the practicability of homomorphic encryption in the application of multi-user cloud computing

a NTRU-based multi-key homomorphic proxy re-encryption (MKH-PRE) scheme was constructed.Firstly

a new form of NTRU-based multi-key ciphertext was proposed based on the idea of ciphertext extension

and the corresponding homomorphic operations and relinearization procedure were designed on the basis of this new ciphertext form

so that a NTRU-based multi-key homomorphic encryption (MKHE) scheme which supported distributed decryption was constructed.Then

resorting to the idea of key switching

the re-encryption key and re-encryption procedure were put forward such that the functionality of proxy re-encryption (PRE) was integrated to this new NTRU-based MKHE scheme.The MKH-PRE scheme preserved the properties of MKHE and PRE

and had a better performance on the client side.The scheme was applied to the privacy-preserving problems in federated learning and an experiment of the application was carried out.The results demonstrate that the accuracy of learning is scarcely affected by the encryption procedure and the computational overhead of this MKH-PRE scheme is acceptable.

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references

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