一种基于GR-LWE问题的密钥交换协议  

A Key Exchange Protocol Based on GR-LWE Problem

作　　者：戚丽君 高菲[1,2] QI Lijun;GAO Fei(School of Cyber Science and Technology,Shandong University,Qingdao Shandong 266237,China;Key Laboratory of Cryptologic Technology and Information Security,Shandong University,Qingdao Shandong 266237,China)

机构地区：[1]山东大学网络空间安全学院(研究院),山东青岛266237 [2]山东大学密码技术与信息安全重点实验室,山东青岛266237

出　　处：《通信技术》2025年第1期75-81,共7页Communications Technology

基　　金：国家重点研发计划(2021YFB3100200)。

摘　　要：密钥交换协议能确保两个用户在不受信任的通道中安全交换密钥,其中Diffie-Hellman协议最为著名。但随着量子计算技术的发展,基于经典数论问题的密钥交换协议逐渐变得脆弱。因此,后量子密码学受到了关注,基于格的密码学成为其中最具吸引力的领域之一。目前,基于容错学习(Learning with Errors,LWE)问题的格密码是主流。提出了一种基于群环上的容错学习(LWE from Group Rings,GR-LWE)问题的密钥交换协议,将密钥交换协议扩展到二面体非交换群环上,提供了长期安全性,并且可抵抗量子计算机的攻击。Key exchange protocols ensure that two users can securely exchange keys over an untrusted channel,among which the Diffie-Hellman protocol is the most famous.However,with the development of quantum computing technology,key exchange protocols based on classical number theory problems gradually become weak.Therefore,post-quantum cryptography gains attention,and lattice-based cryptography becomes one of the most attractive fields.Currently,lattice cryptography based on LWE(Learning with Errors) problem is dominant.This paper proposes a key exchange protocol based on the GR-LWE(LWE from Group Rings) problem,which extends the key exchange protocol to dihedral non-commutative group rings,provides long-term security,and can resist attacks from quantum computers.

关 键 词：格密码 密钥交换协议 非交换群环 GR-LWE 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]