基于理想格的通用可组合两方口令认证密钥交换协议

舒琴; 王圣宝; 路凡义; 韩立东; 谭肖

doi:10.11999/JEIT191029

基于理想格的通用可组合两方口令认证密钥交换协议

doi: 10.11999/JEIT191029

杭州师范大学信息科学与工程学院杭州 311121

基金项目: 国家重点研发计划项目(2017YFB0802000)，国家自然科学基金青年项目(61702152, 61702153)，浙江省教育厅科研项目(Y202044830)

详细信息

作者简介:
舒琴：女，1995年生，硕士，研究方向为基于格的认证协议

王圣宝：男，1978年生，副教授，研究方向为认证及密钥建立与区块链安全

韩立东：男，1982年生，讲师，研究方向为可搜索加密

谭肖：男，1985年生，讲师，研究方向为公钥密码学

通讯作者:
王圣宝　shengbaowang@hznu.edu.cn

中图分类号: TN918; TP309.7
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- 被引次数: 0
出版历程
- 收稿日期: 2019-12-24
- 修回日期: 2021-03-09
- 网络出版日期: 2021-03-12
- 刊出日期: 2021-06-18

Universally Composable Two-Party Password-Based Authenticated Key Exchange from Ideal Lattices

School of Information Science and Engineering, Hangzhou Normal University, Hangzhou 311121, China

Funds: The National Key R&D Program of China (2017YFB0802000), The Youth Program of National Natural Science Foundation of China (61702152, 61702153), The Scientific Research Fund of Zhejiang Provincial Education Department (Y202044830)

摘要

摘要: 大部分现有基于格的两方口令认证密钥交换协议(2PAKE)都是在基于不可区分的公共参考串模型或Bellare-Pointcheval-Rogaway(BBR)模型下被证明安全的。该文提出一个基于环上带误差学习问题的两方口令认证密钥交换协议，并在通用可组合框架下证明其安全性。与同类协议相比，新协议具有更高的安全性和更高的效率。
- 两方密钥交换协议 /
- 口令认证 /
- 环上带误差学习问题 /
- 通用可组合模型
Abstract: Most of the existing two-party password-based Authenticated Key Exchange (2PAKE) protocols from lattices are proven secure using the indistinguishable common reference string model or the Bellare-Pointcheval-Rogaway model. This paper proposes a two-party password-based authenticated key exchange protocol based on the Ring Learning With Errors (RLWE) problem and proves its security under the Universally Composable (UC) framework. Compared with similar protocols, the new protocol achieves a higher level of security and efficiency.
- Two-Party Authenticated Key Exchange protocol (2PAKE) /
- Password authentication /
- Ring Learning With Errors (RLWE) /
- Universally Composable (UC) model

HTML全文

图 1 RLWE-CAPAKE的相互认证及密钥交换过程

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表 1 UC框架不可区分性证明概览

游戏	模型	游戏					模拟器	挑战者
游戏	模型	U1	U2	U3	U4	哈希与加解密	模拟器	挑战者
${\rm{G}} 0$	现实	真实	真实	真实	真实	真实	协议	${\cal{A}}$
${\rm{G}} 1$	混合	真实	真实	真实	真实	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 2$	混合	真实	真实	真实	真实	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 3$	混合	真实	真实	真实	模拟	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 4$	混合	模拟	真实	模拟	真实	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 5$	混合	真实	真实	真实	模拟	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 6$	混合	真实	模拟	真实	模拟	模拟	${\cal{H}}$	${\cal{A}}$
${\rm{G}} 7$	理想	模拟	模拟	模拟	模拟	模拟	${\cal{S}}$	${\cal{A}}$

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表 2 理想格上口令基2PAKE协议的性能比较

协议	通信开销	环运算次数	安全模型	难题假设	误差调和
RLWE-PAK	$2n\;{\log _2}\;q + n$	4	BPR模型	RLWE	Ding式REC
RLWE-SRP	$2n\;{\log _2}\;q + n$	5	UC模型	RLWE	Ding式REC
本文协议	$2n\;{\log _2}\;q + n$	4	UC模型	RLWE	Peikert式REC

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