基于格的口令认证密钥交换协议综述

doi:10.11959/j.issn.1000-436x.2022190

Abstract

Abstract:

With the rapid development of quantum computing technology, password-authenticated key exchange (PAKE) protocol based on conventional difficult problems will face serious security threats in the post-quantum era.Lattice-based cryptosystem has been certified by NIST as the most promising cryptosystem in the post-quantum era due to its high efficiency, high security and support for stronger cryptographic service functions (such as fully homomorphic encryption and multi-linear mapping).Firstly, the research progress of lattice-based PAKE protocol was systematically sort out, mainly including the centralized two-party, three-party PAKE protocol and the distributed PAKE protocol over lattices.Then, the relevant typical schemes were compared and analyzed, respectively.Finally, the future research directions PAKE protocol over lattices were prospected.

Key words: password-authenticated key exchange, lattice, provably secure, quantum resistance

CLC Number:

TP393

Yuanbo GUO, Anqi YIN. Research on password-authenticated key exchange protocol over lattices[J]. Journal on Communications, 2022, 43(12): 172-187.

Figures/Tables 8

参数	含义
κ	安全参数
$\leftarrow / \overset{r}{\leftarrow}$	取样/随机取样
$\|\| a \|\|$	向量 $a$ 的模
\|\|C\|\|	集合C 的大小
ε	错误比例参数
β	平滑参数
pw	口令
D	口令空间
Ham(·,·)	汉明距离函数
$0$	零向量/零矩阵

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协议名称	通信轮(次)数	抗量子	安全模型		计算类型	随机预言机	SS-NIZK	认证方式
协议名称	通信轮(次)数	抗量子	用户端	服务器端	计算类型	随机预言机	SS-NIZK	认证方式
文献[37]	3轮(3次)	√	IND-CCA2	IND-CCA2	小整数模乘/加	×	×	显式认证
文献[55]	3轮(3次)	√	IND-CPA	IND-CCA2	小整数模乘/加	×	×	显式互认证
文献[57]	2轮(2次)	√	IND-CCA2	IND-CCA2	小整数模乘/加	√	√	隐式认证
文献[44]	2轮(2次)	√	IND-CCA2	IND-CPA	小整数模乘/加	×	×	隐式认证
文献[60]	2轮(2次)	√	IND-CPA	IND-CCA2	小整数模乘/加	×	×	隐式认证
文献[33]	1轮(2次)	×	IND-CCA2	IND-CCA2	大整数模幂	√	√	隐式认证
文献[48]	1轮(2次)	√	IND-CCA2	IND-CCA2	小整数模乘/加	√	√	隐式认证
文献[61]	1轮(2次)	√	IND-CCA2	IND-CCA2	小整数模乘/加	√	√	隐式认证

协议名称	服务器端认证数据类型	口令哈希函数是否抗量子	困难问题	信号泄露攻击		匿名性	安全模型
协议名称	服务器端认证数据类型	口令哈希函数是否抗量子	困难问题	主密钥不重用	主密钥重用	匿名性	安全模型
文献[66]	口令的哈希值	×	RLWE	—	—	×	随机预言机
文献[67]	口令的哈希值	×	RLWE	—	—	×	随机预言机
文献[68]	验证器/令牌	×	RLWE	—	—	×	UC模型
文献[54]	口令的哈希值	√	LWE	—	—	×	标准模型
文献[69]	验证器/令牌	×	RLWE	×	×	√	随机预言机
文献[70]	验证器/令牌	×	RLWE	√	×	√	ROR模型^[78]
文献[71]	验证器/令牌	×	RLWE	√	√	√	ROR模型^[78]

方案	抗量子	困难问题	通信轮数	计算类型	密钥交换	认证方式	安全模型	私钥
文献[75]	×	DH	4	大整数模/幂	√	隐式认证	ROR模型	√
文献[78]	√	LWE	3	小整数向量/矩阵	√	显式互认证	标准模型	×
文献[79]	√	RLWE	3	小整数向量/矩阵	√	显式互认证	随机预言机	×
文献[80]	√	LWE	2	小整数向量/矩阵	×	显式互认证	随机预言机	×
文献[81]	√	LWE	2	小整数向量/矩阵	√	显式互认证	随机预言机	×

方案		量子攻击	唯口令	密码学原语		服务器数目	通信轮(次)数	随机预言机	密钥协商方式
方案		量子攻击	唯口令	签名/验签	SS-NIZK	服务器数目	通信轮(次)数	随机预言机	密钥协商方式
文献[82]		√	×	√	√	N	3(6N)	×	密钥传输
文献[83]	被动	√	√	×	×	2	1(4)	×	密钥交换
	主动	√	√	×	√	2	1(4)	×	密钥交换
文献[86]		×	×	√	√	2	2(4)	—	密钥传输
文献[87]		×	×	√	√	2	3(6)	—	密钥传输
文献[88]		×	√	√	×	N	3(6N)	×	密钥交换
文献[89]		×	√	√	×	2	3(6)	×	密钥交换

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[1]	Huanhuan LIAN, Huiying HOU, Yunlei ZHAO. Post-quantum verifier-based three-party password authenticated key exchange protocol [J]. Journal on Communications, 2022, 43(4): 95-106.
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