Research Progress in Lattice-Based Public-Key Encryption with Keyword Search

doi:10.3969/j.issn.1671-1122.2024.06.008

Abstract

Abstract:

With the explosive growth of data and the rapid development of cloud computing, the demand for data secure sharing and querying is gradually increasing among users. Public-key encryption with keyword search allows resource-constrained users to efficiently search for encrypted data stored in the cloud servers, providing an effective solution for cloud data secure queries. However, with the arrival of the quantum era, the existing cryptosystems are facing a huge impact. Lattice-based cryptography has received widespread attention for the advantages of being reducible to the worst-case difficulty assumption, resistance to quantum attacks, and high security. The article provided an overview of the recent research progress of lattice-based public-key encryption with keyword search from the perspective of security and functionality. Firstly, it outlined the research progress of lattice-based public key cryptography, the definition and the security model of public-key encryption with keyword search. Then, it focused on analyzing the recent lattice-based public-key encryption with keyword search schemes, analyzed the research on the security of the schemes from the starting point of attacking means, and compared the algorithmic efficiencies of the schemes in terms of the communication overhead and the computational complexity. Finally, it summarized the application scenarios and the future research trends.

Key words: lattice-based cryptography, public-key encryption, searchable encryption, cloud computing

CLC Number:

TP309

YE Qing, HE Junfei, YANG Zhichao. Research Progress in Lattice-Based Public-Key Encryption with Keyword Search[J]. Netinfo Security, 2024, 24(6): 903-916.

Figures/Tables 10

References 77

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基于格的公钥密码体制	主要特点	局限性
A-D密码体制	格公钥加密方案，具有可证明安全性	运行效率低，不能满足实际应用需求
GGH密码体制	基于CVP困难问题构造，直观、容易理解	缺乏安全保证，当维数小于350时，易被攻破
NTRU密码体制	基于多项式环构造，运行效率较高	原始方案缺乏安全性证明，没有进行困难问题归约

格困难问题	主要特点	代表算法
LWE	计算效率较低，密文、密钥尺寸大，无明显代数结构、安全强度高	FrodoKEM^[21]、SCloud^[22]
RLWE	参数取自特定环结构，密钥尺寸较小、效率更高，特定结构带来潜在的安全威胁	Newhope^[23,24]、 LAC^[25]、TALE^[26]、 AKCN-E8^[27]
MLWE	兼顾安全性和运算效率	KYBER^[28,29]、 Aigis-enc^[30]、 AKCN-MLWE^[31]

PEKS方案	CI	MCI	TI	MTI	FS	安全定义	安全模型	困难假设
文献[64]方案	√	√	×	×	×	IND-CKA	ROM	NTRU
文献[64]方案	√	√	×	×	×	IND-CKA	SM	LWE
文献[53]方案	√	√	×	×	√	IND-CKA	ROM	LWE
文献[49]方案	√	√	√	√	×	IND-CKA IND-IKGA	SM	LWE
文献[51]方案	√	√	√	√	×	IND-CKA	ROM/SM	LWE
文献[55]方案	√	√	√	√	√	IND-CKA IND-IKGA	ROM	LWE
文献[65]方案	√	√	√	√	√	IND-CKA IND-IKGA	ROM	LWE
文献[56]方案	√	√	√	√	√	IND-CPA	SM	RLWE&SIS

PEKS方案	通信开销
PEKS方案	公钥	私钥	密文	陷门
文献[64]方案	n\|q\|	4n²\|q\|	3n\|q\|	2n\|q\|
文献[64]方案	m((l+2)n+1)\|q\|	n²\|q\|	ε(2n\|q\|+\|q\|+1)	2n\|q\|
文献[53]方案	nm\|q\|	nm\|q\|	(l+nl+n)\|q\|	n\|q\|
文献[49]方案	(2m+nε+ nm(l+2))\|q\|	(n+mk+n²)\|q\|	ε(2n\|q\|+ \|q\|+1)	2n\|q\|
文献[51]方案	3mn\|q\|	(3mn+m²)\|q\|	8ml\|q\|	8ml\|q\|
文献[55]方案	m\|q\|+kn\|q\|	n+k\|q\|	ε(\|q\|+(d+ 3)n\|q\|+1)	(d+3)n\|q\|
文献[65]方案	(l+k+2(n+ 1)m)\|q\|	n²\|q\|	(2n+1)\|q\|	2n\|q\|
文献[56]方案	n\|q\|(2\|q\|+2)	n\|q\|(\|q\|+2)	n\|q\|(6\|q\|+5)	n\|q\|(2\|q\|+2)

PEKS方案	存储空间/KB
PEKS方案	公钥	私钥	密文	陷门
文献[64]方案	0.375	384	1.125	0.750
文献[64]方案	19156.790	96	7.520	0.750
文献[53]方案	74.250	74.250	96.750	0.375
文献[49]方案	1043.830	280.180	7.520	0.750
文献[51]方案	222.750	280.180	594	594
文献[55]方案	4.040	0.046	41.266	4.125
文献[65]方案	154.690	96	0.751	0.750
文献[56]方案	9.750	5.235	28.875	9.722