基于椭圆曲线的ElGamal型位置隐私保护方案

doi:10.11959/j.issn.2096-109x.2020031

网络与信息安全学报 ›› 2020, Vol. 6 ›› Issue (3): 30-38.doi: 10.11959/j.issn.2096-109x.2020031

• 专栏：隐私保护新技术探索 • 上一篇下一篇

基于椭圆曲线的ElGamal型位置隐私保护方案

赖慧彬^1,²,许力^1,²(),曾雅丽^1,²,朱瑞^1,²

¹ 福建师范大学数学与信息学院，福建福州 350007
² 福建省网络安全与密码技术重点实验室，福建福州350007

修回日期:2020-02-18 出版日期:2020-06-01 发布日期:2020-07-01
作者简介:赖慧彬（1995- ），女，福建漳州人，福建师范大学硕士生，主要研究方向为网络与信息安全|许力（1970- ），男，福建福州人，博士，福建师范大学教授，主要研究方向为网络与信息安全、无线网络与通信、云计算与物联网|曾雅丽（1990- ），女，福建漳州人，福建师范大学博士生，主要研究方向为网络与信息安全|朱瑞（1995- ），女，福建龙岩人，福建师范大学硕士生，主要研究方向为网络与信息安全
基金资助:
国家自然科学基金(61771140);国家自然科学基金(U1905211);福建省科技厅高校产学研项目(2017H6005);企事业合作项目(DH-1307);企事业合作项目(DH-1412)

Elliptic curve ElGamal encryption based location privacy-preserving scheme

Huibin LAI^1,²,Li XU^1,²(),Yali ZENG^1,²,Rui ZHU^1,²

¹ College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350007,China
² Fujian Provincial Key Laboratory of Network Security and Cryptology,Fuzhou 350007,China

Revised:2020-02-18 Online:2020-06-01 Published:2020-07-01
Supported by:
The National Natural Science Foundation of China(61771140);The National Natural Science Foundation of China(U1905211);Major Science and Technology Project in Fujian Province,China(2017H6005);IUI Cooperation Project(DH-1307);IUI Cooperation Project(DH-1412)

摘要/Abstract

摘要：

针对协作频谱感知场景下次用户的位置隐私问题，提出一种基于椭圆曲线的ElGamal型位置隐私保护方案。首先，次用户通过椭圆曲线上的ElGamal公钥密码体制加密原始感知报告后发送给可信第三方；其次，可信第三方对加密后的感知报告进行第一次解密，并且混淆后，发送给融合中心；再次，融合中心进行第二次解密操作后得到原始感知报告；最后，分析该方案的安全性。该方案使感知报告的加密方式基于椭圆曲线上的公钥密码体制，并使可信第三方对感知报告进行混淆，实现了次用户位置隐私的保护。同时，与其他方案相比，该方案有效地降低了通信开销和存储开销。此外，该方案具有容错机制和动态机制，增强了方案的实用性。

关键词: 位置隐私保护, 椭圆曲线, ElGamal, 协作频谱感知

Abstract:

An elliptic curve ElGamal encryption based location privacy-preserving scheme was proposed to address the location privacy problem of secondary users in collaborative spectrum sensing.Firstly,secondary users encrypted the original sensing reports using the ElGamal public key techniques on the elliptic curve and sent them to the trusted property authority.Secondly,the trusted property authority partially decrypted and randomized sensing reports and then sent the randomized sensing reports to the fusion center.Thirdly,the fusion center finally decrypted and got the original sensing reports.Finally,security of the scheme was analyzed.According to the scheme,the encryption method of sensing reports was based on public key cryptography on elliptic curve.And the trusted property authority randomized encrypted sensing reports.Thus the location privacy of secondary users can be protected.Meanwhile,this scheme effectively reduces communication and storage cost,compared with other schemes.In addition,this scheme also has fault tolerant and dynamic mechanism,which increases the practicability and feasibility.

Key words: location privacy protection, elliptic curve, ElGamal, collaborative spectrum sensing

中图分类号:

TP309

赖慧彬,许力,曾雅丽,朱瑞. 基于椭圆曲线的ElGamal型位置隐私保护方案[J]. 网络与信息安全学报, 2020, 6(3): 30-38.

Huibin LAI,Li XU,Yali ZENG,Rui ZHU. Elliptic curve ElGamal encryption based location privacy-preserving scheme[J]. Chinese Journal of Network and Information Security, 2020, 6(3): 30-38.

图/表 9

图1

表1

符号说明　Table 1 Notation description"

符号	含义
p	大于3的素数
F_p	素数域
E /F_p	有限域F_p上的椭圆曲线
G	椭圆曲线点集
P	E/F_p的一个基点
q	基点P的阶数
s₁	TPA的私钥
s₂	FC的私钥
PK	系统公钥
P_j	$R_{j}^{i}$ 编码到椭圆曲线上的点
Ecpm	椭圆曲线点乘运算
Ecpa	椭圆曲线点加运算
Expp	指数模p运算
Inv	模逆运算
Mulp	模p乘法运算
l_EC	ECC密钥长度
l_EG	ElGamal密钥长度
γ	感知报告的长度

表1

表2

图2

表3

表4

表5

表6

表7

参考文献 26

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方案	位置隐私	容错机制	动态机制
PPSRA	√	×	×
文献[15]	×	√	√
LPP-ECEG	√	√	√

密钥长度/bit	椭圆曲线点加运算/ms	椭圆曲线点乘运算/ms
160	0.056	2.388
224	0.072	4.131
256	0.074	4.822
384	0.112	9.054
512	0.155	17.112

实体	PPSRA	文献[15]	LPP-ECEG
次用户	H +2Expp+Mulp	n(2Expp+Mulp)	n(2Ecpm+Ecpa)
可信第三方	无此实体	n(Expp+Inv+Mulp)	4n (Ecpm+Ecpa)
融合中心	H+nMulp+2Mulp+2Expp2^γ-1nExpp	n(Expp+Inv+Mulp)	n(Ecpm+Ecpa)

方案	通信开销
PPSRA	n?l_EG
文献[15]方案	8?n?l_EG
LPP-ECEG	4?n?(l_EC+1)

加密算法	密钥长度/bit
ElGamal	1 024
ECC	160

基于椭圆曲线的ElGamal型位置隐私保护方案

Elliptic curve ElGamal encryption based location privacy-preserving scheme

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