基于Cocks身份密码体制的高效签密方案

doi:10.11959/j.issn.1000-436X.2020214

通信学报 ›› 2020, Vol. 41 ›› Issue (12): 128-138.doi: 10.11959/j.issn.1000-436X.2020214

基于Cocks身份密码体制的高效签密方案

彭长根¹^,², 张小玉¹^,³, 丁红发²^,⁴, 杨善慧¹^,³

¹ 贵州大学数学与统计学院公共大数据国家重点实验室，贵州贵阳 550025
² 贵州大学计算机科学与技术学院，贵州贵阳 550025
³ 贵州大学密码学与数据安全研究所，贵州贵阳 550025
⁴ 贵州财经大学信息学院，贵州贵阳 550025

修回日期:2020-10-15 出版日期:2020-12-25 发布日期:2020-12-01
作者简介:彭长根（1963- ），男，贵州锦屏人，博士，贵州大学教授、博士生导师，主要研究方向为隐私保护、密码学和大数据安全。
张小玉（1995- ），女，四川苍溪人，贵州大学硕士生，主要研究方向为密码学。
丁红发（1988- ），男，河南南阳人，贵州大学在站博士后，主要研究方向为隐私保护和大数据安全。
杨善慧（1994- ），女，贵州遵义人，贵州大学硕士生，主要研究方向为密码学。
基金资助:
国家自然科学基金资助项目(U1836205);国家自然科学基金资助项目(61662009);国家自然科学基金资助项目(61772008);贵州省科技计划基金资助项目([2018]3001);贵州省科技计划基金资助项目([2018]3007);贵州省科技计划基金资助项目([2017]3002);贵州省科技计划基金资助项目([2019]2004);贵州省科技计划基金资助项目([2018]2162);贵州省科技计划基金资助项目([2018]2159);贵州省科技计划基金资助项目([2020]5017);贵州省科技计划基金资助项目([2020]1Y265);贵州省高等学校创新人才团队基金资助项目([2013]09);“十三五”国家密码发展基金资助项目(MMJJ20170129)

Efficient signcryption scheme based on Cocks’ identity cryptosystem

Changgen PENG¹^,², Xiaoyu ZHANG¹^,³, Hongfa DING²^,⁴, Shanhui YANG¹^,³

¹ College of Mathematics and Statistics, State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China
² College of Computer Science and Technology, Guizhou University, Guiyang 550025, China
³ Institute of Cryptography and Data Security, Guizhou University, Guiyang 550025, China
⁴ College of Information, Guizhou University of Finance and Economics, Guiyang 550025, China

Revised:2020-10-15 Online:2020-12-25 Published:2020-12-01
Supported by:
The National Natural Science Foundation of China(U1836205);The National Natural Science Foundation of China(61662009);The National Natural Science Foundation of China(61772008);The Science and Technology Program of Guizhou Province([2018]3001);The Science and Technology Program of Guizhou Province([2018]3007);The Science and Technology Program of Guizhou Province([2017]3002);The Science and Technology Program of Guizhou Province([2019]2004);The Science and Technology Program of Guizhou Province([2018]2162);The Science and Technology Program of Guizhou Province([2018]2159);The Science and Technology Program of Guizhou Province([2020]5017);The Science and Technology Program of Guizhou Province([2020]1Y265);The Project of Innovative Group in Guizhou Education Department([2013]09);The 13th Five-Year National Cryptography Development Foundation(MMJJ20170129)

摘要/Abstract

摘要：

现有的基于身份签密方案多是基于双（多）线性对构造的，针对其复杂的对运算导致签密效率低下的问题，基于Cocks的身份密码体制提出了一种新的高效签密方案。首先，形式化所提方案的安全模型，给出了保密性和不可伪造性的定义；然后，利用二次剩余难解问题实现了所提方案的具体构造，进一步结合雅可比符号运算巧妙地在一个逻辑步骤内实现了签密算法设计；最后，在随机预言模型下，给出了所提方案满足保密性和不可伪造性的安全性证明。效率分析表明，相对于已有的基于身份签密的方案，所提方案较大幅度地提升了运算效率，同时具备基于身份密码的良好特性。

关键词: 签密, Cocks身份密码体制, 二次剩余问题, 可证明安全

Abstract:

Most of the existing identity-based signcryption schemes are based on bilinear or multilinear pairing operations construction.To solve the problem of low efficiency caused by complex pair operation, a new efficient signcryption scheme based on the identity cryptosystem of Cocks was proposed.Firstly, the security model of the proposed scheme was formalized, and the definition of confidentiality and unforgeability was given.Secondly, the quadratic residue problem was used to realize the concrete construction of the proposed scheme, and the signature algorithm was designed in a logical step by combining Jacobi symbol operation.Finally, the security proofed that the scheme satisfied the confidentiality and unforgeability was given under the random prediction model.The efficiency analysis shows that compared with the existing identity-based signcryption scheme, the proposed scheme greatly improves the computing efficiency and has good characteristics of identity-based cryptosystem.

Key words: signcryption, Cocks’ identity cryptosystem, quadratic residue problem, provable security

中图分类号:

TP30

彭长根, 张小玉, 丁红发, 杨善慧. 基于Cocks身份密码体制的高效签密方案[J]. 通信学报, 2020, 41(12): 128-138.

Changgen PENG, Xiaoyu ZHANG, Hongfa DING, Shanhui YANG. Efficient signcryption scheme based on Cocks’ identity cryptosystem[J]. Journal on Communications, 2020, 41(12): 128-138.

图/表 6

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参考文献 19

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符号	定义
T_m	执行模乘运算所需的时间
T_b	执行双线性配对操作所需的时间，T_b≈87T_m
T_be	执行双线性配对幂运算所需的时间， T_be≈43.5T_m
T_em	执行椭圆曲线标量点乘法运算所需的时间， T_em≈29T_m
T_i	执行模逆运算所需的时间，T_i ≈11.6T_m
T_a	执行雅可比符号运算所需的时间，T_a ≈6.5T_m

方案类别	方案	签密	解签密
	文献[10]	2T_em+T_b≈203T_m	T_b+T_be≈130.5T_m
双线性对	文献[11]	3Tem+T_b+T_be≈217.5T_m	4T_b+4T_be≈522T_m
	文献[15]	4T_be≈174T_m	3T_be+T_b≈217.5T_m
	文献[16]	T_b+5T_em≈232T_m	3T_b+3T_em≈348T_m
椭圆曲线离散对数	文献[13]	7T_em≈203T_m	8T_em≈232T_m
	文献[6]	4T_em≈116T_m	2T_em≈58T_m
二次剩余	CBSC	2T_a≈13T_m	2T_a+2T_i≈36.2T_m

符号	运行时间/ms
T_b	30.624
T _be	14.312
T _em	9.541
T_i	4.832
T_a	2.288

基于Cocks身份密码体制的高效签密方案

Efficient signcryption scheme based on Cocks’ identity cryptosystem

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