基于无证书群签名方案的电子现金系统

doi:10.11959/j.issn.1000-436x.2016107

摘要/Abstract

摘要：

在经典方案ACJT群签名方案的基础上，提出了一种基于椭圆曲线的前向安全的成员可撤销无证书群签名方案，改进了ACJT计算复杂、参数较多、签名较长的不足，减小了计算量及参数个数，缩短了签名长度，提高了方案效率，并基于此群签名方案构建了一个离线公平高效的多银行电子现金系统，该电子现金系统不仅继承了群签名方案的安全性、高效性，还实现了不可伪造性、防止多重支付、防止金额篡改等多种性质，较同类方案具有明显优势。

关键词: 椭圆曲线, 无证书签名, 前向安全, 成员撤销, 群签名, 电子现金

Abstract:

An efficient elliptic certificateless group signature ith forward security and member revocation based on ACJT group signature was proposed.Compared to ACJT which has complex computation,many parameters and long signature length,proposed scheme has less parameters and only involve a small amount of computation.The length of proposed signature is short and the efficiency is high.A fair off-line multi-bank e-cash system based on this group signa-ture scheme was also proposed.The new e-cash system has not only the high security and efficiency,but the unforgeabil-ity.It also can avoid double-spending and tampering money.The scheme has a clear advantage compared with others.

Key words: elliptic curve, certificateless signature, forward security, member revocation, group signature, electronic cash

梁艳,张筱,郑志明. 基于无证书群签名方案的电子现金系统[J]. 通信学报, 2016, 37(5): 184-190.

Yan LIANG,Xiao ZHANG,Zhi-ming ZHENG. Electronic cash system based on certificateless group signature[J]. Journal on Communications, 2016, 37(5): 184-190.

图/表 5

表1

图1

图2

表2

表3

参考文献 26

[1]	CHAUM D . Blind signature for untraceable payments[C]// Advances in Cryptology-CRYPTO'82, New York, c1983: 199-203.
[2]	CHAUM D , HEYST F . Group signature[C]// EUROCRYPT'91,LNCS.Springer-Verlag. c1991: 257-265.
[3]	ATENIESE G , CAMENISCH J , JOYE M , et al. A practical and provably secure coalition-resistant group signature scheme[C]// Advances in Cryptology-CRYPTO'00,LNCS 1880,Springer-Verlag, c2000: 255-270.
[4]	MAITLAND G , BOYD C . Fair electronic cash based on a group sig-nature scheme[C]// Proc of ICICS'01. c2001: 461-465.
[5]	CONSTANTIN P . An off-line electronic cash system with revokable anonymity[C]// The 12th IEEE Mediterranean Electro-Technical Con-ference. Dubrovnik,Croatia, c2004: 763-767.
[6]	HOU X S , TAN C H . A new electronic cash model[J]. Information Technology :Coding and Computing, 2005,1(4-6): 374-379.
[7]	ZHANG J L , MA L Z , WANG Y M . Fair e-cash system without trus-tees for multiple banks[C]// International Conference on Computational Intelligence and Security Workshops. c2007: 585-587.
[8]	FEI X W , LI Q L . New electronic cash system with higher security and efficiency[J]. Application Research of Computers, 2008,25(5): 1543-1545.
[9]	SONG D X . Practical forward secure group signature schemes[C]// The 8th ACM Conf on Computer and Communications Security(CCS 2001), New York, ACM Press, C2001: 225-234.
[10]	TORU N , NOBUO F . Revocable group signature with compact revo-cation list using accumulators[C]// Springer International Publishing Switzerland, C2014: 435-451.
[11]	陈泽文, 王继林, 黄继武 , 等. ACJT群签名方案中成员撤销的高效实现[J]．软件学报, 2005,16(1): 151-157. CHEN Z W , WANG J L , HUANG J W , et al. An efficient revocation algorithm in ACJT group signature[J]. Journal of Software, 2005,16(1): 151-157.
[12]	ZHANG J , WU Q , WANG Y . A novel efficient group signature scheme with forward security[C]// Int'l Conf on Information and Communica-tions Security(ICICS'03), C2003: 292-300.
[13]	WANG G . On the security of a group signature scheme with forward security[C]// Int'l Conf on Information Security and Cryptology-ICISC 2003. Berlin:Springer-Verlag, c2003: 27-39.
[14]	肖平安, 杨凌 . 基于群签名的身份认证方案研究[D]．兰州:兰州大学, 2013: 6-9. XIAO P A , YANG L . Study on identity authentication scheme based group signature[D]. Lanzhou:Lanzhou University, 2013: 6-9.
[15]	李如鹏, 于佳, 李国文 , 等. 高效撤销成员的前向安全群签名方案[J]．计算机研究与发展, 2007,44(7): 1219-1226. LI R P , YU J , LI G W , et al. Forward secure group signature schemes with efficient revocation[J]. Journal of Computer Research and De-velopment, 2007,44(7): 1219-1226.
[16]	陈少真, 李大兴 . 有效取消的向前安全群签名体制[J]．计算机学报, 2006,29(6): 998-1003. CHEN S Z , LI D X . An efficient revocable group signature schemes with forward security[J]. Chinese Journal of Computers, 2006,29(6): 998-1003.
[17]	CAMENISH J , STADLER M . Efficient group signature schemes for large groups[C]// Advances in Cryptology-CRPTO'97,LNCS 1294. Berlin:Springer-Verlag, c1997: 410-424.
[18]	张德栋, 马兆丰, 杨义先 , 等. 群签名中成员撤销问题解决方案[J]．通信学报, 2014,35(3): 193-200. ZHANG D D , MA Z F , YANG Y X , et al. New solution scheme for the member revocation in group signature[J]. Journal on Communications, 2014,35(3): 193-200.
[19]	黎茂棠, 杨晓元, 韩益亮 , 等. 基于ACJT的广义群签密方案[J]．计算机工程与应用, 2008,44(31): 128-131. LI M T , YANG X Y , HAN Y L , et al. New ACJT based generalized group signcryption[J]. Computer Engineering and Applications, 2008,44(31): 128-131.
[20]	张兴兰 . 一种高效的群签名方案[J]．计算机应用研究, 2009,26(11): 4276-4278. ZHANG X L . Efficient group signature scheme[J]. Application Re-search of Computers, 2009,26(11): 4276-4278.
[21]	韩晓花，李乔良，袁遇晴 . 基于椭圆曲线群签名方案的多银行电子现金系统[J]．计算机研究与发展, 2009,46(Suppl.): 306-310. HAN X H , LI Q L , YUAN Y Q . An electronic cash system with mul-tiple banks based on ECC group signature scheme[J]. Journal of Computer Research and Development, 2009,46(Suppl.): 306-310.
[22]	HE D , CHEN J , ZHANG R . An efficient and provably-secure certifi-cateless signature scheme without bilinear pairings[J]. International Journal of Communication Systems 2012(25): 1432-1442.
[23]	SUJATA M , BANSIDHAR M , SUBHALAXMI D . A secure electronic cash based on a certificateless group signcryption scheme[J]. Mathe-matical and Computer Modelling 2013,15(1-2): 186-195.
[24]	ATENIESE G , SONG D , TSUDIK G . Quasi-efficient revocation in group signature[C]// Financial Crypotography(FC'02),LNCS 2357. Berlin:Springer-Verlag, c2002: 183-197.
[25]	SUJATA M , BANSIDHAR M , SUBHALAXMI D . A secure electronic cash based on a certificateless group signcryption scheme[J]. Mathe-matical and Computer Modelling, 2013,58: 186-195.
[26]	SATTAM S . AL-RIYAMI M , KENNETH G . Certificateless public key cryptography[C]// International Association for Cryptologic Research, C2003: 452-473.
[27]	施荣华, 龙成胜 . 信息-一种前向安全的ACJT群签名方案[J]．计算机工程与应用, 2008,44(7): 126-128. SHI R H , LONG C S , ACJT group signature scheme with forward secu-rity[J]. Computer Engineering and Application, 2008,44(7): 126-128.
[26]	XU X . ZHU P , WEN Q Y , et al. A secure and efficient authentication and key agreement scheme based on ECC for telecare medicine information systems[J]// Journal of Medical Systems, 2014,38(1): 1-7.

方案名称	群公钥参数个数	群公钥长度/bit	签名过程参数个数	签名长度/bit	签名、验证及打开算法总时间/ms
ACJT方案	6	6 144	13	8 192	45 840
本文方案	2	320	11	1 136	43.21

方案	模数大小/bit	Sign计算量	Verify计算量	Open计算量	签名长度/bit	群公钥长度/bit	是否具有成员撤销过程	是否具有前向安全性
ACJT	≥1 024	12E+11M	11E+7M	1E+1M	8 192	6 144	×	×
文献[9]	≥1 024	20E+17M	(22+k)E+13M	2E+1M	7 168	6 144	v	v
文献[20]	≥1 024	12E+11M	11E+7M	1E+1M	9 232	6 144	v	v
本文方案	≥160	17C+7J	11C+6J	1C+1J	1 136	320	v	v
其中，E、M分别表示有限域上模幂、模乘运算，C、J表示椭圆曲线点乘、点加运算，k表示被撤销的成员个数，“×”表示不具备该过程，“v”表示具备该过程。并且假定有限域G中元素为1 024 bit,ECC中元素为160 bit，时间长度为16 bit。

方案	理论基础	模数大小/bit	成员可撤销	前向安全性	防止金额篡改	防止多重支付
Zhang方案	有限域离散对数问题	≥1 024	v	×	×	×
FEI方案	有限域离散对数问题	≥1 024	×	×	v	v
本文方案	椭圆曲线离散对数问题	≥160	v	v	v	v
注：其中“v”表示具备该性质，“×”表示不具备该性质。