A Proxy Ring Signature Scheme Based on SM9 Algorithm

doi:10.3969/j.issn.1671-1122.2025.12.006

Abstract

Abstract:

In view of the application requirements of proxy ring signature in scenarios requiring high user identity protection, this paper proposed a proxy ring signature scheme based on SM9 digital signature algorithm. The scheme included six steps: setup, extract, proxydelegation, verifyproxy, sign and verify. The Key Generation Center uses the user ID to calculate the user’s key, and the original signer used the known information to calculate the proxy authorization, and then delegated the proxy authorization to the proxy signer. After the proxy signer verified the authentiecity of the authorization, the proxy ring signature was generated through the signature step, and the generated signature can be verified by the authentication algorithm. The scheme not only realizes the entrustment of signature rights, but also protects the privacy of signers through the anonymity of ring signatures. It is also proved that the scheme is unforgeable under adaptive selective message attacks under random prophecy model. The efficiency analysis shows that the proposed scheme has higher efficiency and better practicability.

Key words: SM9, digital signature, proxy ring signature

CLC Number:

TP309

ZHANG Xuefeng, WANG Kehang. A Proxy Ring Signature Scheme Based on SM9 Algorithm[J]. Netinfo Security, 2025, 25(12): 1901-1913.

Figures/Tables 9

References 23

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特性	文献[7]	文献[16]	文献[19]	文献[23]	本文方案
可验证性	√	√	√	√	√
不可伪造性	√	√	√	√	√
可代理	√	×	×	√	√
匿名性	√	√	√	×	√

符号	定义
$\|{{G}_{1}}\|$	群${{G}_{1}}$中元素的大小
$\|{{G}_{2}}\|$	群${{G}_{2}}$中元素的大小
$\|{{G}_{T}}\|$	群${{G}_{T}}$中元素的大小
$\|Z_{N}^{*}\|$	$Z_{N}^{*}$中元素的大小
$\|G\|$	群$G$中元素的大小
$\|{{Z}_{q}}\|$	${{Z}_{q}}$中元素的大小
$n$	环成员数量

方案	代理委托	签名长度/bit
文献[7]	$\|Z_{N}^{*}\|+\|{{G}_{1}}\|$	$\|Z_{N}^{*}\|+2\|{{G}_{1}}\|$
文献[16]	—	$\|Z_{N}^{*}\|+n\|{{G}_{1}}\|$
文献[19]	—	$\|Z_{N}^{*}\|+n\|{{G}_{1}}\|+\|{{G}_{T}}\|$
文献[23]	$2\|{{G}_{1}}\|+3\|{{G}_{T}}\|$	$\|Z_{N}^{*}\|+\|{{G}_{1}}\|+\|{{G}_{T}}\|$
本文方案	$2\|{{G}_{1}}\|$	$\|Z_{N}^{*}\|+n\|{{G}_{1}}\|+\|{{G}_{T}}\|$

符号	定义	运行时间/$\text{ms}$
$BP$	双线性对运算	12.5270
${{M}_{{{G}_{1}}}}$	群${{G}_{1}}$中的点乘运算	0.0242
${{M}_{{{G}_{2}}}}$	群${{G}_{2}}$中的点乘运算	0.0357
${{M}_{{{G}_{T}}}}$	群${{G}_{T}}$中的乘法运算	3.9232
${{E}_{{{G}_{T}}}}$	群${{G}_{T}}$中的幂运算	1.3327
$H$	哈希操作	10.1442
$n$	环成员数量	—

方案	代理委托	代理验证	签名	验证
文献[7]	—	—	(3n+1)M_G₁+(n-1)H	nM_G₁+2BP+nH
文献[16]	—	—	(n+1)M_G₁+ (n-1)M_G₂+(n-1)M_GT+ nBP+(n-1)E_GT+ (2n-1)H	nM_G₂+nM_GT+ nBP+2nH
文献[19]	—	—	(n+4)M_G₁+M_G₂+ 2M_GT+4BP+H	2M_G₁+M_G₂+4M_GT+ 4BP+3E_GT+2H
文献[23]	2M_G₁+3E_GT+ 2H	M_G₁+M_G₂+ 2BP+E_GT+2H	M_G₁+E_GT+H	2M_G₁+M_GT+ BP+E_GT+4H
本文方案	3M_G₁+E_GT+ H	M_G₂+M_GT+ BP+E_GT	(n+2)M_G₁+2M_G₂+ 3M_GT+3BP+E_GT+H	2M_G₁+M_G₂+4M_GT+ 2BP+2E_GT+H