Hierarchical Identity-Based Signature Scheme Based on SM9

XIE Jia; LUAN Xiaojie; FAN Changyou; WANG Luyu; GAO Juntao; WANG Baocang

doi:10.12263/DZXB.20250954

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Hierarchical Identity-Based Signature Scheme Based on SM9

PAPERS | 更新时间：2026-05-28

- Hierarchical Identity-Based Signature Scheme Based on SM9
- ACTA ELECTRONICA SINICA Vol. 54, Issue 2, Pages: 710-722(2026)
- 作者机构：
  
  1.河南财经政法大学计算机与信息工程学院，河南郑州 450046
  2.西安电子科技大学通信工程学院，陕西西安 710071
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(61802110);the Key Research and Development and Promotion Program of Henan Province(242102210149;222102210326);the Key Research Foundation for Higher Education of Henan Province(23A413001;25A413008);the NG Teng Fong/Sino Foundation for Youth in Henan Universityof Economics and Law, and the Research Foundation in Henan University of Economics and Law
- DOI：10.12263/DZXB.20250954
  CLC： TP309;
- Received：19 December 2025，
  
  Accepted：03 February 2026，
  
  Published：25 February 2026
- 稿件说明：
移动端阅览
谢佳, 栾小杰, 范长友, 等. 基于国密SM9的分层标识签名方案[J]. 电子学报, 2026, 54(02): 710-722.

XIE Jia, LUAN Xiaojie, FAN Changyou, et al. Hierarchical Identity-Based Signature Scheme Based on SM9[J]. Acta Electronica Sinica, 2026, 54(02): 710-722.
谢佳, 栾小杰, 范长友, 等. 基于国密SM9的分层标识签名方案[J]. 电子学报, 2026, 54(02): 710-722. DOI：10.12263/DZXB.20250954

XIE Jia, LUAN Xiaojie, FAN Changyou, et al. Hierarchical Identity-Based Signature Scheme Based on SM9[J]. Acta Electronica Sinica, 2026, 54(02): 710-722. DOI：10.12263/DZXB.20250954

摘要

我国自主研发的SM9密码算法是重要的商用密码标准和国家标准，对于密码算法的国产化替代具有关键作用。然而，原始SM9数字签名作为标识签名机制，存在不具备分层特征的局限性，在大规模网络环境中极易因用户量激增导致密钥生成中心压力过大和网络拥堵。为解决这一难题，本文首次提出了一种基于国密SM9算法的分层标识签名方案。方案创造性地引入分层签名技术，通过各级节点共同分担密钥生成任务，有效减轻了密钥生成中心的私钥生成与分发压力，完美适用于车联网、区块链等大规模、多层级网络场景。在技术实现上，为了适配SM9算法，本方案基于素数阶群，采用高效的分层技术，完成由上一层签名私钥到下一层级签名私钥的分配，以此来形成一种层级式的私钥更新机制；紧接着用户再根据其签名私钥来进行数字签名，生成的签名值仅由三个群元素构成，相较于原始SM9算法仅增加一个群元素，并实现了常数级签名长度，与层级深度无关。在随机谕言机模型下，给出了方案的严格安全性证明，证明方案满足选择消息和身份攻击下的存在性不可伪造，且方案的安全性可规约至（

，

）-SDH困难问题。理论分析与实验结果表明，本方案在签名生成和验证效率上具有显著优势：随着系统层数

的增加，本方案的签名生成和签名验证时间趋于常量级别，明显优于现有基于双线性对的分层标识签名方案。特别地，当系统层数

为2~10时，签名生成和验证时间分别约为2.24 ms和36.08 ms，签名和验证效率较现有最优的分层签名方案分别提升0.03~2.79倍和0.87~1.27倍。且随着

的增大，效率提升就越大，当

为100时，签名生成和验证效率较现有最优的分层签名方案分别提升约34倍和4.5倍。最后，将本方案应用于车联网身份认证场景，成功解决了车联网环境中因用户量激增而导致的网络拥堵问题，实现了轻量化与去中心化的身份认证机制，为构建高效、安全的国产化大规模网络环境提供了重要的技术支撑。

Abstract

The SM9 cryptographic algorithm

independently developed by China

serves as a critical commercial cryptography standard and national standard

playing a key role in the localization and substitution of cryptographic algorithms. However

the original SM9 digital signature

as an identity-based signature mechanism

suffers from the limitation of not supporting hierarchical features. In large-scale network environments

this can easily lead to excessive pressure on the key generation center and network congestion due to the surge in the number of users. To address this challenge

this paper proposes the first hierarchical identity-based signature scheme based on the national cryptographic SM9 algor

ithm. The scheme innovatively introduces hierarchical signature technology

distributing the key generation task across multiple levels of nodes

effectively alleviating the private key generation and distribution pressure on the key generation center. It is ideally suited for large-scale

multi-layered network scenarios such as the Internet of Vehicles and blockchain. In terms of technical implementation

to adapt to the SM9 algorithm

this scheme is based on prime-order groups and employs efficient hierarchical technology to allocate signature private keys from the upper level to the next level

thereby forming a hierarchical private key update mechanism. Subsequently

users generate digital signatures based on their signature private keys. The resulting signature value consists of only three group elements

adding just one more group element compared to the original SM9 algorithm

and achieves a constant signature length independent of the hierarchical depth. Under the random oracle model

a rigorous security proof of the scheme is provided

demonstrating that the scheme satisfies existential unforgeability under chosen message and identity attacks

and its security can be reduced to the (

)-SDH hardness problem. Theoretical analysis and experimental results show that the proposed scheme has significant advantages in signature generation and verification efficiency. As the number of system layers

increases

the signature generation and verification time of this scheme tends to remain constant

significantly outperforming existing hierarchical identity-based signature schemes based on bilinear pairings. Specifically

when the number of system layers

ranges from 2 to 10

the signature generation and verification times are approximately 2.24 ms and 36.08 ms

respectively

improving efficiency by 0.03 to 2.79 times and 0.87 to 1.27 times compared to the current optimal hierarchical signature schemes. Moreover

increases

the efficiency improvement becomes more pronounced: when

is 100

the signature generation and verification efficiency are enhanced by approximately 34 times and 4.5 times

respectively

compared to the existing optimal hierarchical signature schemes. Finally

the proposed scheme is applied to the identity authentication scenario of the Internet of Vehicles

successfully resolving network congestion caused by the surge in users in the IoV environment. It realizes a lightweight and decentralized identity authentication mechanism

providing crucial technical support for building efficient and secure large-scale network environments with localized cryptographic solutions.

关键词

Keywords

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