带鲁棒性的子分组多重Schnorr签名方案

doi:10.11959/j.issn.2096-109x.2024059

网络与信息安全学报 ›› 2024, Vol. 10 ›› Issue (4): 132-142.doi: 10.11959/j.issn.2096-109x.2024059

• 学术论文 • 上一篇

带鲁棒性的子分组多重Schnorr签名方案

张振琦¹, 朱秋池¹, 王志伟¹^,²()

^1.南京邮电大学计算机学院，江苏南京 210023
^2.南京邮电大学江苏省大数据安全与智能处理重点实验室，江苏南京 210023

收稿日期:2023-12-15 修回日期:2024-07-28 出版日期:2024-08-25 发布日期:2024-09-14
通讯作者: 王志伟 E-mail:zhwwang@njupt.edu.cn
作者简介:张振琦（2000- ），男，河南商丘人，南京邮电大学硕士生，主要研究方向为密码协议。
朱秋池（2000- ），女，江苏盐城人，南京邮电大学硕士生，主要研究方向为应用密码学。
王志伟（1976- ），男，南京邮电大学教授，主要研究方向为云/雾计算安全、区块链、密码协议。
基金资助:
国家自然科学基金(62372245)

Robust Schnorr-based subgroup multi-signature scheme

Zhenqi ZHANG¹, Qiuchi ZHU¹, Zhiwei WANG¹^,²()

^1.School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
^2.Jiangsu Key Laboratory of Big Data Security and Intelligent Processing, Nanjing University of Posts and Telecommunications, Nanjing 210023，China

Received:2023-12-15 Revised:2024-07-28 Online:2024-08-25 Published:2024-09-14
Contact: Zhiwei WANG E-mail:zhwwang@njupt.edu.cn
Supported by:
The National Natural Science Foundation of China(62372245)

摘要/Abstract

摘要：

共识机制是区块链系统的核心技术，但是目前的共识机制存在3个问题，即共识效率低、可靠性和安全性低、计算复杂度高。针对这些问题，提出了一种新的子分组多重Schnorr签名方案，该方案既拥有Schnorr数字签名密码体制的计算复杂度低优势，又拥有子分组多重签名的优势（它可以从集合的全体成员中选择不定数量的成员组成子分组，以代替群组产生多重签名，由于子分组是不可预知的，因此可以有效避免出现 $B y z a n t i n e$ 叛徒，提高了方案的安全性，解决了共识机制存在的可靠性和安全性低、计算复杂度高的问题）。该方案引入了公共第三方（PTP，public third party），PTP由可自动公开执行的智能合约充当，完全公开透明，不仅可以抵御流氓密钥攻击，还减少了签名过程的总通信轮次和时间开销，解决了共识机制存在的共识效率低问题。同时，详细证明了该方案具有鲁棒性，可以提高共识机制的安全性；基于离散对数假设，该方案在随机预言模型下具有不可伪造性。理论分析和实验结果证明，该方案拥有更小的公钥长度、私钥长度、单签名长度和多重签名长度，拥有更少的通信轮次，签名生成算法和验证签名算法的时间开销更小，应用在共识机制上具有更优越的性能。

关键词: Schnorr签名, 多重签名, 鲁棒性, 离散对数假设, 随机预言模型

Abstract:

The consensus mechanism has been considered as the core technology of blockchain systems. However, current consensus mechanisms have encountered three issues: low consensus efficiency, low reliability and security, and high computational complexity. To address these issues, a new Schnorr-based subgroup multi-signature scheme was proposed. This scheme retained the advantage of low computational complexity inherent in the Schnorr digital signature cryptosystem while incorporating the benefits of subgroup multi-signature. It allowed an indeterminate number of members from the entire set to form subgroups to generate multi-signatures, which replaced the group signature. The unpredictability of the subgroups effectively avoided the occurrence of Byzantine traitors, thus enhancing security and solving the problems of low reliability, security, and high computational complexity in consensus mechanisms. Additionally, a public third party was introduced, implemented by automatically and publicly executed smart contracts. It was completely open and transparent, capable of resisting the rogue public-key attack, and reduced the total number of communication rounds and time overhead in the signing process, addressing the issue of low consensus efficiency. The robustness of this scheme was proven in detail, demonstrating an improvement in the security of consensus mechanisms. Based on the discrete logarithm assumption, the scheme was shown to be unforgeable in the random oracle model. Theoretical analysis and experimental results show that the scheme possesses smaller public key length, private key length, single signature length, and multi-signature length, with fewer communication rounds and reduced time overhead in the signature generation and verification algorithms, providing superior performance when applied to consensus mechanisms.

Key words: Schnorr signature, multi-signature, robustness, discrete logarithmic assumption, random oracle model

中图分类号:

TP303

张振琦, 朱秋池, 王志伟. 带鲁棒性的子分组多重Schnorr签名方案[J]. 网络与信息安全学报, 2024, 10(4): 132-142.

Zhenqi ZHANG, Qiuchi ZHU, Zhiwei WANG. Robust Schnorr-based subgroup multi-signature scheme[J]. Chinese Journal of Network and Information Security, 2024, 10(4): 132-142.

图/表 6

表1

不同方案的性能对比"

方案	私钥长度	公钥长度	签名长度	通信轮次
mBCJ	$\| Z p \|$	$2 \| G \| + \| Z p \|$	$2 \| G \| + 3 \| Z p \|$	$4 n (n - 1)$
MuSig2	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$4 n (n - 1)$
DWMS	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$4 n (n - 1)$
MEMS	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$5 n$
RSMSP	$\| Z p \|$	$\| G \|$	$\| G \|$	$2 n (n - 1)$
本文	$\| Z p \|$	$\| G \|$	$\| Z p \|$	$5 n$

表1

表2

时间开销与安全性对比"

方案	签名算法开销	验证算法开销	聚合算法开销	鲁棒性	困难问题
mBCJ	$5 e x p$	$6 e x p$	$0$	否	$D L$
MuSig2	$(2 V - 1) e x p$	$2 e x p$	$n e x p$	否	$O M D L$
DWMS	$(m n + m) e x p$	$2 e x p$	$n e x p$	否	$O M D L$
MEMS	$1 e x p$	$2 e x p$	$n e x p$	否	$D L$
RSMSP	$n e x p$	$2 e x p$	$n e x p$	是	$C D H$
本文	$1 e x p$	$2 e x p$	$n e x p$	是	$D L$

表2

图1

图2

图3

图4

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方案	私钥长度	公钥长度	签名长度	通信轮次
mBCJ	$\| Z p \|$	$2 \| G \| + \| Z p \|$	$2 \| G \| + 3 \| Z p \|$	$4 n (n - 1)$
MuSig2	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$4 n (n - 1)$
DWMS	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$4 n (n - 1)$
MEMS	$\| Z p \|$	$\| G \|$	$\| G \| + \| Z p \|$	$5 n$
RSMSP	$\| Z p \|$	$\| G \|$	$\| G \|$	$2 n (n - 1)$
本文	$\| Z p \|$	$\| G \|$	$\| Z p \|$	$5 n$

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带鲁棒性的子分组多重Schnorr签名方案

Robust Schnorr-based subgroup multi-signature scheme

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