基于哈希证明系统的区块链两方椭圆曲线数字签名算法研究

doi:10.3969/j.issn.1671-1122.2021.01.003

信息网络安全 ›› 2021, Vol. 21 ›› Issue (1): 19-26.doi: 10.3969/j.issn.1671-1122.2021.01.003

基于哈希证明系统的区块链两方椭圆曲线数字签名算法研究

刘峰¹^,², 杨杰², 齐佳音²()

1.华东师范大学计算机科学与技术学院,上海 200062
2.上海对外经贸大学人工智能与变革管理研究院,上海 200336

收稿日期:2020-10-28 出版日期:2021-01-10 发布日期:2021-02-23
通讯作者: 齐佳音 E-mail:qijiayin@139.com
作者简介:刘峰（1988—）,男,湖北,博士研究生,主要研究方向为区块链、数据科学|杨杰（1998—）,男,江苏,硕士研究生,主要研究方向为区块链、密码学、隐私保护|齐佳音（1972—）,女,陕西,教授,博士,主要研究方向为人工智能
基金资助:
国家重点研发计划(2017YFB0803304);国家自然科学基金(72042004)

Two-Party ECDSA for Blockchain Based on Hash Proof Systems

LIU Feng¹^,², YANG Jie², QI Jiayin²()

1. School of Computer Science and Technology, East China Normal University, Shanghai 200062, China
2. Institute of Artificial Intelligence and Change Management,Shanghai University of International Business and Economics, Shanghai 200336, China

Received:2020-10-28 Online:2021-01-10 Published:2021-02-23
Contact: QI Jiayin E-mail:qijiayin@139.com

摘要/Abstract

摘要：

椭圆曲线数字签名算法（ECDSA）是区块链密码学技术中常见的数字签名之一,其在加密货币、密钥身份认证等方面已被广泛应用。然而当前的区块链ECDSA算法灵活性较低、匿名性较弱且分散性不高,性能相对高效的应用实例也十分有限。基于哈希证明系统,文章提出一种适用于区块链的两方椭圆曲线数字签名算法。通过给定签名算法的数理逻辑及其安全模型,融入区块链进行测评,证明了方案的可行性。最后,对签名方案的安全性进行了分析,证实该方案无需交互性安全假设便可在零知识性的基础上减少通信开销。

关键词: 哈希证明系统, 椭圆曲线数字签名算法, 区块链, 安全性证明, 隐私保护

Abstract:

Elliptic curve signature ECDSA is one of the common digital signatures in blockchain cryptography technology, which has been widely used in cryptocurrency, key identity authentication, etc. However, current blockchain ECDSA algorithm is inflexible, weakly anonymous and poorly decentralized, and have limited examples of relatively high-performing applications. This study intended to propose a two-party elliptic curve signature suitable for blockchain with the help of Hash proof systems. Given the mathematical logic of the signature algorithm and its security model, its incorporation into the blockchain was evaluated to show the feasibility of the scheme. Finally, the security of the signature scheme was analyzed, and a simulation-based security proof was used to demonstrated that the scheme did not require interactive security assumptions and can reduce the overhead in communication with zero knowledge proof.

Key words: Hash proof system, ECDSA, blockchain, security proof, privacy protection

中图分类号:

TP309

刘峰, 杨杰, 齐佳音. 基于哈希证明系统的区块链两方椭圆曲线数字签名算法研究[J]. 信息网络安全, 2021, 21(1): 19-26.

LIU Feng, YANG Jie, QI Jiayin. Two-Party ECDSA for Blockchain Based on Hash Proof Systems[J]. Netinfo Security, 2021, 21(1): 19-26.

图/表 5

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参考文献 18

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符号标记	解释说明
$X$	NP问题的一个实例集合
$L$	归属$X$的NP语言集合
$W$	证明给定元素在$L$内的证据集合
$R$	定义语言$L$的二元关系,$R\subset X\times W$
${{Z}_{q}}$	整数模$q$的乘法群
$Z_{q}^{*}$	单位群
${{R}_{DL}}$	椭圆曲线离散对数知识的功能性函数
$F_{zk-com}^{{{R}_{DL}}}$	零知识性承诺函数
$F_{zk-proof}^{{{R}_{DL}}}$	零知识性承诺证明函数
${{R}_{HPS-DL}}$	基于哈希证明系统的零知识功能函数
$F_{zk}^{{{R}_{HPS-DL}}}$	零知识性哈希证明函数
$contrac{{t}_{bp}}$	用于背书备份加密信息的智能合约
$contrac{{t}_{ver}}$	用于验证共享公钥及签名的智能合约

基于哈希证明系统的区块链两方椭圆曲线数字签名算法研究

Two-Party ECDSA for Blockchain Based on Hash Proof Systems

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