格上基于身份的变色龙签名方案

张彦华; 陈岩; 刘西蒙; 尹毅峰; 胡予濮

doi:10.11999/JEIT230155

格上基于身份的变色龙签名方案

doi: 10.11999/JEIT230155

1.
郑州轻工业大学计算机与通信工程学院郑州 450001
2.
福州大学数学与计算机科学学院福州 350108
3.
西安电子科技大学通信工程学院西安 710071

基金项目: 国家自然科学基金(61802075)，河南省自然科学基金(222300420371，202300410508)，河南省网络密码技术重点实验室开放课题(LNCT2022-A09)，河南省高等学校重点科研项目(22A520047)

详细信息

作者简介:
张彦华：男，讲师，研究方向为格公钥密码学、属性基密码学和后量子密码学等

陈岩：男，硕士生，研究方向为格公钥密码、基于身份的密码等

刘西蒙：男，研究员，研究方向为私计算、密文数据挖掘等

尹毅峰：男，教授，研究方向为群组密钥协商等

胡予濮：男，教授，研究方向为多线性映射、后量子密码学等

通讯作者:
张彦华 yhzhang@email.zzuli.edu.cn

中图分类号: TP309
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出版历程
- 收稿日期: 2023-03-14
- 修回日期: 2023-07-12
- 网络出版日期: 2023-07-21
- 刊出日期: 2024-02-29

Identity-Based Chameleon Signature Schemes over Lattices

1.
College of Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China
2.
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China
3.
School of Telecommunications Engineering, Xidian University, Xi’an 710071, China

Funds: The National Natural Science Foundation of China (61802075), The Natural Science Foundation of Henan Province (222300420371, 202300410508), The Open Subjects of Henan Provincial Key Laboratory of Network Cryptography (LNCT2022-A09), The Key Scientific Research Project of Higher Education of Henan Province (22A520047)

摘要

摘要: 变色龙签名(CS)是一种比较理想的指定验证者签名，其采用变色龙哈希函数来实现签名的不可传递性，使得任意第三方不信任指定验证者所披露的内容，且避免了不可否认签名必须在线交互验证的缺陷。在满足不可传递性的同时，变色龙签名还要求满足不可伪造性以及签名者可拒绝性和不可抵赖性等。针对基于大整数分解或离散对数等数论难题的变色龙签名无法抵御量子计算机攻击，以及用户对公钥数字证书依赖的问题，该文给出了格上基于身份的变色龙签名(IBCS)，新方案避免了已有方案存在的签名者无法拒绝指定验证者伪造的签名的安全性漏洞，并将最终签名的传输开销由平方级降为线性级；进一步地，针对变色龙签名在仲裁阶段不可传递性失效的问题，给出了格上抗消息暴露的基于身份的变色龙签名，新方案使得签名者能够在不暴露消息内容的条件下拒绝任意敌手伪造的变色龙签名。特别地，基于格上经典的小整数解问题，两个方案在随机预言机模型下是可证明安全的。
- 变色龙签名 /
- 格 /
- 基于身份的密码 /
- 不可传递性 /
- 抗消息暴露
Abstract: Chameleon Signature (CS) is an ideal designated verifier signature, it realizes non-transferability by using chameleon hash function, makes any third party distrust the content disclosed by a designated verifier, and avoids the shortcoming of online interactive verification of undeniable signature. In addition to non-transferability, CS also should satisfy unforgeability, deniability, non-repudiation for the signer, and so on. To solve the problems that cryptosystems based on the number theory problems such as integer factorization or discrete logarithm cannot resist quantum computing attacks and users rely on digital certificates, an Identity-Based Chameleon Signature (IBCS) over lattices is proposed, the new scheme avoids the security vulnerability that the signer cannot reject the forged signature of the designated verifier in the existing schemes, and reduces the transmission cost of the final signature from square to linear; Furthermore, to solve the failure problem of non-transferability in the arbitration phase, an IBCS scheme with exposure-freeness over lattices is proposed, the new scheme enables the signer to reject a forged signature of any adversary without exposing the real message. Particularly, based on the hardness of the small integer solution problem, both schemes can be proved secure in the random oracle model.
- Chameleon Signature (CS) /
- Lattice /
- Identity-based cryptography /
- Non-transferability /
- Exposure- freeness

HTML全文

表 1 效率分析

方案	公共参数长度	签名长度	不可伪造性	不可传递性	可拒绝性	不可抵赖性	抗消息暴露性	安全模型
文献[12]	$\tilde {\mathcal{O} }\left( { {n^2} } \right)$	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \times $	$ \surd $	$ \times $	$ \surd $	$ \times $	随机预言机
文献[13]	$ \tilde {\mathcal{O}}\left( {{n^3}} \right) $	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \surd $	$ \surd $	$ \times $	$ \surd $	$ \times $	标准
文献[14]	$ \tilde {\mathcal{O}}\left( {{k_0} \cdot {n^2}} \right) $	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \surd $	$ \times $	$ - $	$ - $	$ - $	标准
文献[15]	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \tilde {\mathcal{O}}\left( {{k_1} \cdot n} \right) $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \times $	随机预言机
本文方案1	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \tilde {\mathcal{O}}\left( n \right) $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \times $	随机预言机
本文方案2	$ \tilde {\mathcal{O}}\left( {{n^2}} \right) $	$ \tilde {\mathcal{O}}\left( n \right) $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	$ \surd $	随机预言机
注：$ {k_0} $表示同态计算的数据集尺寸，$ {k_1} $表示有向无环图的内部顶点数；$ \times $表示不满足，$ \surd $表示满足，$ - $表示不考虑。

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