层次型无证书全同态签名方案
Leveled Certificateless Fully Homomorphic Signature Scheme
DOI: 10.12677/csa.2025.1510250, PDF,    科研立项经费支持
作者: 李明祥*, 李润亚：河北金融学院金融研究所，河北 保定
关键词: 全同态签名；无证书；格；小整数解问题；Fully Homomorphic Signature； Certificateless； Lattices； Small Integer Solution Problem
摘要: 公钥密码体制具体可分为基于PKI的公钥密码体制、基于身份的公钥密码体制和无证书公钥密码体制。基于PKI的密码体制存在公钥证书管理问题。基于身份的密码体制消除了公钥证书管理问题，但却引入了密钥托管问题。无证书密码体制消除了公钥证书管理问题，同时又避免了密钥托管问题，它是一种具有卓越性能的公钥密码体制。全同态签名体制允许在不知晓签名私钥的情况下对已签名的数据执行任意的计算操作，并同态地导出计算结果的有效签名。全同态签名体制在云计算、物联网等许多领域具有广泛的应用前景。目前，人们已提出了几个基于PKI的全同态签名方案和几个基于身份的全同态签名方案，却尚未提出无证书全同态签名方案。因此，本文首先给出了层次型无证书全同态签名方案的形式化定义和选择性选择身份和固定性选择消息攻击下的存在性不可伪造性(EU-sID-sCMA)的安全模型。其次，设计了一个基于格的层次型无证书全同态签名方案。再次，在标准模型下基于小整数解问题的困难性证明了所设计的方案满足EU-sID-sCMA安全性。最后，给出了所设计的方案的具体参数设置。
Abstract: The public key cryptosystem can be divided into the PKI-based public key cryptosystem, the identity-based public key cryptosystem, and the certificateless public key cryptosystem. The PKI-based cryptosystem has a public key certificate management issue. The identity-based cryptosystem eliminates the public key certificate management issue but introduces a key escrow problem. The certificateless cryptosystem eliminates the public key certificate management issue while avoiding the key escrow problem. Therefore, it is a public key cryptosystem with excellent properties. A fully homomorphic signature scheme allows anyone to perform arbitrary computations on signed data without having the private signing key and to derive a valid signature for the result homomorphically. The fully homomorphic signature scheme has significant potential applications in various fields, such as cloud computing and the Internet of Things. So far, several PKI-based and identity-based fully homomorphic signature schemes have been proposed, but no certificateless fully homomorphic signature scheme has been presented. As a result, this paper first gives a formal definition and a security model for existential unforgeability under selective chosen-identity and static chosen-message attacks (EU-sID-sCMA) for a leveled certificateless fully homomorphic signature scheme. Secondly, this paper designs a leveled certificateless fully homomorphic signature scheme from lattices. Thirdly, this paper proves that the proposed scheme satisfies the EU-sID-sCMA security based on the hardness of the small integer solution problem in the standard model. Finally, this paper provides the practical parameter settings of the proposed scheme.
文章引用：李明祥, 李润亚. 层次型无证书全同态签名方案[J]. 计算机科学与应用, 2025, 15(10): 52-66. https://doi.org/10.12677/csa.2025.1510250

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