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作为应对量子时代密码危机的有效措施,抗量子计算攻击的公钥密码体制得到了国内外学者的广泛关注.基于格的公钥密码体制除抗量子计算攻击外,还有其他优良特性,如最差情况/平均情况等价性以及运算高效性等,因此基于格的公钥密码体制成为抗量子计算密码领域的一个研究热点.签名私钥泄露是签名体制面临的最严重的安全威胁.前向安全签名体制能有效减轻签名私钥泄露所带来的危害,因此它是一种极具应用价值的带附加性质的签名体制.有鉴于此,本文首先基于格技术构造了一个前向安全签名方案,该方案的签名过程由Gentry等提出的带前像抽样的陷门单向函数实现,密钥更新过程由Cash等提出的被称为盆景树的密码结构实现.且我们所提出的方案使用了二叉树结构.然后,在随机预言模型下基于小整数解(SIS)问题困难性证明了所提出的方案的前向安全性,即在适应性选择消息攻击下的存在性不可伪造性.最后,以所提出的方案为基础,本文构造了一个基于格的前向安全的身份基签名方案.
As an effective measure to deal with cryptanalysis in the quantum age, the public-key cryptosystem against quantum computing attacks has drawn wide attention from domestic and foreign scholars.Grid-based public-key cryptosystems have other excellent features in addition to quantum-resistant attacks, such as Therefore, the public key cryptosystem based on lattice has become a research hotspot in the field of quantum cryptography.Signature private key leakage is the most serious security threat to the signature system. Therefore, it is a valuable signature system with additional properties.In view of this, this paper constructs a forward secure signature scheme based on lattice technology , The signature process of the scheme is realized by a one-way trapdoor-like function with sampling as before, which is proposed by Gentry et al. The key update process is implemented by a cryptographic structure called Bonsai Tree proposed by Cash et al. And the scheme we proposed uses Binary tree structure.Thirdly, the forward security of the proposed scheme is proved based on the difficulty of SIS problem under the random oracle model, that is, Adaptive chosen existence can not be forged message attack. Finally, the proposed scheme is based, before we construct a lattice-based group signature scheme to secure identity.