基于格的数字签名方案研究

发布时间：2018-06-29 00:28

本文选题：公钥密码学 + 数字签名　；参考：《中国科学技术大学》2014年博士论文

【摘要】：数字签名方案是公钥密码学的重要组成部分,它可以用来鉴别用户的身份和数据的完整性。随着网络通信的普及和新兴应用的涌现,需要处理的安全问题越来越多,数字签名方案因而发挥着越来越重要的作用。基于格上困难问题的数字签名方案是一类特殊的数字签名方案,相比其他种类的数字签名方案来说,这类数字签名方案具有更坚实的安全基础和更高的计算效率。此外,基于格的数字签名方案还能够抵御未来量子计算机的攻击,是公钥密码学的一个研究热点。尽管目前已经有一些基于格的数字签名方案出现,但是种类还是偏少,并且它们的存储和通信开销普遍较大,这大大限制了此类数字签名方案的应用和大规模普及。有鉴于此,本文从丰富格上数字签名方案的种类及提高它们的效率两方面着手,取得了以下研究成果： 1.设计了首个基于格的消息恢复签名方案,并在随机预言模型下证明了方案的安全性。相比已有的格上数字签名,该签名方案更加高效。 2.提出了环签名方案的一种较强的安全模型,并在该模型下设计了一种可证安全的格上环签名方案,该方案比以往的格上环签名方案更高效。 3.采用新的设计方法提出了一种新的可证安全的格上身份基签名方案,该方案比以往的格上身份基签名方案效率更高。此外,根据这个新的身份基签名方案提出了格上第一个允许消息恢复的身份基签名方案。该方案在随机预言模型下是可证安全的,且效率比格上标准的身份基签名方案更高。 4.提出了两个新的格上分层的身份基签名方案。以往的格上分层的身份基签名方案,用户的签名私钥和签名长度大小都随着用户身份深度的增加而增加,不利于此类签名方案在大规模用户环境下的应用。为此,分别提出了标准模型下可证安全的和随机预言模型下可证安全的格上分层的身份基签名方案,它们的签名私钥和签名长度大小均是较小的固定值,因而能更好的满足实际应用需要。 5.将格上数字签名方案从传统的公钥密码系统和身份基密码系统推广到无证书密码系统和基于证书的密码系统中,分别设计了首个格上无证书签名方案和基于证书的签名方案,并在随机预言模型下证明了这两个方案的安全性。由于无证书签名和基于证书的签名具有较高的安全性和效率,这使得格上数字签名方案向实用化方向又迈进了一步。
[Abstract]:Digital signature scheme is an important part of public key cryptography, it can be used to identify the identity of users and the integrity of data. With the popularization of network communication and the emergence of new applications, more and more security problems need to be dealt with, so digital signature schemes play a more and more important role. The digital signature scheme based on the difficult problem on the lattice is a kind of special digital signature scheme. Compared with other digital signature schemes, this kind of digital signature scheme has more solid security foundation and higher computational efficiency. In addition, the lattice-based digital signature scheme can resist the attack of future quantum computers, and it is a hotspot in public key cryptography. Although there are some lattice-based digital signature schemes, there are still a few types, and their storage and communication costs are generally large, which greatly limits the application and large-scale popularity of this kind of digital signature schemes. In view of this, this paper starts with the types of digital signature schemes on rich lattices and improves their efficiency, and obtains the following research results: 1. The first lattice-based message recovery signature scheme is designed, and the security of the scheme is proved under the stochastic prophecy model. Compared with the existing digital signature on the lattice, this signature scheme is more efficient. 2. 2. In this paper, a strong security model of ring signature scheme is proposed, and a provable secure upper ring signature scheme is designed under this model. The scheme is more efficient than the previous scheme. Using a new design method, a new verifiable secure signature scheme is proposed, which is more efficient than the previous scheme. In addition, according to the new identity-based signature scheme, the first identity-based signature scheme on the lattice that allows message recovery is proposed. The proposed scheme is provable and secure in random oracle model and is more efficient than the standard signature scheme based on identity. 4. Two new hierarchical identity base signature schemes are proposed. In previous hierarchical signature schemes, the signature private key and signature length increase with the increase of the user's identity depth, which is not conducive to the application of this signature scheme in the large-scale user environment. For this reason, we propose a hierarchical identity base signature scheme with provable security in standard model and probabilistic security in random prophecy model. Their signature private key and signature length are both small fixed values. Thus can better meet the actual application needs. 5. The digital signature scheme on lattice is extended from the traditional public key cryptosystem and the identity based cryptosystem to the certificate-free cryptosystem and the certificate-based cryptosystem. The first signature-free signature scheme and the certificate-based signature scheme are designed, respectively. The security of the two schemes is proved under the stochastic prediction model. Due to the high security and efficiency of the non-certificate signature and the certificate-based signature, the digital signature scheme on the lattice has taken a step forward in the practical direction.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.1;O153.1

【相似文献】