论文标题
量词后多阶段的秘密共享方案，使用不均匀的线性递归和Ajtai功能
Post-quantum Multi-stage Secret Sharing Schemes using Inhomogeneous Linear Recursion and Ajtai's Function
论文作者
论文摘要
Shamir和Blakley于1979年首先提出了秘密分享。为了避免原始方案的缺陷，研究人员提出了改进方案，其中多秘密共享方案（MSS）很重要。 MSS有三类，但是，我们专注于多阶段的秘密共享方案（MSSS）在此工作中以任何命令恢复秘密。通过观察文献中的不均匀线性递归（ILR），我们根据其中的不同变量结论了一般公式，并将ILR分为两种类型。利用这两种ILR，我们提出了四个具有Ajtai功能的可验证MSSS，这是一个基于晶格的功能。我们的计划具有以下优势。首先，我们的计划可以检测经销商和参与者的作弊，并且是多用途的。其次，我们有几种恢复秘密的方法。第三，由于方法的普遍性，我们可以将我们的方案变成其他类型的MSS。第四，由于我们利用基于晶格的功能来掩盖共享，因此我们的方案可以抵抗具有计算安全性量子计算机的攻击。最后，尽管我们的方案比一些已知的方案需要更多的内存消耗，但我们需要更少的时间消耗，这使得我们的方案更合适，面对有限的计算能力。
Secret sharing was firstly proposed in 1979 by Shamir and Blakley respectively. To avoid deficiencies of original schemes, researchers presented improvement schemes, among which the multi-secret sharing scheme (MSS) is significant. There are three categories of MSSs, however, we focus on multi-stage secret sharing scheme (MSSS) recovering secrets with any order in this work. By observing inhomogeneous linear recursions (ILRs) in the literature, we conclude a general formula and divide ILRs into two types according to different variables in them. Utilizing these two kinds of ILRs, we propose four verifiable MSSSs with Ajtai's function, which is a lattice-based function. Our schemes have the following advantages. Firstly, our schemes can detect cheat of the dealer and participants, and are multi-use. Secondly, we have several ways to restore secrets. Thirdly, we can turn our schemes into other types of MSSs due to the universality of our method. Fourthly, since we utilize a lattice-based function to mask shares, our schemes can resist the attack from the quantum computer with computational security. Finally, although our schemes need more memory consumption than some known schemes, we need much less time consumption, which makes our schemes more suitable facing limited computing power.
