This paper first gives a regularity theorem and its corollary. Then, a new construction of generating hard random lattices with short bases is obtained by using this corollary. This construction is from a new perspective and uses a random matrix whose entries obeyed Gaussian sampling which ensures that the corresponding schemes have a wider application future in cryptography area. Moreover, this construction is more specific than the previous constructions, which makes it can be implemented easier in practical applications.

中文翻译：

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一种生成具有短碱基的硬随机晶格的新方法

本文首先给出了一个正则定理及其推论。然后，使用该推论获得了一种生成具有短碱基的硬随机晶格的新结构。这种结构是从一个新的角度出发的，它使用一个随机矩阵，其条目服从高斯采样，从而确保了相应的方案在密码学领域中具有更广阔的应用前景。而且，该结构比以前的结构更具体，这使得它可以在实际应用中更容易地实现。