论文标题
钝的格子底座
Obtuse Lattice Bases
论文作者
论文摘要
晶格的减少是一种算法，将晶格的给定基础转换为另一个晶格基础，因此找到最短的向量和最接近的向量等问题变得更容易解决。我们定义了一类称为钝化碱的基础，并表明任何晶格基础都可以转换为钝化基础。最短的向量$ \ mathbf {s} $可以写入$ \ mathbf {s} = v_1 \ mathbf {b} _1+\ dots+v_n \ v_n \ mathbf {b} _n $ where $ \ \ \ mathbf {b} _1 _1 _1，\ dots和dots， $ v_1，\ dots，v_n $是整数。当输入基础是钝的时，所有这些整数都可以选择为最短的向量呈阳性。钝基底座的这种属性使晶格枚举算法用于找到最短的向量呈指数速度。我们已经实施了用于制作基础钝的算法，并测试了一些小基础。
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called obtuse bases and show that any lattice basis can be transformed to an obtuse basis. A shortest vector $\mathbf{s}$ can be written as $\mathbf{s}=v_1\mathbf{b}_1+\dots+v_n\mathbf{b}_n$ where $\mathbf{b}_1,\dots,\mathbf{b}_n$ are the input basis vectors and $v_1,\dots,v_n$ are integers. When the input basis is obtuse, all these integers can be chosen to be positive for a shortest vector. This property of obtuse bases makes the lattice enumeration algorithm for finding a shortest vector exponentially faster. We have implemented the algorithm for making bases obtuse, and tested it some small bases.
