摘要： 提出了最短向量已知格的概念。通过对循环格的分析，得到了循环格是最短向量已知格的两个定理。为了得到随机性更好的最短向量已知格，提出了伪循环格的概念，并且给出了伪循环格是最短向量已知格的充分条件。相关的定理都是构造性的，通过简单的算法就可以快速生成最短向量已知格。格基进行随机化的一般性算法。

关键词: 最短向量已知格, 循环格, 伪循环格, 格基规约

Abstract:

SVK-lattices, in which the shortest vector in the lattice is known, are proposed for the first time. Several theorems about the relationship between cyclic lattices and SVK-lattices are proved. By these constructive theorems, SVK-lattices can be generated simply. Pseudo-cyclic lattices whose random properties better than cyclic lattices also are investigated for the first time. An algorithm for randomizing SVK-lattices which are obtained by cycle lattices or pseudo- cycle lattices are given at the end of this paper. Some examples are shown in appendix.

Key words: SVK-lattice, Cyclic lattice, Pseudo-cyclic lattice, Lattice reduce

中图分类号: 

• TP309