【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。最后给出了对格基进行随机化的一般性算法。更多还原

【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.更多还原