Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 이향숙 | - |
dc.date.accessioned | 2023-01-04T16:31:02Z | - |
dc.date.available | 2023-01-04T16:31:02Z | - |
dc.date.issued | 2022 | - |
dc.identifier.issn | 0304-9914 | - |
dc.identifier.issn | 2234-3008 | - |
dc.identifier.other | OAK-32642 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/262952 | - |
dc.description.abstract | For two dimensional lattices, a Gaussian basis achieves all two successive minima. For dimension larger than two, constructing a pairwise Gaussian basis is useful to compute short vectors of the lattice. For three dimensional lattices, Semaev showed that one can convert a pairwise Gaussian basis to a basis achieving all three successive minima by one simple reduction. A pairwise Gaussian basis can be obtained from a given basis by executing Gauss algorithm for each pair of basis vectors repeatedly until it returns a pairwise Gaussian basis. In this article, we prove a necessary and sufficient condition for a pairwise Gaussian basis to achieve the first k successive minima for three dimensional lattices for each k is an element of {1, 2, 3} by modifying Semaev's condition. Our condition directly checks whether a pairwise Gaussian basis contains the first k shortest independent vectors for three dimensional lattices. LLL is the most basic lattice basis reduction algorithm and we study how to use LLL to compute a pairwise Gaussian basis. For delta >= 0.9, we prove that LLL(delta) with an additional simple reduction turns any basis for a three dimensional lattice into a pairwise SV-reduced basis. By using this, we convert an LLL reduced basis to a pairwise Gaussian basis in a few simple reductions. Our result suggests that the LLL algorithm is quite effective to compute a basis with all three successive minima for three dimensional lattices. | - |
dc.language | English | - |
dc.publisher | KOREAN MATHEMATICAL SOC | - |
dc.subject | Lattice | - |
dc.subject | pairwise-Gaussian basis | - |
dc.subject | lattice basis reduction | - |
dc.subject | LLL | - |
dc.title | ON PAIRWISE GAUSSIAN BASES AND LLL ALGORITHM FOR THREE DIMENSIONAL LATTICES | - |
dc.type | Article | - |
dc.relation.issue | 6 | - |
dc.relation.volume | 59 | - |
dc.relation.index | SCIE | - |
dc.relation.index | SCOPUS | - |
dc.relation.index | KCI | - |
dc.relation.startpage | 1047 | - |
dc.relation.lastpage | 1065 | - |
dc.relation.journaltitle | JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | - |
dc.identifier.doi | 10.4134/JKMS.j210496 | - |
dc.identifier.wosid | WOS:000885919200001 | - |
dc.author.google | Kim, Kitae | - |
dc.author.google | Lee, Hyang-Sook | - |
dc.author.google | Lim, Seongan | - |
dc.author.google | Park, Jeongeun | - |
dc.author.google | Yie, Ikkwon | - |
dc.contributor.scopusid | 이향숙(34870017000) | - |
dc.date.modifydate | 20230411110859 | - |