Paper Info
Title
Two Types of Special Bases for Integral Lattices.
Abstract
Lattice basis reduction algorithms, such as LLL, play a very important role in cryptography, which usually aim to find a lattice basis with good \"orthogonality\". However, not every lattice has an orthogonal basis, which means that we can only find some nearly orthogonal bases for these lattices. In this paper, we show that every integral lattice must have two types of special bases related to the orthogonality. First, any integral lattice with rank more than 1 has a class of bases such that the angle between any two basis vectors lies in $$[\\frac{\\pi }{3},\\frac{2\\pi }{3}]$$. Second, any integral lattice with rank more than 2 has a class of bases such that any basis can be divided into two sets and the vectors in every set are pairwise orthogonal. To obtain such results, we introduce the technique called unimodular congruence transformation for the Gram matrix.
Year
DOI
Venue
2015
10.1007/978-3-319-31875-2_8
WISA
Field
DocType
Citations 
Combinatorics,Computer science,Orthogonality,Orthogonal basis,Lattice problem,Theoretical computer science,Integer lattice,Unimodular matrix,Gramian matrix,Basis (linear algebra),Lattice reduction
Conference
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Renzhang Liu102.37
Yanbin Pan23513.29