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- W2486989386 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 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 $$[frac{pi }{3},frac{2pi }{3}]$$. 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." @default.
- W2486989386 created "2016-08-23" @default.
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- W2486989386 date "2016-01-01" @default.
- W2486989386 modified "2023-09-24" @default.
- W2486989386 title "Two Types of Special Bases for Integral Lattices" @default.
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- W2486989386 doi "https://doi.org/10.1007/978-3-319-31875-2_8" @default.
- W2486989386 hasPublicationYear "2016" @default.
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