Polynomial time bounded distance decoding near Minkowski’s bound in discrete logarithm lattices
IACR Cryptology ePrint Archive(2018)
摘要
We propose a concrete family of dense lattices of arbitrary dimension n in which the lattice bounded distance decoding (BDD) problem can be solved in deterministic polynomial time. This construction is directly adapted from the Chor–Rivest cryptosystem (IEEE-TIT 1988). The lattice construction needs discrete logarithm computations that can be made in deterministic polynomial time for well-chosen parameters. Each lattice comes with a deterministic polynomial time decoding algorithm able to decode up to large radius. Namely, we reach decoding radius within O(log n) Minkowski’s bound, for both ℓ _1 and ℓ _2 norms.
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关键词
Dense lattices, Bounded distance decoding (BDD), Minkoswki’s bound, 94B35, 94B65, 11H31, 11H71
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