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Polynomial Time Bounded Distance Decoding near Minkowski's Bound in Discrete Logarithm Lattices

Léo Ducas 1 Cécile Pierrot 1, 2
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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 determin-istic 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 1 and 2 norms.
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Submitted on : Tuesday, October 9, 2018 - 7:41:04 PM
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Léo Ducas, Cécile Pierrot. Polynomial Time Bounded Distance Decoding near Minkowski's Bound in Discrete Logarithm Lattices. Designs, Codes and Cryptography, Springer Verlag, 2018, ⟨10.1007/s10623-018-0573-3⟩. ⟨hal-01891713⟩

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