Welcome to the resource topic for 2019/1035
Title:
An LLL Algorithm for Module Lattices
Authors: Changmin Lee, Alice Pellet-Mary, Damien Stehlé, Alexandre Wallet
Abstract:The LLL algorithm takes as input a basis of a Euclidean lattice, and, within a polynomial number of operations, it outputs another basis of the same lattice but consisting of rather short vectors. We provide a generalization to R-modules contained in K^n for arbitrary number fields K and dimension n, with R denoting the ring of integers of K. Concretely, we introduce an algorithm that efficiently finds short vectors in rank-n modules when given access to an oracle that finds short vectors in rank-2 modules, and an algorithm that efficiently finds short vectors in rank-2 modules given access to a Closest Vector Problem oracle for a lattice that depends only on K. The second algorithm relies on quantum computations and its analysis is heuristic. In the special case of free modules, we propose a dequantized version of this algorithm.
ePrint: https://eprint.iacr.org/2019/1035
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