Abstract
The purpose of this work is to propose an efficient algorithm to solve the closest vector problem (CVP) in the tensor product of two root lattices of type \(D_n\) (\(n\ge 2\)). In 2018, Léo Ducas and Wessel van Woerden proposed a polynomial algorithm allowing to solve this problem in the tensor product of two root lattices of type \(A_n\) (\(n\ge 1\)). In our present case, we show that the root lattice \(D_{nm}\) is a full-rank sub-lattice of the tensor product \(D_n\otimes D_m\) (\(n,m\ge 2\)) of the root lattices \(D_n\) and \(D_m\), enabling us to derive a polynomial algorithm for solving the CVP in \(D_n\) (\(n\ge 2\)). The proposed algorithm performs at most \(O(n+m)\) arithmetic operations.
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Tchinda, A.G.F., Fouotsa, E. & Jugnia, C.N. A Polynomial Algorithm for Solving the Closest Vector Problem in Tensored Root Lattices of Type D. SN COMPUT. SCI. 4, 19 (2023). https://doi.org/10.1007/s42979-022-01440-2
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DOI: https://doi.org/10.1007/s42979-022-01440-2