Shortest vectors in rotated integer lattices
Find a shortest nonzero vector in polynomial time from an arbitrary basis of a lattice isometric to .
Inferred from the community field; finer classification has not been reviewed.
Problem statement
Find a shortest nonzero vector in polynomial time from an arbitrary basis of a lattice isometric to .
Lean 4
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Background
Editorial selection inspected on 9 September 2026. Current research status has not been independently reassessed; consult the original source and subsequent literature.
Source conventions: CVP is closest vector, SVP is shortest nonzero vector, and SIVP asks for independent vectors minimizing their largest norm. Gap denotes the associated promise decision problem. Approximation factors precede the problem name; Euclidean norm is the default. The source suppresses lower-order terms and input-length factors in exponential running times. Reduction arrows refer to efficient oracle reductions. The source's 2022 best-known bounds are not asserted to be current.
- [1]Simons Institute — Lattices '22 problems: Shortest vectors in rotated integer lattices (inspected 2026-09-09) link
Recorded progress
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Discussion
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