Solving the Shortest Vector Problem in 2^(0.6039n) Time via Mid-point Hessian

Minki Hhan

ePrint 2026/1597

Time bound

2^{0.6039 n + o(n)}

Space bound

2^{0.5 n + o(n)}

Source / version date

3 Aug 2026

Comparison variant

Constant approximation · large-factor limit

Cost scale

2^{(c + ε) n}, any fixed ε > 0

Norm

Euclidean ℓ₂

Success guarantee

High probability

Computation model

Classical randomized; polynomial factors suppressed

reference

Hhan26a

Approximation guarantee

Exact output (μ = 1), hence meets every relaxed constant-factor guarantee

Assumptions and source notes

The exact-SVP theorem immediately supplies this approximation guarantee without changing time or space. This is a transferred guarantee, not another algorithm or a separate new result. Preprint claim, also arXiv:2608.02478. Uses the Hessian of the periodic Gaussian at a half shortest vector. First arXiv date shown. Source checked; proof not independently audited.

Primary source ↗

@misc{paper-2fcc11c09e6a,
  author = {Minki Hhan},
  title = {{Solving the Shortest Vector Problem in 2^(0.6039n) Time via Mid-point Hessian}},
  year = {2026},
  url = {https://eprint.iacr.org/2026/1597},
  cr_date = {2026-08-03},
  cr_status = {preprint},
  cr_author_ids = {minki-hhan},
  howpublished = {Cryptology ePrint Archive, Paper 2026/1597}
}