Smooth Sailing through Spherical Shells: Provable Random-Lattice Sieving in Time 2^(0.292n)

Emmanouil Doulgerakis · Thijs Laarhoven

arXiv 2609.37482

Time bound

(3/2)^{n/2 + o(n)}

Space bound

2^{0.2075187496 n + o(n)}

Source / version date

26 Sept 2026

Comparison variant

Classical · Haar random

Cost scale

2^{c n + o(n)}

Norm

Euclidean ℓ₂

Success guarantee

1−o(1) over lattice and algorithm

Computation model

Classical randomized; polynomial factors suppressed

Lattice distribution

Haar-random unimodular lattices

reference

DL26

Assumptions and source notes

Preprint claim for Haar-random unimodular lattices: exact SVP with success 1−o(1) over lattice and algorithm randomness. This is a distributional theorem, not an arbitrary-lattice worst-case theorem. Source checked; proof not independently audited.

Primary source ↗

@misc{paper-b05644e2a691,
  author = {Emmanouil Doulgerakis and Thijs Laarhoven},
  title = {{Smooth Sailing through Spherical Shells: Provable Random-Lattice Sieving in Time 2^(0.292n)}},
  year = {2026},
  url = {https://arxiv.org/abs/2609.37482},
  cr_date = {2026-09-26},
  cr_status = {preprint},
  cr_author_ids = {emmanouil-doulgerakis; thijs-laarhoven},
  howpublished = {arXiv:2609.37482}
}