Provable Lattice Reduction of $\mathbb Z^n$ with Blocksize $n/2$

Léo Ducas

Paper 2023/447

Provable Lattice Reduction of $\mathbb Z^n$ with Blocksize $n/2$

Léo Ducas

, Centrum Wiskunde & Informatica, Leiden University

Abstract

The Lattice Isomorphism Problem (LIP) is the computational task of recovering, assuming it exists, a orthogonal linear transformation sending one lattice to another. For cryptographic purposes, the case of the trivial lattice $\mathbb Z^n$ is of particular interest ($\mathbb Z$LIP). Heuristic analysis suggests that the BKZ algorithm with blocksize $\beta = n/2 + o(n)$ solves such instances (Ducas, Postlethwaite, Pulles, van Woerden, ASIACRYPT 2022). In this work, I propose a provable version of this statement, namely, that $\mathbb Z$LIP can indeed be solved by making polynomially many calls to a Shortest Vector Problem (SVP) oracle in dimension at most $n/2 + 1$.

Note: Update: many typos fixed, and substantial editorial improvements.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: Lattice Isomorphism Problem Lattice Reduction Provable Algorithm
Contact author(s): ducas @ cwi nl
History: 2023-09-05: last of 2 revisions; 2023-03-27: received; See all versions
Short URL: https://ia.cr/2023/447
License: CC0

BibTeX

@misc{cryptoeprint:2023/447,
      author = {Léo Ducas},
      title = {Provable Lattice Reduction of $\mathbb Z^n$ with Blocksize $n/2$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/447},
      year = {2023},
      url = {https://eprint.iacr.org/2023/447}
}