## CryptoDB

### Paper: Faster Enumeration-based Lattice Reduction: Root Hermite Factor k^(1/(2k)) in Time k^(k/8 + o(k))

Authors: Martin Albrecht , Royal Holloway, University of London Shi Bai , Department of Mathematical Sciences, Florida Atlantic University Pierre-Alain Fouque , Univ. Rennes, CNRS, IRISA, Rennes, France Paul Kirchner , Univ. Rennes, CNRS, IRISA, Rennes, France Damien Stehlé , Univ. Lyon, EnsL, UCBL, CNRS, Inria, LIP, F-69342 Lyon Cedex 07, France Weiqiang Wen , Univ. Rennes, CNRS, IRISA, Rennes, France DOI: 10.1007/978-3-030-56880-1_7 (login may be required) Search ePrint Search Google Slides CRYPTO 2020 We give a lattice reduction algorithm that achieves root Hermite factor k^(1/(2k)) in time k^(k/8 + o(k)) and polynomial memory. This improves on the previously best known enumeration-based algorithms which achieve the same quality, but in time k^(k/(2e) + o(k)). A cost of k^(k/8 + o(k)) was previously mentioned as potentially achievable (Hanrot-Stehlé’10) or as a heuristic lower bound (Nguyen’10) for enumeration algorithms. We prove the complexity and quality of our algorithm under a heuristic assumption and provide empirical evidence from simulation and implementation experiments attesting to its performance for practical and cryptographic parameter sizes. Our work also suggests potential avenues for achieving costs below k^(k/8 + o(k)) for the same root Hermite factor, based on the geometry of SDBKZ-reduced bases.
##### BibTeX
@inproceedings{crypto-2020-30367,
title={Faster Enumeration-based Lattice Reduction: Root Hermite Factor k^(1/(2k)) in Time k^(k/8 + o(k))},
publisher={Springer-Verlag},
doi={10.1007/978-3-030-56880-1_7},
author={Martin Albrecht and Shi Bai and Pierre-Alain Fouque and Paul Kirchner and Damien Stehlé and Weiqiang Wen},
year=2020
}