Faster enumeration-based lattice reduction: Root hermite factor k1/(2k) time kk/8+o(k)

  • Martin R. Albrecht
  • , Shi Bai
  • , Pierre Alain Fouque
  • , Paul Kirchner
  • , Damien Stehlé
  • , Weiqiang Wen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We give a lattice reduction algorithm that achieves root Hermite factor k1/(2k) in time kk/8+o(k) and polynomial memory. This improves on the previously best known enumeration-based algorithms which achieve the same quality, but in time kk/(2e) + o(k). A cost of kk/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 kk/8 + o(k) for the same root Hermite factor, based on the geometry of SDBKZ-reduced bases.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, CRYPTO 2020, Proceedings
EditorsDaniele Micciancio, Thomas Ristenpart
PublisherSpringer
Pages186-212
Number of pages27
ISBN (Print)9783030568795
DOIs
Publication statusPublished - 1 Jan 2020
Externally publishedYes
Event40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, United States
Duration: 17 Aug 202021 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12171 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th Annual International Cryptology Conference, CRYPTO 2020
Country/TerritoryUnited States
CitySanta Barbara
Period17/08/2021/08/20

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