Making the BKW Algorithm Practical for LWE

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

The Learning with Errors (LWE) problem is one of the main mathematical foundations of post-quantum cryptography. One of the main groups of algorithms for solving LWE is the Blum-Kalai-Wasserman (BKW) algorithm. This paper presents new improvements for BKW-style algorithms for solving LWE instances. We target minimum concrete complexity and we introduce a new reduction step where we partially reduce the last position in an iteration and finish the reduction in the next iteration, allowing non-integer step sizes. We also introduce a new procedure in the secret recovery by mapping the problem to binary problems and applying the FastWalsh Hadamard Transform. The complexity of the resulting algorithm compares favourably to all other previous approaches, including lattice sieving. We additionally show the steps of implementing the approach for large LWE problem instances. The core idea here is to overcome RAM limitations by using large file-based memory.

Details

Authors
Organisations
External organisations
  • University of Bergen
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Other Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • BKW, LWE, Lattice-Based Cryptography, FWHT, Post- Quantum Cryptography
Original languageEnglish
Title of host publicationProgress in Cryptology – INDOCRYPT 2020
Subtitle of host publication21st International Conference on Cryptology in India Bangalore, India, December 13–16, 2020 Proceedings
PublisherSpringer
Pages417-439
Number of pages23
ISBN (Electronic)978-3-030-65277-7
ISBN (Print)978-3-030-65276-0
Publication statusPublished - 2020 Dec
Publication categoryResearch
Peer-reviewedYes
EventInternational Conference on Cryptology in India - INDOCRYPT 2020 - Bangalore, India
Duration: 2020 Dec 132020 Dec 16
Conference number: 21
https://indocrypt2020.iiitb.ac.in/

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume12578
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Conference on Cryptology in India - INDOCRYPT 2020
Abbreviated titleINDOCRYPT 2020
CountryIndia
CityBangalore
Period2020/12/132020/12/16
Internet address