Development of a dual version of DeepBKZ and its application to solving the LWE challenge

Masaya Yasuda, Junpei Yamaguchi, Michiko Ooka, Satoshi Nakamura

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.

Original languageEnglish
Title of host publicationProgress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings
EditorsAbderrahmane Nitaj, Tajjeeddine Rachidi, Antoine Joux
PublisherSpringer Verlag
Pages162-182
Number of pages21
ISBN (Print)9783319893389
DOIs
Publication statusPublished - Jan 1 2018
Event10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018 - Marrakesh, Morocco
Duration: May 7 2018May 9 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10831 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018
CountryMorocco
CityMarrakesh
Period5/7/185/9/18

Fingerprint

Decoding
Subroutines
Enumeration
Dual Basis
Pruning
Experiments
Lattice Basis Reduction
Costs
Cryptanalysis
Insertion
Experiment
Extremes
Alternatives
Demonstrate

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yasuda, M., Yamaguchi, J., Ooka, M., & Nakamura, S. (2018). Development of a dual version of DeepBKZ and its application to solving the LWE challenge. In A. Nitaj, T. Rachidi, & A. Joux (Eds.), Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings (pp. 162-182). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10831 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-89339-6_10

Development of a dual version of DeepBKZ and its application to solving the LWE challenge. / Yasuda, Masaya; Yamaguchi, Junpei; Ooka, Michiko; Nakamura, Satoshi.

Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings. ed. / Abderrahmane Nitaj; Tajjeeddine Rachidi; Antoine Joux. Springer Verlag, 2018. p. 162-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10831 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yasuda, M, Yamaguchi, J, Ooka, M & Nakamura, S 2018, Development of a dual version of DeepBKZ and its application to solving the LWE challenge. in A Nitaj, T Rachidi & A Joux (eds), Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10831 LNCS, Springer Verlag, pp. 162-182, 10th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2018, Marrakesh, Morocco, 5/7/18. https://doi.org/10.1007/978-3-319-89339-6_10
Yasuda M, Yamaguchi J, Ooka M, Nakamura S. Development of a dual version of DeepBKZ and its application to solving the LWE challenge. In Nitaj A, Rachidi T, Joux A, editors, Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings. Springer Verlag. 2018. p. 162-182. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-89339-6_10
Yasuda, Masaya ; Yamaguchi, Junpei ; Ooka, Michiko ; Nakamura, Satoshi. / Development of a dual version of DeepBKZ and its application to solving the LWE challenge. Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings. editor / Abderrahmane Nitaj ; Tajjeeddine Rachidi ; Antoine Joux. Springer Verlag, 2018. pp. 162-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{e4c9265185084a81abf462834903aa1b,
title = "Development of a dual version of DeepBKZ and its application to solving the LWE challenge",
abstract = "Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.",
author = "Masaya Yasuda and Junpei Yamaguchi and Michiko Ooka and Satoshi Nakamura",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/978-3-319-89339-6_10",
language = "English",
isbn = "9783319893389",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "162--182",
editor = "Abderrahmane Nitaj and Tajjeeddine Rachidi and Antoine Joux",
booktitle = "Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings",
address = "Germany",

}

TY - GEN

T1 - Development of a dual version of DeepBKZ and its application to solving the LWE challenge

AU - Yasuda, Masaya

AU - Yamaguchi, Junpei

AU - Ooka, Michiko

AU - Nakamura, Satoshi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.

AB - Lattice basis reduction is a strong tool in cryptanalysis. In 2017, DeepBKZ was proposed as a new variant of BKZ, and it calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. In this paper, we develop a dual version of DeepBKZ (which we call “Dual-DeepBKZ”), to reduce the dual basis of an input basis. For Dual-DeepBKZ, we develop a dual version of DeepLLL, and then combine it with the dual enumeration by Micciancio and Walter. It never computes the dual basis of an input basis, and it is as efficient as the primal DeepBKZ. We also demonstrate that Dual-DeepBKZ solves several instances in the TU Darmstadt LWE challenge. We use Dual-DeepBKZ in the bounded distance decoding (BDD) approach for solving an LWE instance. Our experiments show that Dual-DeepBKZ reduces the cost of Liu-Nguyen’s BDD enumeration more effectively than BKZ. For the LWE instance of (n, α) = (40, 0.015) (resp., (n, α) = (60, 0.005)), our results are about 2.2 times (resp., 4.0 times) faster than Xu et al.’s results, for which they used BKZ in the fplll library and the BDD enumeration with extreme pruning while we used linear pruning in our experiments.

UR - http://www.scopus.com/inward/record.url?scp=85045921584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045921584&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-89339-6_10

DO - 10.1007/978-3-319-89339-6_10

M3 - Conference contribution

AN - SCOPUS:85045921584

SN - 9783319893389

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 162

EP - 182

BT - Progress in Cryptology - AFRICACRYPT 2018 - 10th International Conference on Cryptology in Africa, Proceedings

A2 - Nitaj, Abderrahmane

A2 - Rachidi, Tajjeeddine

A2 - Joux, Antoine

PB - Springer Verlag

ER -