Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction

Jintai Ding, Momonari Kudo, Shinya Okumura, Tsuyoshi Takagi, Chengdong Tao

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

Abstract

Okumura proposed a candidate of post-quantum cryptosystem based on Diophantine equations of degree increasing type (DEC). Sizes of public keys in DEC are small, e.g., 1,200 bits for 128 bit security, and it is a strongly desired property in post-quantum erea. In this paper, we propose a polynomial time attack against DEC. We show that the one-wayness of DEC is reduced to finding special (relatively) short vectors in some lattices. The usual LLL algorithm does not work well for finding the most important target vector in our attack. The most technical point of our method is to heuristically find a special norm called a weighted norm to find the most important target vector. We call this method "weighted LLL algorithm" in this paper. Our experimental results suggest that our attack can break the one-wayness of DEC for 128 bit security with sufficiently high probability.

Original languageEnglish
Title of host publicationAdvances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings
EditorsKatsunari Yoshioka, Kazuto Ogawa
PublisherSpringer Verlag
Pages305-315
Number of pages11
ISBN (Print)9783319445236
DOIs
Publication statusPublished - Jan 1 2016
Event11th International Workshop on Security on Advances in Information and Computer Security, IWSEC 2016 - Tokyo, Japan
Duration: Sep 12 2016Sep 14 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9836 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Workshop on Security on Advances in Information and Computer Security, IWSEC 2016
CountryJapan
CityTokyo
Period9/12/169/14/16

Fingerprint

Public-key Cryptosystem
Diophantine equation
Cryptanalysis
LLL Algorithm
Cryptography
Attack
Weighted Norm
Target
Cryptosystem
Public key
Polynomial time
Polynomials
Norm
Experimental Results

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Ding, J., Kudo, M., Okumura, S., Takagi, T., & Tao, C. (2016). Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction. In K. Yoshioka, & K. Ogawa (Eds.), Advances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings (pp. 305-315). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9836 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44524-3_18

Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction. / Ding, Jintai; Kudo, Momonari; Okumura, Shinya; Takagi, Tsuyoshi; Tao, Chengdong.

Advances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings. ed. / Katsunari Yoshioka; Kazuto Ogawa. Springer Verlag, 2016. p. 305-315 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9836 LNCS).

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

Ding, J, Kudo, M, Okumura, S, Takagi, T & Tao, C 2016, Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction. in K Yoshioka & K Ogawa (eds), Advances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9836 LNCS, Springer Verlag, pp. 305-315, 11th International Workshop on Security on Advances in Information and Computer Security, IWSEC 2016, Tokyo, Japan, 9/12/16. https://doi.org/10.1007/978-3-319-44524-3_18
Ding J, Kudo M, Okumura S, Takagi T, Tao C. Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction. In Yoshioka K, Ogawa K, editors, Advances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings. Springer Verlag. 2016. p. 305-315. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-44524-3_18
Ding, Jintai ; Kudo, Momonari ; Okumura, Shinya ; Takagi, Tsuyoshi ; Tao, Chengdong. / Cryptanalysis of a public key cryptosystem based on diophantine equations via weighted LLL reduction. Advances in Information and Computer Security - 11th International Workshop on Security, IWSEC 2016, Proceedings. editor / Katsunari Yoshioka ; Kazuto Ogawa. Springer Verlag, 2016. pp. 305-315 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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