Acceleration of index calculus for solving ECDLP over prime fields and its limitation

Momonari Kudo, Yuki Yokota, Yasushi Takahashi, Masaya Yasuda

研究成果: 著書/レポートタイプへの貢献会議での発言

抄録

In 2018, Amadori et al. proposed a new variant of index calculus to solve the elliptic curve discrete logarithm problem (ECDLP), using Semaev’s summation polynomials. The variant drastically decreases the number of required Gröbner basis computations, and it outperforms other index calculus algorithms for the ECDLP over prime fields. In this paper, we provide several improvements to accelerate to solve systems of multivariate equations arising in the variant. A main improvement is to apply the hybrid method, which mixes exhaustive search and Gröbner bases techniques to solve multivariate systems over finite fields. We also make use of symmetries of summation polynomials. We show experimental results of our improvements, and give their complexity analysis to discuss a limitation of our acceleration in both theory and practice.

元の言語英語
ホスト出版物のタイトルCryptology and Network Security - 17th International Conference, CANS 2018, Proceedings
編集者Panos Papadimitratos, Jan Camenisch
出版者Springer Verlag
ページ377-393
ページ数17
ISBN(印刷物)9783030004330
DOI
出版物ステータス出版済み - 1 1 2018
イベント17th International Conference on Cryptology and Network Security, CANS 2018 - Naples, イタリア
継続期間: 9 30 201810 3 2018

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
11124 LNCS
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他17th International Conference on Cryptology and Network Security, CANS 2018
イタリア
Naples
期間9/30/1810/3/18

Fingerprint

Discrete Logarithm Problem
Elliptic Curves
Calculus
Polynomials
Summation
Polynomial
Complexity Analysis
Exhaustive Search
Hybrid Method
Accelerate
Galois field
Symmetry
Decrease
Experimental Results

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

これを引用

Kudo, M., Yokota, Y., Takahashi, Y., & Yasuda, M. (2018). Acceleration of index calculus for solving ECDLP over prime fields and its limitation. : P. Papadimitratos, & J. Camenisch (版), Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings (pp. 377-393). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 11124 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-00434-7_19

Acceleration of index calculus for solving ECDLP over prime fields and its limitation. / Kudo, Momonari; Yokota, Yuki; Takahashi, Yasushi; Yasuda, Masaya.

Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings. 版 / Panos Papadimitratos; Jan Camenisch. Springer Verlag, 2018. p. 377-393 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻 11124 LNCS).

研究成果: 著書/レポートタイプへの貢献会議での発言

Kudo, M, Yokota, Y, Takahashi, Y & Yasuda, M 2018, Acceleration of index calculus for solving ECDLP over prime fields and its limitation. : P Papadimitratos & J Camenisch (版), Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 11124 LNCS, Springer Verlag, pp. 377-393, 17th International Conference on Cryptology and Network Security, CANS 2018, Naples, イタリア, 9/30/18. https://doi.org/10.1007/978-3-030-00434-7_19
Kudo M, Yokota Y, Takahashi Y, Yasuda M. Acceleration of index calculus for solving ECDLP over prime fields and its limitation. : Papadimitratos P, Camenisch J, 編集者, Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings. Springer Verlag. 2018. p. 377-393. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-00434-7_19
Kudo, Momonari ; Yokota, Yuki ; Takahashi, Yasushi ; Yasuda, Masaya. / Acceleration of index calculus for solving ECDLP over prime fields and its limitation. Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings. 編集者 / Panos Papadimitratos ; Jan Camenisch. Springer Verlag, 2018. pp. 377-393 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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