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

Momonari Kudo, Yuki Yokota, Yasushi Takahashi, Masaya Yasuda

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

Abstract

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.

Original languageEnglish
Title of host publicationCryptology and Network Security - 17th International Conference, CANS 2018, Proceedings
EditorsPanos Papadimitratos, Jan Camenisch
PublisherSpringer Verlag
Pages377-393
Number of pages17
ISBN (Print)9783030004330
DOIs
Publication statusPublished - Jan 1 2018
Event17th International Conference on Cryptology and Network Security, CANS 2018 - Naples, Italy
Duration: Sep 30 2018Oct 3 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11124 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th International Conference on Cryptology and Network Security, CANS 2018
CountryItaly
CityNaples
Period9/30/1810/3/18

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)

Cite this

Kudo, M., Yokota, Y., Takahashi, Y., & Yasuda, M. (2018). Acceleration of index calculus for solving ECDLP over prime fields and its limitation. In P. Papadimitratos, & J. Camenisch (Eds.), 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); Vol. 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. ed. / 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); Vol. 11124 LNCS).

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

Kudo, M, Yokota, Y, Takahashi, Y & Yasuda, M 2018, Acceleration of index calculus for solving ECDLP over prime fields and its limitation. in P Papadimitratos & J Camenisch (eds), 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), vol. 11124 LNCS, Springer Verlag, pp. 377-393, 17th International Conference on Cryptology and Network Security, CANS 2018, Naples, Italy, 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. In Papadimitratos P, Camenisch J, editors, 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. editor / 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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