### 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 |
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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 2018 → 10 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) |
---|---|

巻 | 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 |
---|---|

国 | イタリア |

市 | Naples |

期間 | 9/30/18 → 10/3/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*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.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*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

}

TY - GEN

T1 - Acceleration of index calculus for solving ECDLP over prime fields and its limitation

AU - Kudo, Momonari

AU - Yokota, Yuki

AU - Takahashi, Yasushi

AU - Yasuda, Masaya

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-00434-7_19

DO - 10.1007/978-3-030-00434-7_19

M3 - Conference contribution

SN - 9783030004330

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

SP - 377

EP - 393

BT - Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings

A2 - Papadimitratos, Panos

A2 - Camenisch, Jan

PB - Springer Verlag

ER -