### 抄録

At SAC2017, Akiyama et al. proposed the indeterminate equation encryption scheme whose security is based on a solution problem of indeterminate equation. It is an extension of algebraic surface encryption scheme. A public key X for this scheme is a polynomial in two variables over a finite ring. Akiyama et al. also proposed two attacks, the linear algebraic attack (LAA) and the key recovery attack (KRA), by using the lattice structure associated with this scheme. In this paper, we give an improvement on LAA. Also we explain the relation between our improvement and the improvement on LAA proposed by Xagawa and examine parameters that those attacks fail by experiments. As a result, we conclude that if the total degree of the public key X is one, then KRA is more efficient than LAA and if that of X is two, then LAA is more efficient than KRA.

元の言語 | 英語 |
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ホスト出版物のタイトル | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |

出版者 | Institute of Electrical and Electronics Engineers Inc. |

ページ | 389-393 |

ページ数 | 5 |

ISBN（電子版） | 9784885523182 |

DOI | |

出版物ステータス | 出版済み - 3 8 2019 |

外部発表 | Yes |

イベント | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, シンガポール 継続期間: 10 28 2018 → 10 31 2018 |

### 出版物シリーズ

名前 | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |
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### 会議

会議 | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 |
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国 | シンガポール |

市 | Singapore |

期間 | 10/28/18 → 10/31/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Information Systems

### これを引用

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018*(pp. 389-393). [8664254] (Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ISITA.2018.8664254

**An Improvement on the Linear Algebraic Attack for the Indeterminate Equation Encryption Scheme.** / Ikematsu, Yasuhiko; Akiyama, Koichiro; Takagi, Tsuyoshi.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018.*, 8664254, Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, Institute of Electrical and Electronics Engineers Inc., pp. 389-393, 15th International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, シンガポール, 10/28/18. https://doi.org/10.23919/ISITA.2018.8664254

}

TY - GEN

T1 - An Improvement on the Linear Algebraic Attack for the Indeterminate Equation Encryption Scheme

AU - Ikematsu, Yasuhiko

AU - Akiyama, Koichiro

AU - Takagi, Tsuyoshi

PY - 2019/3/8

Y1 - 2019/3/8

N2 - At SAC2017, Akiyama et al. proposed the indeterminate equation encryption scheme whose security is based on a solution problem of indeterminate equation. It is an extension of algebraic surface encryption scheme. A public key X for this scheme is a polynomial in two variables over a finite ring. Akiyama et al. also proposed two attacks, the linear algebraic attack (LAA) and the key recovery attack (KRA), by using the lattice structure associated with this scheme. In this paper, we give an improvement on LAA. Also we explain the relation between our improvement and the improvement on LAA proposed by Xagawa and examine parameters that those attacks fail by experiments. As a result, we conclude that if the total degree of the public key X is one, then KRA is more efficient than LAA and if that of X is two, then LAA is more efficient than KRA.

AB - At SAC2017, Akiyama et al. proposed the indeterminate equation encryption scheme whose security is based on a solution problem of indeterminate equation. It is an extension of algebraic surface encryption scheme. A public key X for this scheme is a polynomial in two variables over a finite ring. Akiyama et al. also proposed two attacks, the linear algebraic attack (LAA) and the key recovery attack (KRA), by using the lattice structure associated with this scheme. In this paper, we give an improvement on LAA. Also we explain the relation between our improvement and the improvement on LAA proposed by Xagawa and examine parameters that those attacks fail by experiments. As a result, we conclude that if the total degree of the public key X is one, then KRA is more efficient than LAA and if that of X is two, then LAA is more efficient than KRA.

UR - http://www.scopus.com/inward/record.url?scp=85063873116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063873116&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664254

DO - 10.23919/ISITA.2018.8664254

M3 - Conference contribution

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 389

EP - 393

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -