### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 389-393 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523182 |

DOIs | |

Publication status | Published - Mar 8 2019 |

Externally published | Yes |

Event | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, Singapore Duration: Oct 28 2018 → Oct 31 2018 |

### Publication series

Name | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |
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### Conference

Conference | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 |
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Country | Singapore |

City | Singapore |

Period | 10/28/18 → 10/31/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Information Systems

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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, Singapore, 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

AN - SCOPUS:85063873116

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 -