### 抄録

One of the most efficient post-quantum signature schemes is Rainbow whose hardness is based on the multivariate quadratic polynomial (MQ) problem. ELSA, a new multivariate signature scheme proposed at Asiacrypt 2017, has a similar construction to Rainbow. Its advantages, compared to Rainbow, are its smaller secret key and faster signature generation. In addition, its existential unforgeability against an adaptive chosen-message attack has been proven under the hardness of the MQ-problem induced by a public key of ELSA with a specific parameter set in the random oracle model. The high efficiency of ELSA is derived from a set of hidden quadratic equations used in the process of signature generation. However, the hidden quadratic equations yield a vulnerability. In fact, a piece of information of these equations can be recovered by using valid signatures and an equivalent secret key can be partially recovered from it. In this paper, we describe how to recover an equivalent secret key of ELSA by a chosen message attack. Our experiments show that we can recover an equivalent secret key for the claimed 128-bit security parameter of ELSA on a standard PC in 177Â s with 1326 valid signatures.

元の言語 | 英語 |
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ホスト出版物のタイトル | Advances in Information and Computer Security - 13th International Workshop on Security, IWSEC 2018, Proceedings |

編集者 | Kan Yasuda, Atsuo Inomata |

出版者 | Springer Verlag |

ページ | 3-18 |

ページ数 | 16 |

ISBN（印刷物） | 9783319979151 |

DOI | |

出版物ステータス | 出版済み - 1 1 2018 |

イベント | 13th International Workshop on Security, IWSEC 2018 - Sendai, 日本 継続期間: 9 3 2018 → 9 5 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) |
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巻 | 11049 LNCS |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### 会議

会議 | 13th International Workshop on Security, IWSEC 2018 |
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国 | 日本 |

市 | Sendai |

期間 | 9/3/18 → 9/5/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*Advances in Information and Computer Security - 13th International Workshop on Security, IWSEC 2018, Proceedings*(pp. 3-18). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 11049 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-97916-8_1

**Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 2017.** / Hashimoto, Yasufumi; Ikematsu, Yasuhiko; 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

*Advances in Information and Computer Security - 13th International Workshop on Security, IWSEC 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 11049 LNCS, Springer Verlag, pp. 3-18, 13th International Workshop on Security, IWSEC 2018, Sendai, 日本, 9/3/18. https://doi.org/10.1007/978-3-319-97916-8_1

}

TY - GEN

T1 - Chosen Message Attack on Multivariate Signature ELSA at Asiacrypt 2017

AU - Hashimoto, Yasufumi

AU - Ikematsu, Yasuhiko

AU - Takagi, Tsuyoshi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - One of the most efficient post-quantum signature schemes is Rainbow whose hardness is based on the multivariate quadratic polynomial (MQ) problem. ELSA, a new multivariate signature scheme proposed at Asiacrypt 2017, has a similar construction to Rainbow. Its advantages, compared to Rainbow, are its smaller secret key and faster signature generation. In addition, its existential unforgeability against an adaptive chosen-message attack has been proven under the hardness of the MQ-problem induced by a public key of ELSA with a specific parameter set in the random oracle model. The high efficiency of ELSA is derived from a set of hidden quadratic equations used in the process of signature generation. However, the hidden quadratic equations yield a vulnerability. In fact, a piece of information of these equations can be recovered by using valid signatures and an equivalent secret key can be partially recovered from it. In this paper, we describe how to recover an equivalent secret key of ELSA by a chosen message attack. Our experiments show that we can recover an equivalent secret key for the claimed 128-bit security parameter of ELSA on a standard PC in 177Â s with 1326 valid signatures.

AB - One of the most efficient post-quantum signature schemes is Rainbow whose hardness is based on the multivariate quadratic polynomial (MQ) problem. ELSA, a new multivariate signature scheme proposed at Asiacrypt 2017, has a similar construction to Rainbow. Its advantages, compared to Rainbow, are its smaller secret key and faster signature generation. In addition, its existential unforgeability against an adaptive chosen-message attack has been proven under the hardness of the MQ-problem induced by a public key of ELSA with a specific parameter set in the random oracle model. The high efficiency of ELSA is derived from a set of hidden quadratic equations used in the process of signature generation. However, the hidden quadratic equations yield a vulnerability. In fact, a piece of information of these equations can be recovered by using valid signatures and an equivalent secret key can be partially recovered from it. In this paper, we describe how to recover an equivalent secret key of ELSA by a chosen message attack. Our experiments show that we can recover an equivalent secret key for the claimed 128-bit security parameter of ELSA on a standard PC in 177Â s with 1326 valid signatures.

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U2 - 10.1007/978-3-319-97916-8_1

DO - 10.1007/978-3-319-97916-8_1

M3 - Conference contribution

AN - SCOPUS:85052056127

SN - 9783319979151

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

SP - 3

EP - 18

BT - Advances in Information and Computer Security - 13th International Workshop on Security, IWSEC 2018, Proceedings

A2 - Yasuda, Kan

A2 - Inomata, Atsuo

PB - Springer Verlag

ER -