### 抄録

Cayley hash functions are a family of cryptographic hash functions constructed from Cayley graphs, with appealing properties such as a natural parallelism and a security reduction to a clean, well-defined mathematical problem. As this problem involves non-Abelian groups, it is a priori resistant to quantum period finding algorithms and Cayley hash functions may therefore be a good foundation for post-quantum cryptography. Four particular parameter sets for Cayley hash functions have been proposed in the past, and so far dedicated preimage algorithms have been found for all of them. These algorithms do however not seem to extend to generic parameters, and as a result it is still an open problem to determine the security of Cayley hash functions in general. In this paper, we study the case of Chiu's Ramanujan graphs. We design a polynomial time preimage attack against the resulting Cayley hash function, showing that these particular parameters like the previous ones are not suitable for the construction. We extend our attacks on hash functions based on similar Cayley graphs as Chiu's Ramanujan graphs. On the positive side, we then suggest some possible ways to construct the Cayley hashes that may not be affected by this type of attacks. Our results contribute to a better understanding of the hard problems underlying the security of Cayley hash functions.

元の言語 | 英語 |
---|---|

ページ（範囲） | 1891-1899 |

ページ数 | 9 |

ジャーナル | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

巻 | E100A |

発行部数 | 9 |

DOI | |

出版物ステータス | 出版済み - 9 1 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics

### これを引用

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E100A*(9), 1891-1899. https://doi.org/10.1587/transfun.E100.A.1891

**Full cryptanalysis of hash functions based on cubic Ramanujan graphs.** / Jo, Hyungrok; Petit, Christophe; Takagi, Tsuyoshi.

研究成果: ジャーナルへの寄稿 › 記事

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, 巻. E100A, 番号 9, pp. 1891-1899. https://doi.org/10.1587/transfun.E100.A.1891

}

TY - JOUR

T1 - Full cryptanalysis of hash functions based on cubic Ramanujan graphs

AU - Jo, Hyungrok

AU - Petit, Christophe

AU - Takagi, Tsuyoshi

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Cayley hash functions are a family of cryptographic hash functions constructed from Cayley graphs, with appealing properties such as a natural parallelism and a security reduction to a clean, well-defined mathematical problem. As this problem involves non-Abelian groups, it is a priori resistant to quantum period finding algorithms and Cayley hash functions may therefore be a good foundation for post-quantum cryptography. Four particular parameter sets for Cayley hash functions have been proposed in the past, and so far dedicated preimage algorithms have been found for all of them. These algorithms do however not seem to extend to generic parameters, and as a result it is still an open problem to determine the security of Cayley hash functions in general. In this paper, we study the case of Chiu's Ramanujan graphs. We design a polynomial time preimage attack against the resulting Cayley hash function, showing that these particular parameters like the previous ones are not suitable for the construction. We extend our attacks on hash functions based on similar Cayley graphs as Chiu's Ramanujan graphs. On the positive side, we then suggest some possible ways to construct the Cayley hashes that may not be affected by this type of attacks. Our results contribute to a better understanding of the hard problems underlying the security of Cayley hash functions.

AB - Cayley hash functions are a family of cryptographic hash functions constructed from Cayley graphs, with appealing properties such as a natural parallelism and a security reduction to a clean, well-defined mathematical problem. As this problem involves non-Abelian groups, it is a priori resistant to quantum period finding algorithms and Cayley hash functions may therefore be a good foundation for post-quantum cryptography. Four particular parameter sets for Cayley hash functions have been proposed in the past, and so far dedicated preimage algorithms have been found for all of them. These algorithms do however not seem to extend to generic parameters, and as a result it is still an open problem to determine the security of Cayley hash functions in general. In this paper, we study the case of Chiu's Ramanujan graphs. We design a polynomial time preimage attack against the resulting Cayley hash function, showing that these particular parameters like the previous ones are not suitable for the construction. We extend our attacks on hash functions based on similar Cayley graphs as Chiu's Ramanujan graphs. On the positive side, we then suggest some possible ways to construct the Cayley hashes that may not be affected by this type of attacks. Our results contribute to a better understanding of the hard problems underlying the security of Cayley hash functions.

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U2 - 10.1587/transfun.E100.A.1891

DO - 10.1587/transfun.E100.A.1891

M3 - Article

AN - SCOPUS:85028760405

VL - E100A

SP - 1891

EP - 1899

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 9

ER -