### Abstract

We give a characterization for the intractability of hyperelliptic discrete logarithm problem from a viewpoint of computational complexity theory. It is shown that the language of which complexity is equivalent to that of the hyperelliptic discrete logarithm problem is in NP ∩ co-AM, and that especially for elliptic curves, the corresponding language is in NP ∩ co-NP. It should be noted here that the language of which complexity is equivalent to that of the discrete logarithm problem defined over the multiplicative group of a finite field is also characterized as in NP ∩ co-NP.

Original language | English |
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Title of host publication | Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings |

Editors | Donald W. Davies |

Publisher | Springer Verlag |

Pages | 337-351 |

Number of pages | 15 |

ISBN (Print) | 9783540546207 |

DOIs | |

Publication status | Published - Jan 1 1991 |

Externally published | Yes |

Event | Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991 - Brighton, United Kingdom Duration: Apr 8 1991 → Apr 11 1991 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 547 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991 |
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Country | United Kingdom |

City | Brighton |

Period | 4/8/91 → 4/11/91 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Shizuya, H., Itoh, T., & Sakurai, K. (1991). On the complexity of hyperelliptic discrete logarithm problem. In D. W. Davies (Ed.),

*Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings*(pp. 337-351). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 547 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_29