### Abstract

The elliptic curve discrete logarithm problem (ECDLP) over a field K is as follows: given an elliptic curve E over K, a point S ∈ E(K), and a point T ∈ E(K) with T ∈ hSi, find the integer d such that T = dS. The hardness of the ECDLP over a finite field is essential for the security of all elliptic curve cryptographic schemes. Semaev, Smart, and Satoh and Araki independently proposed an efficient attack for the ECDLP over F _{p} in the anomalous case, which is called the anomalous attack. In this paper, we generalize the method of the anomalous attack and give an algorithm for solving the ECDLP over the p-adic field Q _{p}.

Original language | English |
---|---|

Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | International Journal of Pure and Applied Mathematics |

Volume | 77 |

Issue number | 1 |

Publication status | Published - May 28 2012 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**A generalization of the anomalous attack for the ECDLP over Q _{p} .** / Yasuda, Masaya.

Research output: Contribution to journal › Article

_{p}',

*International Journal of Pure and Applied Mathematics*, vol. 77, no. 1, pp. 1-9.

}

TY - JOUR

T1 - A generalization of the anomalous attack for the ECDLP over Q p

AU - Yasuda, Masaya

PY - 2012/5/28

Y1 - 2012/5/28

N2 - The elliptic curve discrete logarithm problem (ECDLP) over a field K is as follows: given an elliptic curve E over K, a point S ∈ E(K), and a point T ∈ E(K) with T ∈ hSi, find the integer d such that T = dS. The hardness of the ECDLP over a finite field is essential for the security of all elliptic curve cryptographic schemes. Semaev, Smart, and Satoh and Araki independently proposed an efficient attack for the ECDLP over F p in the anomalous case, which is called the anomalous attack. In this paper, we generalize the method of the anomalous attack and give an algorithm for solving the ECDLP over the p-adic field Q p.

AB - The elliptic curve discrete logarithm problem (ECDLP) over a field K is as follows: given an elliptic curve E over K, a point S ∈ E(K), and a point T ∈ E(K) with T ∈ hSi, find the integer d such that T = dS. The hardness of the ECDLP over a finite field is essential for the security of all elliptic curve cryptographic schemes. Semaev, Smart, and Satoh and Araki independently proposed an efficient attack for the ECDLP over F p in the anomalous case, which is called the anomalous attack. In this paper, we generalize the method of the anomalous attack and give an algorithm for solving the ECDLP over the p-adic field Q p.

UR - http://www.scopus.com/inward/record.url?scp=84861372903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861372903&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84861372903

VL - 77

SP - 1

EP - 9

JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

SN - 1311-8080

IS - 1

ER -