## 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 |
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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 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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