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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1-9
Number of pages9
JournalInternational Journal of Pure and Applied Mathematics
Volume77
Issue number1
Publication statusPublished - May 28 2012
Externally publishedYes

Fingerprint

Discrete Logarithm Problem
Elliptic Curves
Anomalous
Hardness
Attack
P-adic Fields
Generalization
Galois field
Generalise
Integer

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.

In: International Journal of Pure and Applied Mathematics, Vol. 77, No. 1, 28.05.2012, p. 1-9.

Research output: Contribution to journalArticle

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