IJPAM: Volume 77, No. 1 (2012)
FOR THE ECDLP OVER
Fujitsu Laboratories Ltd.
1-1, Kamikodanaka 4-chome, Nakahara-ku, Kawasaki
Abstract. The elliptic curve discrete logarithm problem (ECDLP) over a field is as follows: given an elliptic curve over , a point , and a point with , find the integer such that . 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 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 -adic field .
Received: May 16, 2011
AMS Subject Classification: 14G52, 11G07
Key Words and Phrases: ECDLP, formal groups, the anomalous attack
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395