The hardness of the elliptic curve discrete logarithm problem (ECDLP) on a finite field is essential for the security of all elliptic curve cryptographic schemes. The ECDLP on 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 ∈ (S), find the integer d such that T = dS. A number of ways of approaching the solution to the ECDLP on a finite field is known, for example, the MOV attack [5], and the anomalous attack [7,10]. In this paper, we propose an algorithm to solve the ECDLP on the p-adic field Qp. Our method is to use the theory of formal groups associated to elliptic curves, which is used for the anomalous attack proposed by Smart [10], and Satoh and Araki [7]. © Springer-Verlag Berlin Heidelberg 2010.
CITATION STYLE
Yasuda, M. (2010). The elliptic curve discrete logarithm problems over the p-adic field and formal groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6047 LNCS, pp. 110–122). https://doi.org/10.1007/978-3-642-12827-1_9
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