The elliptic curve discrete logarithm problems over the p-adic field and formal groups

Masaya Yasuda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

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].

Original languageEnglish
Title of host publicationInformation Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings
Pages110-122
Number of pages13
DOIs
Publication statusPublished - Dec 23 2010
Externally publishedYes
Event6th International Conference on Information Security Practice and Experience, ISPEC 2010 - Seoul, Korea, Republic of
Duration: May 12 2010May 13 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6047 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Information Security Practice and Experience, ISPEC 2010
CountryKorea, Republic of
CitySeoul
Period5/12/105/13/10

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Yasuda, M. (2010). The elliptic curve discrete logarithm problems over the p-adic field and formal groups. In Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings (pp. 110-122). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6047 LNCS). https://doi.org/10.1007/978-3-642-12827-1_9