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 language | English |
|---|---|
| Title of host publication | Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings |
| Pages | 110-122 |
| Number of pages | 13 |
| DOIs | |
| Publication status | Published - Dec 23 2010 |
| Externally published | Yes |
| Event | 6th International Conference on Information Security Practice and Experience, ISPEC 2010 - Seoul, Korea, Republic of Duration: May 12 2010 → May 13 2010 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 6047 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 6th International Conference on Information Security Practice and Experience, ISPEC 2010 |
|---|---|
| Country | Korea, Republic of |
| City | Seoul |
| Period | 5/12/10 → 5/13/10 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
The elliptic curve discrete logarithm problems over the p-adic field and formal groups. / Yasuda, Masaya.
Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings. 2010. p. 110-122 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6047 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - The elliptic curve discrete logarithm problems over the p-adic field and formal groups
AU - Yasuda, Masaya
PY - 2010/12/23
Y1 - 2010/12/23
N2 - 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].
AB - 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].
UR - http://www.scopus.com/inward/record.url?scp=78650279088&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78650279088&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-12827-1_9
DO - 10.1007/978-3-642-12827-1_9
M3 - Conference contribution
AN - SCOPUS:78650279088
SN - 3642128262
SN - 9783642128264
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 110
EP - 122
BT - Information Security Practice and Experience - 6th International Conference, ISPEC 2010, Proceedings
ER -