TY - GEN

T1 - The elliptic curve discrete logarithm problems over the p-adic field and formal groups

AU - Yasuda, Masaya

PY - 2010

Y1 - 2010

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].

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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

T2 - 6th International Conference on Information Security Practice and Experience, ISPEC 2010

Y2 - 12 May 2010 through 13 May 2010

ER -