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 -