TY - GEN

T1 - Integer variable x-based ate pairing

AU - Nogami, Yasuyuki

AU - Akane, Masataka

AU - Sakemi, Yumi

AU - Kato, Hidehiro

AU - Morikawa, Yoshitaka

PY - 2008/9/30

Y1 - 2008/9/30

N2 - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

AB - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

KW - Ate pairing

KW - Miller's algorithm

UR - http://www.scopus.com/inward/record.url?scp=52449098485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449098485&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85538-5_13

DO - 10.1007/978-3-540-85538-5_13

M3 - Conference contribution

AN - SCOPUS:52449098485

SN - 3540855033

SN - 9783540855033

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 178

EP - 191

BT - Pairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings

T2 - 2nd International Conference on Pairing-Based Cryptography, Pairing 2008

Y2 - 1 September 2008 through 3 September 2008

ER -