TY - JOUR
T1 - Efficient scalar multiplications on elliptic curves with direct computations of several doublings
AU - Sakai, Yasuyuki
AU - Sakurai, Kouichi
PY - 2001/1/1
Y1 - 2001/1/1
N2 - We introduce efficient algorithms for scalar multiplication on elliptic curves defined over IFp. The algorithms compute 2kP directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.
AB - We introduce efficient algorithms for scalar multiplication on elliptic curves defined over IFp. The algorithms compute 2kP directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.
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M3 - Article
AN - SCOPUS:0035126332
SN - 0916-8508
VL - E84-A
SP - 120
EP - 129
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IS - 1
ER -