Efficient scalar multiplications on elliptic curves with direct computations of several doublings

Yasuyuki Sakai; Kouichi Sakurai

Efficient scalar multiplications on elliptic curves with direct computations of several doublings

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce efficient algorithms for scalar multiplication on elliptic curves defined over IF_p. The algorithms compute 2^kP 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.

Original language	English
Pages (from-to)	120-129
Number of pages	10
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E84-A
Issue number	1
Publication status	Published - Jan 1 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

Cite this

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Efficient scalar multiplications on elliptic curves with direct computations of several doublings

Abstract

All Science Journal Classification (ASJC) codes

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