[Resource Topic] 2002/112: An Efficient Procedure to Double and Add Points on an Elliptic Curve

Welcome to the resource topic for 2002/112

Title:
An Efficient Procedure to Double and Add Points on an Elliptic Curve

Authors: Kirsten Eisentraeger, Kristin Lauter, Peter L. Montgomery

Abstract:

We present an algorithm that speeds exponentiation on a
general elliptic curve by an estimated 3.8% to 8.5% over the best
known general exponentiation methods when using affine coordinates.
This is achieved by eliminating a field multiplication when we compute 2P + Q from given points P, Q on the curve. We give
applications to simultaneous multiple exponentiation and to the
Elliptic Curve Method of factorization. We show how this
improvement together with another idea can speed the
computation of the Weil and Tate pairings by up to 7.8%.

ePrint: https://eprint.iacr.org/2002/112

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