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An Efficient Procedure to Double and Add Points on an Elliptic Curve
Authors: Kirsten Eisentraeger, Kristin Lauter, Peter L. MontgomeryAbstract:
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%.
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