Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

Details Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation

2002-08-05

arxiv.org/abs/math/0208038v2

Mathematics

Number Theory

12 pages, added some consequences for computing the Weil Pairing, to appear in Proceedings of RSA-CT 2003

Scientific paper

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8 % to 8.5 % over the best known general 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 scalar multiplication 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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