2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64664We 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 %.12 pages, added some consequences for computing the Weil Pairing, to appear in Proceedings of RSA-CT 2003Number Theory14G50; 11T71text