Tanja Lange
Tanja Lange
Tanja Lange
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Elliptic geared for cryptoIntroduce further parameter d to cover more curves over kx 2 (+ y 2 = c 2 (1 + dx 2 y 2 ), c, d ≠ 0, dc 4 ≠ 1.)xP y Q + y P x QP + Q =c(1 + dx P x Q y P y Q ) , y P y Q − x P x Q.c(1 − dx P x Q y P y Q )A = Z P · Z Q ; B = A 2 ; C = X P · X Q ; D = Y P · Y Q ;E = d · C · D; F = B − E; G = B + E;X P +Q = A · F · ((X P + Y P ) · (X Q + Y Q ) − C − D);Y P +Q = A · G · (D − C); Z P +Q = c · F · G.D. J. Bernstein & T. <strong>Lange</strong> http://hyperelliptic.org/tanja/newelliptic – p. 15
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