Fast Point Multiplication on Elliptic Curves of Even Order
Every elliptic curve of even order over a flnite fleld of characteristic > 3 is birationally equivalent to a curve in the Jacobi quartic form. In this paper, new explicit formulae for group operations on a Jacobi quartic curve are presented. The algorithm for doubling uses only 1M +6S, for the mixed-addition uses only 8M + 2S and the unifled addition formula only 9M + 2S to the best case. For elliptic curve of even order, these algorithm are more e‐cient than the other algorithms in the literature.