Speeding up the computations of elliptic curves cryptoschemes

The basic operation in elliptic curve cryptoschemes is multiplication. In this paper, we first propose an efficient algorithm for the computation on an elliptic curve. Our algorithm is a combination of the addition-subtraction chains and the “sliding window” variant of the “M-ary method.” We then extend the idea to the case of multi-multiplication on the elliptic curve. It is shown that the performances of both algorithms are superior to the previous methods.