Abstract

We discuss new algorithms for multiplying points on elliptic curves defined over small finite fields of characteristic two. This algorithm is an extension of previous results by Koblitz, Meier, and Staffelbach. Experimental results show that the new methods can give a running time improvement of up to 50 % compared with the ordinary binary algorithm for multiplication. Finally, we present a table of elliptic curves, which are well suited for elliptic curve public key cryptosystems, and for which the new algorithm can be used.

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