Efficient Algorithms for Multiplication on Elliptic Curves

We describe new fast algorithms for multiplying points on elliptic curves over finite fields of characteristic greater three. In contrary to the standard binary algorithm, these algorithms use representations of the multiplier with negative coefficients. Timings of the new algorithms show that they are up to 25% faster than the standard binary multiplication algorithm. This running time improvement is especially important for using elliptic curve cryptosystems on smart cards.