An improvement of the Guajardo-Paar method for multiplication on non-supersingular elliptic curves

Calculation of multiples of elliptic points plays a central role in elliptic curve public key cryptosystems. We present improved formulae for computing repeated doubling points on non supersingular elliptic curves over finite fields of characteristic two. These formulae, in combination with variants of the sliding window method, lead to efficient algorithms for computing a multiple of a point in such elliptic curves. For many practical implementations of the finite field GF(2ⁿ), our formulae can achieve a running time improvement of up to 25% when compared to Guajardo and Paar´s formulae (J. Guajardo and C. Paar, 1997)