Accelerating Elliptic Curve Point Multiplication Using Alternative Scalar
Weidong Qiu · Information Security and Communications Privacy · 2012
In the acceleration of elliptic curve point multiplication,significant research is focused on finding equivalent and efficient representation of the scalar. Because point multiplication occurs within a finite group of order n,and based on this property,Q=kP=(n-k)(-P),where n-k and -P could be easily computed. Thus two alternative scalars k and n-k are left. By choosing the scalar that involves less computation,current methods of point multiplication could be further accelerated. The theory and practice shows that by using alternative scalar,the number of point additions in repeated double-and-add algorithm could be reduced by 5% on average.