Towards high speed scalar multiplication over GF(p)

摘要

Elliptic curve cryptography(ECC) has gained tremendous popularity and the selection of coordinate systems has a significant impact on basic point doubling and point addition operations. In this paper, we investigate into the best suited coordinate systems corresponding to scalar multiplication with a fixed point as well as with an unfixed point and give out implementation schemes in both cases. Besides, we look into parameter selection involved in both schemes, which impacts both the speed of scalar multiplication and storage requirement.