Fast finite field arithmetic on an elliptic curve

摘要

(57) discloses a method of obtaining a point kP by k times the point P [Abstract] elliptic curve E over. This method of two points comprising the steps of representing a vector of binary number that is recorded in the register a number k, the step of creating a pair of sequences _(1, P ₂ P) of points, form the said pair The difference is the maximum P, respectively (mP, (m + 1) P) and (mP, (m + 1) P) from one or ((2m + 1) P 2mP,) ((2m + 1) P, (2m + 2) P) of selecting a pair of points of continuous by calculating. In this calculation, it is not used in the calculation of the y-coordinate of the point, it is possible to extract the y-coordinate at the end of the calculation. It is possible to avoid having to reverse operation during the calculation by doing so, to speed up the cryptographic processor functions. Furthermore, in the present specification discloses a method of authentication between two parties faster than traditional signature.