Point Doubling, Point Addition, Jacobi-to-Affine Transformation,

Preparation, Montgomery Transformation, Affine-to-Jacobi Transformation, Point Addition,

Point Doubling, Jacobi-to-Affine Transformation,

Montgomery Back-transformation, Point Validation.

By using a Linux User Space Application the correct functionality should be verified by performing Point Validations in GF(2m) for the supported ECC precision widths. Based on a

given Point and elliptic curve equation a statement must be made whether the Point is on the curve or not.For the validation of the calculation inside of the CryptoCore the open-source mathematics

software SageMath should be used.In order to be able to illustrate the time required for ECC Point Validation with different precision widths the Real Time Library support (-lrt) should be included.

Point Addition:

With 2 distinct points, P and Q, addition is defined as the negation of the point resulting from the intersection of the curve, E, and the straight line defined by the points P and Q, giving the point, R.

P+Q=R

(x1,y1)+(x2,y2)=(x3,y3)

An elliptic curve in short Weierstrass form has parameters a2 a6 and coordinates x y satisfying the following equations:

y^2+x*y=x^3+a2*x^2+a6

Affine addition formulas: (x1,y1)+(x2,y2)=(x3,y3) where