Use of the CryptoCore for Elliptic Curve Point Validation in GF(2m)

<center><p><b><fontsize="6">Use of the CryptoCore for Elliptic Curve Point Validation in GF(2m)</font></p></b></center>

" Initial Version 0.1 "

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@@ -22,11 +22,11 @@ being the order of the generator Point. If any of this tests fails, the Point wi

By nature, due to uniqueness reasons the validation must be performed in affine coordinate

representation of the Point.

Goal:

<p><b>Goal:</p></b>

Within this project work a Linux device driver should be extended by following ECC GF(2m)

Functions:

<p><b>Functions:</p></b>

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

Point Doubling, Jacobi-to-Affine Transformation,

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@@ -36,7 +36,7 @@ given Point and elliptic curve equation a statement must be made whether the Poi

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:

<p><b>Point Addition:</p></b>

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.

The validation of the elliptic curve domain parameters can be simplified into two categories; validating an Elliptic Curve, and validating a Base Point.

The validation of the elliptic curve has criteria for binary Galois fields .

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@@ -106,15 +106,15 @@ G = hP, where P = (xP , yP), and h is the cofactor.