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

" Initial Version 0.1 "

Elliptic Curve Cryptography (ECC) defines asymmetric cryptographic systems, which perform operations on elliptic curves over finite fields. Such methods are secure only if discrete

logarithms in the group of points of the elliptic curve cannot be efficiently calculated. The

computation on elliptic curves is done by the operations Point Addition, Point Doubling and

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@@ -21,12 +23,29 @@ By nature, due to uniqueness reasons the validation must be performed in affine

representation of the Point.

Goal:

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

Point Doubling, Point Addition, 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.

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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.