East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SCALAR MULTIPLICATION ON GENERALIZED HUFF CURVES USING THE SKEW-FROBENIUS MAP

  • Gyoyong Sohn (Department of Mathematics Education, Daegu National University of Education)
  • Received : 2024.06.14
  • Accepted : 2024.09.30
  • Published : 2024.09.30
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Abstract

This paper presents the Frobenius endomorphism on generalized Huff curve and provides the characteristic polynomial of the map. By applying the Frobenius endomorphism on generalized Huff curve, we construct a skew-Frobenius map defined on the quadratic twist of a generalized Huff curve. This map offers an efficiently computable homomorphism for performing scalar multiplication on the generalized Huff curve over a finite field. As an application, we describe the GLV method combined with the Frobenius endomorphism over the curve to speed up the scalar multiplication.

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References

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