Scalar multiplication on Jacobi curves using the Frobenius map
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In this paper, we consider the scalar multiplication on Ja- cobi curves over a nite eld using the Frobenius expansion. Applying the Frobenius endomorphism on Jacobi curves, we construct a Frobe- nius map de ned on the quadratic twist of Jacobi curves. To speed up the scalar multiplication on Jacobi curves, we use the GLV method combined with the Frobenius endomorphism over the curves.
Abstract
In this paper, we consider the scalar multiplication on Ja- cobi curves over a nite eld using the Frobenius expansion. Applying the Frobenius endomorphism on Jacobi curves, we construct a Frobe- nius map de ned on the quadratic twist of Jacobi curves. To speed up the scalar multiplication on Jacobi curves, we use the GLV method combined with the Frobenius endomorphism over the curves.
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