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Scalar multiplication on Jacobi curves using the Frobenius map. (English) Zbl 1440.94081

Summary: In this paper, we consider the scalar multiplication on Jacobi curves over a finite field using the Frobenius expansion. Applying the Frobenius endomorphism on Jacobi curves, we construct a Frobenius map defined 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.

MSC:

94A60 Cryptography
14G50 Applications to coding theory and cryptography of arithmetic geometry
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14H25 Arithmetic ground fields for curves
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