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- W1489407962 abstract "In [8] Koblitz suggested to make use of a Frobenius expansion to speed up the scalar multiplications in the Jacobians of hyperelliptic curves over the characteristic 2 field. Recently, Günther et. al.[6] have modified Koblitz’s Frobenius expansion method and applied it to the Koblitz curves of genus 2 over F2to speed up the scalar multiplication. In this paper, we show that the method given in [6] can be extended to the case when the hyperelliptic curves are defined over the finite field of any characteristic. For cryptographic purposes, we restrict our interest only to those with genus 2, 3, 4. We give a theoretical efficiency of our method by comparing to the double-and-add method over the Jacobians. As a result, with some reference tables we can reduce the cost of doubleand-add method to nearly 41%." @default.
- W1489407962 created "2016-06-24" @default.
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- W1489407962 date "2002-01-01" @default.
- W1489407962 modified "2023-09-26" @default.
- W1489407962 title "Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map" @default.
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- W1489407962 doi "https://doi.org/10.1007/3-540-36231-2_23" @default.
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