Abstract
Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations.In this paper, we generalize their ideas to hyperelliptic curves of genus 2.W e consider the following two hyperelliptic curves Cα: v2 + uv = u5 + αu2 + 1 defined over F2 with α = 0, 1, and show how to speed up the arithmetic in the Jacobian JCα(F2n) by making use of the Frobenius automorphism.With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian.If we allow 6 precomputations, we are even able to speed up by a factor of 7.
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CITATION STYLE
Günther, C., Lange, T., & Stein, A. (2001). Speeding up the arithmetic on Koblitz curves of genus two. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2012, pp. 106–117). Springer Verlag. https://doi.org/10.1007/3-540-44983-3_8
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