Speeding up the Arithmetic on Koblitz Curves of Genus Two

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.We consider the following two hyperelliptic curves C_α : v2 + uv = u5 + αu2 + 1 defined over F₂ with α = 0, 1, and show how to speed up the arithmetic in the Jacobian J_Cα(F_2n) 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.