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 Cα : v 2 + uv = u 5 + α u 2 + 1 defined over F2 with α = 0, 1, and show how to speed up the arithmetic in the Jacobian JC α (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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