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 a : v 2 + uv = u 5 + au 2 + 1 defined over F2 with a = 0, 1, and show how to speed up the arithmetic in the Jacobian JCa(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.
|Title of host publication||Selected areas in cryptography : 7th Annual International Workshop, SAC 2000 Waterloo, Ontario, Canada, August 14–15, 2000 : proceedings|
|Editors||D.R. Stinson, S. Tavares|
|Place of Publication||Berlin|
|Publication status||Published - 2001|
|Name||Lecture Notes in Computer Science|