[Resource Topic] 2004/107: Classification of genus 2 curves over $\mathbb{F}_{2^n}$ and optimization of their arithmetic

Resource Public-key cryptography
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Welcome to the resource topic for 2004/107

Title:
Classification of genus 2 curves over \mathbb{F}_{2^n} and optimization of their arithmetic

Authors: Bertrand BYRAMJEE, Sylvain DUQUESNE

Abstract:

To obtain efficient cryptosystems based on hyperelliptic curves, we studied genus 2 isomorphism classes of hyperelliptic curves in characteristic 2. We found general and optimal form for these curves, just as the short Weierstrass form for elliptic curves. We studied the security and the arithmetic on their jacobian. We also rewrote and optimized the formulas of Lange in characteristic 2, and we introduced a new system of coordinate. Therefore, we deduced the best form of hyperelliptic curves of genus 2 in characteristic 2 to use in cryptography.

ePrint: https://eprint.iacr.org/2004/107

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