Welcome to the resource topic for
**2005/228**

**Title:**

Efficient Doubling on Genus 3 Curves over Binary Fields

**Authors:**
Xinxin Fan, Thomas Wollinger, Yumin Wang

**Abstract:**

The most important and expensive operation in a hyperelliptic curve

cryptosystem (HECC) is scalar multiplication by an integer k, i.e., computing an integer k times a divisor D on the Jacobian. Using some recoding algorithms for scalar k, we can reduce a number of divisor class additions during the process of computing scalar multiplication. So divisor doubling will account for the main part in all kinds of scalar multiplication algorithms. In order to accelerate the genus 3 HECC over binary fields we investigate how to

compute faster doubling in this paper.

By constructing birational transformation of variables, we derive

explicit doubling formulae for all types of defining equations of

the curve. For each type of curve, we analyze how many field operations are needed. So far all proposed curves are secure,

though they are more special types. Our results allow to choose

curves from a large enough variety which have extremely fast

doubling needing only one third the time of an addition in the

best case. Furthermore, an actual implementation of the new formulae

on a Pentium-M processor shows its practical relevance.

**ePrint:**
https://eprint.iacr.org/2005/228

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