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CTRSA
2006
Springer

Efficient Doubling on Genus 3 Curves over Binary Fields

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Efficient Doubling on Genus 3 Curves over Binary Fields
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...
Xinxin Fan, Thomas J. Wollinger, Yumin Wang
Added 22 Aug 2010
Updated 22 Aug 2010
Type Conference
Year 2006
Where CTRSA
Authors Xinxin Fan, Thomas J. Wollinger, Yumin Wang
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