Montgomery Ladder for All Genus 2 Curves in Characteristic 2
نویسنده
چکیده
Using the Kummer surface, we generalize Montgomery ladder for scalar multiplication to the Jacobian of genus 2 curves in characteristic 2. Previously this method was known for elliptic curves and for genus 2 curves in odd characteristic. We obtain an algorithm that is competitive compared to usual methods of scalar multiplication and that has additional properties such as resistance to side-channel attacks. Moreover it provides a significant speed-up of scalar multiplication in many cases. This new algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on embedded systems (such as smart cards).
منابع مشابه
Fast genus 2 arithmetic based on Theta functions
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive fast formulae for the scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder. Our formulae can be used to design very efficient genus 2 cryptosystems that should be fast...
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