Fast, uniform scalar multiplication for genus 2 Jacobians with fast KummersReport as inadecuate




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1 University of Chicago 2 Microsoft Research Redmond 3 GRACE - Geometry, arithmetic, algorithms, codes and encryption Inria Saclay - Ile de France 4 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau

Abstract : We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudo-multiplication, before recovering the proper -signed- output back on the Jacobian. This extends the work of López and Dahab, Okeya and Sakurai, and Brier and Joye to genus 2, and also to two-dimensional scalar multiplication. The technique is especially interesting in genus 2, because Kummer surfaces can outperform comparable elliptic curve systems.

Keywords : signatures scalar multiplication genus 2 Kummer surface pseudomultiplication uniform constant-time hyperelliptic curve cryptography





Author: Ping Ngai Chung - Craig Costello - Benjamin Smith -

Source: https://hal.archives-ouvertes.fr/



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