Cryptology ePrint Archive: Report 2016/777

Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers

Ping Ngai Chung and Craig Costello and Benjamin Smith

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 pseudomultiplication, before recovering the proper "signed" output back on the Jacobian. This extends the work of Lopez 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.

Category / Keywords: implementation / Hyperelliptic curve cryptography, Kummer surface, genus 2, scalar multiplication, signatures, uniform, constant-time

Original Publication (with minor differences): SAC 2016

Date: received 11 Aug 2016

Contact author: smith at lix polytechnique fr

Available format(s): PDF | BibTeX Citation

Note: Derived from part of the (much longer) eprint 2015/983.

Version: 20160817:065633 (All versions of this report)

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