Paper 2016/777

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

Ping Ngai Chung, 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.

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

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Published elsewhere. Minor revision. SAC 2016
Keywords
Hyperelliptic curve cryptographyKummer surfacegenus 2scalar multiplicationsignaturesuniformconstant-time
Contact author(s)
smith @ lix polytechnique fr
History
2016-08-17: received
Short URL
https://ia.cr/2016/777
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/777,
      author = {Ping Ngai Chung and Craig Costello and Benjamin Smith},
      title = {Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers},
      howpublished = {Cryptology ePrint Archive, Paper 2016/777},
      year = {2016},
      note = {\url{https://eprint.iacr.org/2016/777}},
      url = {https://eprint.iacr.org/2016/777}
}
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