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

Ping Ngai Chung (1) , Craig Costello (2) , Benjamin Smith (3, 4)

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

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.

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

Domaines: Cryptographie et sécurité [cs.CR]

Ping Ngai Chung, Craig Costello, Benjamin Smith. Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers. Selected Areas in Cryptography - SAC 2016, Aug 2016, St John's, Canada. pp.18, ⟨10.1007/978-3-319-69453-5_25⟩. ⟨hal-01353480⟩