Section:
New Results
Faster elliptic
and hyperelliptic curve cryptography
B. Smith made several contributions to the development of faster
arithmetic on elliptic curves and genus 2 Jacobians in 2015.
First, an extended and more detailed treatment of his -curve
construction for endomorphism-accelerated elliptic curves
(previously presented at ASIACRYPT 2013, and the basis of a
successful implementation with C. Costello and H. Hisil
presented at EUROCRYPT 2014) appeared in the Journal of Cryptology.
A simplified approach to essential precomputations was published in
the proceedings of AGCT-14.
Finally, with C. Costello and P.-N. Chung,
he gave a new, efficient, uniform, and constant-time scalar multiplication
algorithm for genus 2 Jacobians exploiting fast Kummer surface
arithmetic and features of differential addition chains.
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