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 $\mathbb{Q}$-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.