Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products
arXiv:1601.03680
Abstract
Let $E$ be an elliptic curve, $\mathcal{K}_1$ its Kummer curve $E/\{\pm1\}$, $E^2$ its square product, and $\mathcal{K}_2$ the split Kummer surface $E^2/\{\pm1\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\mathcal{K}_1$, we study the explicit arithmetic of $\mathcal{K}_2$.
Coding and Cryptology --- Third International Workshop (IWCC 2011, Qingdao), Lecture Notes in Computer Science, 6639, 238-245, 2011