Title: Arithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products
Abstract: Let E be an elliptic curve, $\mathcal{K}_1$ its Kummer curve E/{±1}, E 2 its square product, and $\mathcal{K}_2$ the split Kummer surface E 2/{±1}. 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 $\mathcal{K}_2$ .