Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products

David Kohel (1)

1 I2M - Institut de Mathématiques de Marseille

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 $\mathcal{K}_2$.

Domaines: Théorie des nombres [math.NT]

David Kohel. Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products. Coding and Cryptology: Third International Workshop, IWCC 2011, Qingdao, China, May 30-June 3, 2011. Proceedings, 6639, pp.238-245, 2011, Lecture Notes in Computer Science, ⟨10.1007/978-3-642-20901-7_15⟩. ⟨hal-01257337⟩