Paper 2018/305

Efficient four-dimensional GLV curve with high security

Olivier Bernard and Renaud Dubois and Simon Masson

Abstract

We apply Smith's construction to generate four-dimensional GLV curves with fast arithmetic in the group law as well as in the base field. As Costello and Longa did in [5] for a 128-bit security level, we btained an interesting curve for fast GLV scalar multiplication, providing a high level of security (254 bits). Our curve is defined over a well-known finite field: $\mathbb{F}_{p^2}$ where $p = 2^{255} - 19$. We finally explicit the two endomorphisms used during GLV decomposition.