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**2018/305**

**Title:**

Efficient four-dimensional GLV curve with high security

**Authors:**
Olivier Bernard, Renaud Dubois, 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.

**ePrint:**
https://eprint.iacr.org/2018/305

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