• isogeny-based cryptography
• binary fields
• crs
• key-exchange protocol

We adapt the ordinary isogeny-based cryptosystems of Couveignes, Rostovtsev and Stolbunov (CRS) to the case where the base field is a binary field. To make the protocol work in this setting, we modify some of the algorithms used in the original protocol. In particular, we study and implement an algorithm of Lercier for the computation of isogenies between elliptic curves defined over binary fields, an algorithm to compute fast scalar multiplication using only the x-coordinates of the point and a version of the SEA algorithm in characteristic two, due to Vercauteren. Then we describe in detail the whole cryptosystem by providing pseudocodes of the different algorithms involved and give an overview of the other isogeny-based cryptosystems. Finally we talk about our implementation and give some experimental results, comparing these results with the ones obtained using a revised version of CRS due to De Feo, Kieffer and Smith.