Isogeny-based cryptography in Julia/Nemo: a case study

The Couveignes-Rostovtsev-Stolbunov key-exchange protocol based on isogenies of elliptic curves is of interest because it may resist quantum attacks, but its efficient implementation remains a challenge. We briefly present the computations involved, and efficient algorithms to achieve the critical steps, with timing results for our implementations in Sage and Julia/Nemo.