Isogeny based cryptography
Published:
Isogeny-based cryptography is a kind of elliptic-curve cryptography, whose security relies on (various incarnations of) the problem of finding an explicit isogeny between two given isogenous supersingular elliptic curves over a finite field $\mathbb F_q$. However, given an elliptic curve $E$ in Weierstrass form over a finite field $\mathbb F_q$ and a point $P$ on $E$ of order $n$, one can compute a cyclic separable isogeny of degree $n$ using Velu’s formulas in SageMath (implemented by D. Shumow in 2009).