More on the topic
The potential appearance of a quantum computer able to implement Shor's algorithm poses a threat to traditional Diffie-Hellman-type key-agreement protocols based on the discrete logarithm problem. So, it has been proposed to use supersingular isogeny-based cryptography as a countermeasure.
An isogeny is a homomorphous rational map between two elliptic curves. If this kind of map is present between two curves, they are considered isogenous. An isogeny graph is a graph having a vertex set that is a set of isomorphism classes of elliptic curves. Two vertices of this graph are connected by an edge if and only if the representatives of the corresponding isomorphism classes are isogenous. If we confine ourselves to isogenies of degree l, we will get a graph of l-isogenies.
Upon closer examination of the so-called supersingular elliptic curves (considered "weak" in classical cryptography), it turned out that the graph of their l-isogenies has several properties allowing one to construct robust cryptographic schemes based on the assumed computational complexity of pathfinding between two graph vertices. These properties were studied by Couveignes (1997), Charles – Goren –Lauter (2006), Rostovtsev – Stolbunov (2006) and, finally, De Feo – Jao –Plût (2011), who were first to develop a stable and efficient key-agreement protocol known as SIDH. The SIKE algorithm, an alternate candidate from the 3rd
round of the NIST post-quantum competition
that provided the shortest public keys and ciphertexts, was based on SIDH.
The task of creating efficient supersingular isogeny-based authenticated key agreement schemes and digital signature protocols remains unfinished. The task of accelerating cryptographic supersingular isogeny-based algorithms is relevant as well.