What is Supersingular isogeny key exchange?

Supersingular isogeny Diffie–Hellman key exchange is a post-quantum cryptographic algorithm used to establish a secret key between two parties over an otherwise insecure communications channel. It is analogous to the Diffie–Hellman key exchange, but is based on walks in a supersingular isogeny graph and is designed to resist cryptanalytic attack by an adversary in possession of a quantum computer. SIDH boasts one of the smallest key sizes of all post-quantum key exchanges; with compression, SIDH used 2688-bit public keys at a 128-bit quantum security level. SIDH also distinguishes itself from similar systems such as NTRU and Ring-LWE by supporting perfect forward secrecy, a property that prevents compromised long-term keys from compromising the confidentiality of old communication sessions. These properties makes SIDH a natural candidate to replace Diffie–Hellman and elliptic curve Diffie–Hellman , which are widely used in Internet communication. However, SIDH is vulnerable to a key-recovery attack and is therefore insecure.