In some aspects, a key establishment protocol is executed to generate a shared secret. A
first entity calculates a first image curve Eg representing an image of an elliptic curve E
under a first isogeny B; calculates the shared secret based on the first image curve EB;
receives a second image curve EA and a first pair of elliptic curve points {P.(PR), P.(Qx)} and
from a second entity; obtains a basis {R, S}; calculates a third image curve EBA representing
an image of the second image curve EA under a second isogeny UB; calculates a third pair …