Patent ID: 10630476

Abstract:
In some aspects, a key establishment protocol is executed to generate a shared secret. A first entity calculates a first image curve EA representing an image of an elliptic curve E under a first isogeny ϕA; calculates a first pair of elliptic curve points {ϕA(PB), ϕA(QB)}; calculates secret integers {c, d}; sends the first image curve EA and the first pair of elliptic curve points {ϕA(PB), ϕA(QB)} to a second entity; receives a second image curve EBA and a third pair of elliptic curve points {ψB(R), ψB(S)} from the second entity; calculates a third image curve EÃBA representing an image of the second image curve EBA under a second isogeny {tilde over (ϕ)}A, wherein the second isogeny {tilde over (ϕ)}A is identified based on the secret integers {c, d} and the third pair of elliptic curve points {ψB(R), ψB(S)}; and calculates the shared secret based on the third image curve EÃBA.