BROADCASTING IN SUPERSINGULAR ISOGENY-BASED CRYPTOSYSTEMS

摘要

In some aspects, a key establishment protocol is executed to generate a shared secret. A first entity calculates a first image curve E_B representing an image of an elliptic curve E under a first isogeny Φ_Β; calculates the shared secret based on the first image curve E_B; receives a second image curve E_A and a first pair of elliptic curve points {Φ_Α(Ρ_Β),Φ_Α(Q_Β)} and from a second entity; obtains a basis {R, S}; calculates a third image curve E_BA representing an image of the second image curve E_A under a second isogeny Ψ_B; calculates a third pair of elliptic curve points { Ψ_B(R),Ψ_B(S)}; and sends the third image curve E_BA and the third pair of elliptic curve points { Ψ_B(R),Ψ_B(S)} to the second entity, wherein the third image curve E_BA and the third pair of elliptic curve points { Ψ_B(R),Ψ_B(S)} enable the second entity to compute the shared secret.