Obtaining keys from broadcasters 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_A representing an image of an elliptic curve E under a first isogeny ϕ_A; calculates a first pair of elliptic curve points {ϕ_A(P_B), ϕ_A(Q_B)}; calculates secret integers {c, d}; sends the first image curve E_A and the first pair of elliptic curve points {ϕ_A(P_B), ϕ_A(Q_B)} to a second entity; receives a second image curve E_BA and a third pair of elliptic curve points {ψ_B(R), ψ_B(S)} from the second entity; calculates a third image curve E_ÃBA representing an image of the second image curve E_BA 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 {ψ_B(R), ψ_B(S)}; and calculates the shared secret based on the third image curve E_ÃBA.