| abstract |
In some aspects, a key establishment protocol is executed to generate a shared secret. A first entity calculates a first image curve E n A n representing an image of an elliptic curve E under a first isogeny Φ n A n ; calculates a first pair of elliptic curve points { Φ n A ( P n B ),Φ A ( Q n B )}; calculates secret integers { c, d }; sends the first image curve E n A and the first pair of elliptic curve points { Φ n A ( P n B ),Φ A ( Q n B )} to a second entity; receives a second image curve E n AB n and a third pair of elliptic curve points { ψ n B ( R ), ψ n B ( S )} from the second entity; calculates a third image curve E n ÃBA representing an image of the second image curve E n BA under a second isogeny Φ̃ n A , wherein the second isogeny Φ̃ n A is identified based on the secret integers { c, d } and the third pair of elliptic curve points { ψ n B ( R ), ψ n B ( S )}; and calculates the shared secret based on the third image curve E n ÃBA. |