The universal composition (UC) theorem: Protocol “emulates” protocol F.

The universal composition (UC) theorem: Protocol “emulates” protocol F.
(That is, for any adversary A there exists an adversary A` such that no Z can tell whether it is interacting with ( , A) or with ( F,A`).)
Corollary: If F securely realizes functionality G then so does .

(That is, for any adversary A there exists an adversary A` such that no Z can tell whether it is interacting with ( , A) or with ( F,A`).)