Difference in the Powers of Simulator and Environment in Universal Composability I know that in UC model, environment controls the real world adversaries but there is still a simulator wrapped around these real-world adversaries in the ideal world (which we sometimes collectively call ideal adversaries). I wanted to know if all the interaction that happens between the real world adversary wrapped inside the simulator and the environment in the ideal world has to go through the simulator?
If this is true, then the simulator can look at all the messages between the adversary and the environment.
Can someone clarify the powers that simulators have in UC versus the powers that environment have in UC?
Can environment also interact with the honest parties? As far as I know, the environment can only interact with adversarial parties and then try to distinguish the real execution of the protocol from the ideal one.
In the real world we do have adversary and environment. The environment interacts with the protocol (real function) and the adversary. The parties are part of the environment. The real function leaks information to the environment/adversary
However, in the ideal world there is no such leakage. Therefore, in order to prevent the environment from distinguishing between these two worlds we need a simulator to create these leakage by getting some information from the ideal world. Here, the simulator is acting like the adversary for the real world. The environment thus is able to interact only with the ideal functionality and the simulator where the simulator is the adversary for the ideal world