He records all messages, decomposes the messages as far as possible and generates all possible new compositions. Furthermore, any object he has at his hands is considered as a key and tried to used for encryption as well as for decryption. All these messages are posted. The set of messages the intruder has available is represented by the predicate Im . The participants are Alice, Bob, Trust and Intruder.
Intruder records all messages.
He decomposes and decrypts all messages he owns the key for. He composes all possible messages. He considers every item to be a key and uses it for encryption. He sends everything. Finally we must formalize the insecurity requirement.