What does it mean that a protocol realizes "strong mutual authentication"? And What does it mean that a protocol realizes "weak mutual authentication"? Can you define them formally ?
I have found a definition for "strong mutual authentication" (not formal):
Strong mutual authentication requires not only matching conversation records: all principals’ records of the content and the order of all messages must coincide, but also matching views of the intent: all principals’ views of the purported sources and the intended destinations of all messages should also coincide.