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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.

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@owlstead : The question I get is the first part of a multiple parts question , when it is asked they didn't specify which protocol it is, so I didn't think the name is important. Later part ask to prove that $CREE_0$ - nest is "weak mutual authentication". – user3283751 Jun 7 '14 at 17:39
@owlstead : I can provide $CREE_0$ - nest 's definition if you want. – user3283751 Jun 7 '14 at 17:53
OK, but I'm not sure that posting the protocol will help solve this issue; it is still unclear what the word "strong" means in relation to the protocol, we may need the context for the security claim. – Maarten Bodewes Jun 8 '14 at 10:08
Sorry, chat is not currently available, it says I have to log in (which I already have). I can see you are trying to salvage the question, and we are trying to answer, but "strong" in itself does not have any meaning. So without the particular claim, we can simply only guess. Maybe you haven't got enough context either, but in that case you should ask the authors for more detail. We want to answer, we just cannot. – Maarten Bodewes Jun 8 '14 at 13:50
Yes, that link contains one definition of strong authentication. If you are sure that is the definition of strong authentication you want to use, by all means edit it into your question. – Maarten Bodewes Jun 9 '14 at 18:02

Strong with regards to cryptographic protocol usually means that the protocol is secure if the underlying primitives can be proved cryptographically strong. In your case, that could be because authentication is performed using a symmetric cipher and a key that is only distributed for 2 participants.

But as indicated in the comments, "strong" depends on context, you won't get any assurances from it by itself.

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