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I'm trying to get my head around this scenario. I understand that a private key can be used for signing a message to provide authentication and public key can be used for encrypting and its corresponding private key can be used to decrypt it. I came across this scenario and Ive been trying to research why this scenario will not work:

Suppose I changed the protocol in Kaufman & Perlman Plausibile Deniability Based on Public Key Technology, so that Alice first signs S, and then encrypts with Bob's public key. So instead of sending [{S}Bob]Alice to Bob, she sends {[S]Alice}Bob. Will this work?(can Bob be sure that the message came from Alice, but not be able to prove it to a third party?.

Why is the latter scenario a problem? Cant Bob just firstly use his private key to decrypt {[S]Alice}Bob and then use a Alice public key to verify [S]?

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    $\begingroup$ "some of my classmates argue that the digital signature will get loss"; how would it get lost? Bob's public key decryption algorithm will retrieve the entire encrypted message, which in this case includes the signature... $\endgroup$
    – poncho
    Nov 25, 2022 at 22:57

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Why is the latter scenario a problem?

The issue isn't whether Bob can be sure that $S$ came from Alice, but whether he can prove it to anyone else.

He has $S$ along with the signature signed with Alice's private key; he can show that to anyone else; if they have Alice's public key (which we assume they do), they can validate the signature, and know that $S$ originally came from Alice.

This violates the 'plausible deniability' goal.

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  • $\begingroup$ So what is the problem with the latter scenario? and whats the difference between the first scenario and the second? I believe its only a matter of process right? the first scenario is to use Alice public key to authenticate then decrypt S with Bob's private key - the latter is to decrypt with Bob's private key and then use Alice public key to authenticate. So whats the issue with the second one? $\endgroup$
    – Yusuf Ning
    Nov 25, 2022 at 23:50
  • $\begingroup$ And how does the first scenario help Alice to maintain 'plausible deniability? Cant Bob just use Alice public key to verify that [{S}Bob]Alice is from Alice and tell everyone that the {S}Bob is from Alice? $\endgroup$
    – Yusuf Ning
    Nov 26, 2022 at 1:45

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