Suppose you changed the protocol in $20\mathrm{.}8\mathrm{.}2$ Plausible 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$.$ Does this work? $($i$.$e$.,$ can

Bob be sure that the message came from Alice, but not be able to prove it to a third party$)$