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I have a problem I need to solve with the following scenario and I hope someone can help me find an approach or direction to start tackling it.

Consider Alice as a sender who has $n$ strings which she encrypts with her private key $k$ and some encryption algorithm $E$. Bob has access only to the encrypted strings and wants to inspect them to see if they contain any one of possible blacklisted words, which if detected should obligate Alice to reveal the matching string to Bob in clear-text. Otherwise, Alice is entitled to her privacy and Bob should not be aware of the clear-text content of her data.

How would you suggest the parties to communicate in order to achieve such a common goal ? What cryptographic primitives would you suggest me to use? I thought of using oblivious transfer in some way, but I find it a little hard to form a clear idea how.

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  • $\begingroup$ private -> secret ​ ? ​ ​ ​ (If there are PKE schemes then there are PKE schemes for which "encrypting" with a private key always yields the empty string.) ​ ​ ​ ​ ​ ​ ​ ​ $\endgroup$ – user991 Jul 13 '16 at 0:47
  • $\begingroup$ Actually, if my suggested replacement is correct, then what stops Alice from just going through the protocol with some different k' instead of k? ​ ​ $\endgroup$ – user991 Jul 13 '16 at 0:51

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