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One of the attacks on plain RSA involves a sender who encrypts two related messages using the same public key. Formulate an appropriate definition of security ruling out such attacks.And show that any CPA-secure public-key encryption scheme satisfies your definition. What does formulating an appropriate definition of security mean? It is a question from introduction to modern cryptography textbook

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What does formulating an appropriate definition of security mean?

In the context, that's defining a criteria/experiment allowing to define/test if an encryption scheme succumbs or not to the same kind of attack as the one hinted for plain RSA (which I guess is the Franklin-Reiter related message attack).

Coming with the experiment defining CPA security would formally be an acceptable answer, but the next part would then be totally trivial:

show that any CPA-secure public-key encryption scheme satisfies your definition.

Thus, I guess it really is asked a criteria/experiment that uncovers the hinted weakness of plain RSA, but is somewhat different from (perhaps simpler than) CPA security, and may accept some encryption scheme that is not CPA-secure.

It is not easy to come up with a precise criteria/experiment matching that. Beyond understanding the extent of what's wrong with plain RSA, perhaps the exercise really is about making one grasp CPA security, and get that despite its apparent complexity, it is sort of a local optimum between simplicity and effectiveness at screening out poor encryption schemes.

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