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Does it make sense to use a public-key cryptosystem in counter mode to achieve data confidentiality (i.e. encrypt counter using receivers public key and then

Does it make sense to use a public-key cryptosystem in counter mode to achieve data confidentiality (i.e. encrypt counter using receivers public key and then XOR with message)? Justify your answer by drawing a diagram between Alice and Bob (and Eve if necessary) that represents a scenario where this system works OR does not work.

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