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My question is a bit naive, but what if someone generates the same RSA key pair as someone else? This person would have the same private key and so would be able to decrypt messages not intended to him.

I bet that the answer will be: “It is very unlikely”, but I would like a more persuasive answer to realize that it can't happen in practice.

A related question: when someone generates a key pair, how can he/she be sure that nobody has already generated this key pair? Would the answer again be, that it is “very unlikely”?

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