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Actually, if RSA is being used in a deterministic way (and the public exponent $e$ is relatively small), someone could recover the value $N$. We know that $P^e = C \bmod N$; that's equivalent to $P^e - C = kN$ for some integer $k$; if $e$ is small, then Shor's algorithm might be able to factor $P^e - C$; allowing you to recover $N$. Alternatively, if you ...


1

I'ld say the answer is “no”. Usually you need to factor the modulus $N$ to break RSA. Now $N$ is not available to the attacker. So with a single plain text and cipher text I'm pretty sure the attacker has too little information to retrieve N or any other key component. Your pre-condition of not having the public key and therefore the modulus $N$ available ...



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