Question: In the RSA encryption scheme, to generate the ( public - key,private - key ) pair, we start from generating two large random primes ,

In the RSA encryption scheme, to generate the (public-key,private-key) pair, we start from generating two large random primes , and will be part of the public key. It is crucial to generate random so that attackers won't be able to guess them. Another important purpose is to ensure different users do not happen to end up with the same (or ). Consider two RSA users Alice and Bob, where Alice generates and publishes her public key ; Similarly Bob has with public key . Now suppose unluckily, , knowing this fact, show how an attacker can break both of their encryption schemes.

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