Question

Suppose two users Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eA and eB are relatively prime. Charles wants to send the message m to Alice and Bob, so he Ow find m if she intercepts CA and CB.

Answer 1

Alice and Bob have the same RSA modulus and their encryption exponents are relatively prime. Intercepting the encrypted messages does not allow Charles to directly find the original message unless he has the private keys.

Step-by-step explanation:

In the given scenario, Alice and Bob have the same RSA modulus n, and their encryption exponents eA and eB are relatively prime. When Charles sends a message m to Alice and Bob, he encrypts it using their respective public keys, which are based on their modulus and encryption exponents. If Charles intercepts the encrypted messages CA and CB, he cannot directly find the original message m because breaking RSA encryption is computationally difficult.

However, if Charles knows the private keys corresponding to Alice and Bob's public keys, he can decrypt the messages CA and CB to obtain the original message m. This is because the private key, consisting of the decryption exponent and the modulus, allows the receiver to decrypt messages encrypted using their respective public keys.

In summary, Charles cannot directly find the original message m if he intercepts the encrypted messages CA and CB, unless he has access to the private keys of Alice and Bob.