Suppose that Alice\'s RSA encryption key is (e,N) and that C is the ciphertext p

Question

Suppose that Alice's RSA encryption key is (e,N) and that C is the ciphertext produced when she encrypts the plaintext message P. Show that Eve can recover P after intercepting C if she manages to obtain the result of Alice's decryption of C' = Cr^e, where r is a random integer that Eve has selected. (Alice might decrypt C because she has been fooled into thinking it is a valid message from Bob. Eve is able to obtain the result if Alice is not careful how she throws away what seems to her to be nonsense.)

Explanation / Answer

ciphertext c=me mod n may ask the holder of the secret key to decrypt an unsuspicious-looking

ciphertext c' = c re mod n for some value r chosen by the attacker.

Because of the multiplicative property, c' is the encryption of mrmod n.

Hence, if the attacker is successful with the attack, he will learn (mrmod n) from which he can derive the message m by multiplying mr with the modular inverse of r modulo n.

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