In this exercise, you are asked to attack an RSA encrypted message. Imagine being the attacker: You obtain the ciphertext y = 1141 by eavesdropping on a certain connection. The public key is kpub = (n,e)=(2623,2111).
1. Consider the encryption formula. All variables except the plaintext x are known. Why can't you simply solve the equation for x?
2. In order to determine the private key d, you have to calculate d ≡ e-1 mod Φ(n). There is an efficient expression for calculating Φ(n). Can we use this formula here?
3. Calculate the plaintext x by computing the private key d through factoring n = p · q. Does this approach remain suitable for numbers with a length of 1024 bit or more?