I'm trying to teach myself cryptography and I know that RSA is a large part of this topic and stumbled across the following question which I feel if clarified would help me understand a large part of RSA. If anyone could help I would really appreciate it. The question is as follows:
- Alice generates an RSA key pair, and publishes her public key $(N = 221, e = 5).$
(a) Find Alice’s chosen primes p and q.
(b) Find the exponent that Alice uses for decryption, d.
(c) Bob wants to send the message m = 2 to Alice. Find the ciphertext he sends.
(d) Would you consider Bob’s ciphertext to be secure? Say why.
(e) Bob gets the message m = 42 signed with σ = 144 in an e-mail from Alice. Using only her public key, check if Bob should believe Alice sent this message.