Explain RSA mathematically: (1) Choose p=61, q=53, compute n, φ(n), (2) Choose e=17, compute d, (3) Encrypt M=65, decrypt to verify, (4) Explain why RSA is secure (factoring problem), (5) Implement digital signature: sign hash with private key, verify with public key. Use small primes for hand calculation, then implement in Python.
