Implementing RSA

• Bob generates two large primes, p and q
  Probabilistic primality testing O((lg n)³)
• Bob computes n = pq and $\phi$(n) = (p-1)(q-1)
• Bob chooses random e (1 < e < $\phi(n)$) such that gcd(e, $\phi$(n)) = 1
  Euclidean algorithm
• Bob computes d = e^-1 mod $\phi$(n)
  Extended Euclidean Algorithm O((lg n)²)
• Bob publishes n and e in a directory as his public key