Implementing RSA

• Bob generates two large primes, p & q

  • Probabilistic primality testing O((log n) 3)

• Bob computes n = pq and f(n) =(p-1)(q-1)

• Bob chooses random e (1 < e < f(n)) such that gcd(e, f(n) ) = 1

  • Euclidean algorithm

• Bob computes d = e -1 mod f(n)

  • Extended Euclidean Algorithm O((log n)2)

• Bob publishes n and e in a directory as his public key.

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