University of Virginia, Department of Computer Science
CS588: Cryptology - Principles and Applications, Fall 2001

Manifest: Monday 24 September 2001
Assignments Due
Wednesday, 26 SeptemberProblem Set 2
Monday, 1 OctoberProjects Preliminary Proposal

Before 25 September: Reread parts of RSA paper you didn't understand.
Optional reading for more information: (see web version for links)

RSA Algorithm
  1. Pick 2 large secret primes, p and q.
  2. Let non-secret n = pq.
  3. Choose e (non-secret) and d (secret) so: ed ≡ 1 mod (p - 1)(q - 1).
  4. Encryption function (non-secret): E(M) = Me mod n.
  5. Decryption function (secret): D(C) = Cd mod n.
A Dash of Number Theory
Euler's totient function: φ (n) = the number of positive integers < n which are relatively prime to n.
If n is prime, φ (n) = n - 1.

If p and q are prime: φ (p * q) = φ (p) * φ (q)

Euler's Theorem: 1 ≡ xφ (a) mod a.

Prime Number Theorem: π (x) (the number of primes not greater than x) is asymtotic to x / ln x.


Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory of numbers.

G. H. Hardy, The Mathematician's Apology, 1940.

CS 655 University of Virginia
Department of Computer Science
CS 588: Cryptology - Principles and Applications
David Evans