University of Virginia, Department of Computer Science
CS551: Security and Privacy on the Internet, Fall 2000

Manifest: Wednesday 20 September 2000

Assignments Due
27 SeptemberProblem Set 2

Readings
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 equiv 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: theta (n) = the number of positive integers < n which are relatively prime to n.
If n is prime, theta (n) = n - 1.

theta (a * b) = theta (a) * theta (b)
1 equiv xtheta (a) mod a.

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

Questions

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 551: Security and Privacy on the Internet
David Evans
evans@cs.virginia.edu