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

Manifest: Wednesday 20 September 2000

 Assignments Due 27 September Problem Set 2

Before 25 September: Reread parts of RSA paper you didn't understand.

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

(a * b) = (a) * (b)
1 x (a) mod a.

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

Questions
• Why doesn't Diffie-Hellman solve all our problems?
• What is public-key cryptogrphy?
• What are the requirements on E and D?
• How does RSA work?
• How do you prove RSA's choice of E and D satisfy the requirements?

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.