Manifest: Monday 24 September 2001

Assignments Due
Wednesday, 26 September	Problem Set 2
Monday, 1 October	Projects Preliminary Proposal

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

• RSA Security on the RSA Patent
• Junger decision allowing publication of RSA source code
• The Primes Pages

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) = M^e mod n.
5. Decryption function (secret): D(C) = C^d 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 ≡ x^{φ (a)} mod a.

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

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

David Evans evans@virginia.edu