University of Virginia, Department of Computer ScienceCS588: Cryptology - Principles and Applications, Fall 2001 |

Manifest: Monday 24 September 2001

Assignments DueWednesday, 26 SeptemberProblem Set 2 Monday, 1 OctoberProjects Preliminary Proposal

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

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

- Pick 2 large secret primes,
pandq.- Let non-secret
n=pq.- Choose
e(non-secret) andd(secret) so:ed≡ 1 mod (p- 1)(q- 1).- Encryption function (non-secret):
E(M) =M^{e}modn.- Decryption function (secret):
D(C) =C^{d}modn.Euler's totient function: φ ( A Dash of Number Theoryn) = the number of positive integers <nwhich are relatively prime ton.

Ifnis prime, φ (n) =n- 1.If

pandqare prime: φ (p*q) = φ (p) * φ (q)

Euler's Theorem:1 ≡x^{φ (a) }moda.

Prime Number Theorem:π (x) (the number of primes not greater thanx) is asymtotic tox/ lnx.

Questions

- Why doesn't Diffie-Hellman solve all our problems?
- What is public-key cryptogrphy?
- What are the requirements on
EandD?- How does RSA work?
- How do you prove RSA's choice of
EandDsatisfy 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 Evansevans@cs.virginia.edu |