University of Virginia, Department of Computer ScienceCS551: Security and Privacy on the Internet, Fall 2000 |

Manifest: Wednesday 20 September 2000

Assignments Due27 SeptemberProblem Set 2

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:ed1 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: ( A Dash of Number Theoryn) = the number of positive integers <nwhich are relatively prime ton.

Ifnis prime, (n) =n- 1.(

a*b) = (a) * (b)

1x^{ (a) }moda.

Prime Number Theorem:(x) is asymtotic tox/ lnx.

(x) = the number of primes not greater thanx.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 551: Security and Privacy on the Internet |
David Evansevans@cs.virginia.edu |