Notes for November 1, 1999
- Greetings and Felicitations!
- Puzzle of the Day
- Public-Key Cryptography
- Basic idea: 2 keys, one private, one public
- Cryptosystem must satisfy:
- given public key, CI to get private key;
- cipher withstands chosen plaintext attack;
- encryption, decryption computationally feasible
[note: commutativity not required]
- Benefits: can give confidentiality or authentication or both
- Use of PKC
- Normally used as key interchange system to exchange secret keys (cheap)
- Then use secret key system (too expensive to use PKC for this)
- Provides both authenticity and confidentiality
- Go through algorithm:
Idea: C = Me mod n,
M = Cd mod n,
with ed mod PHI(n) = 1.
Proof: MPHI(n) mod n = 1
[by Fermat's theorem as generalized by Euler];
follows immediately from
ed mod PHI(n) = 1.
Public key is (e, nn); private key is d.
Choose n = pq; then PHI(n) = (p-1)(q-1).
p = 5, q = 7; n = 35, PHI(n) = (5-1)(7-1) = 24.
Pick d = 11. Then de mod PHI(n) = 1,
so choose e = 11. To encipher 2,
C = Me mod n
= 211 mod 35 = 2048 mod 35 = 18.
M = Cd mod n
= 1811 mod 35 = 18.
p = 53, q = 61, n = 3233, PHI(n) = (53-1)(61-1) = 3120.
Take d = 791; then e = 71.
Encipher M = RENAISSANCE:
A = 00, B = 01, ..., Z = 25, blank = 26.
M = RE NA IS SA NC Eblank = 1704 1300 0818 1800 1302 0426
C = (1704)71 mod 3233 = 3106; etc.
= 3106 0100 0931 2691 1984 2927
- validating client (user) identity
- validating server (system) identity
- validating both (mutual authentication)
- What you know
- What you have
- What you are
- How UNIX does selection
- Problem: common passwords; Go through Morris and Thompson;
Klein and mine, etc.
- May be pass phrases:
goal is to make search space as large as possible and
distribution as uniform as possible
- Other ways to force good password selection: random, pronounceable,
- Go through problems, approaches to each, esp. proactive
Send email to
Department of Computer Science
University of California at Davis
Davis, CA 95616-8562
Page last modified on 11/1/99