Notes for November 2, 1998
- Greetings and Felicitations!
- Projects sent back; do you want me to post a list of names and projects?
- Midterm is Friday; open book, open notes; review session dueing
- Puzzle of the Day
- All about "impossibilities" ...
- Go through the algorithm
- 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: M = 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, n); 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
ed 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 = 2.
- Example: 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. Then:
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
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Page last modified on 11/5/98