Notes for January 23, 1998
[ ended here ]
- Greetings and felicitations!
- Reading: Pfleeger, pp. 91-118
- Point is that PGP relies on 2 keys,
derives strength from weakest of them
- 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, 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 de mod PHI(n) = 1, so choose e = 11.
To encipher 2, C = Me mod n =
211 mod 35 = 2048 mod 35 = 18, and
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
- 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, computer-aided selection
- Go through problems, approaches to each, esp. proactive
- Password Storage
- In the clear; MULTICS story
- Encipheres; key must be kept available; get to it and it's all over
- Hashed; present idea of one-way functions using identity and sum
- Show UNIX version
- Attack Schemes Directed to the Passwords
- Exhaustive search: UNIX is 1-8 chars, say 96 possibles;
it's about 7e16
- Inspired guessing: think of what people would like (see above)
- Random guessing: can't defend against it; bad login messages aid it
- Scavenging: passwords often typed where they might be recorded as
login name, in other contexts, etc.
- Ask the user: very common with some public access services
- Expected time to guess
- Password aging
- Pick age so when password is guessed, it's no longer valid
- Implementation: track previous passwords vs. upper,
lower time bounds
- Ultimate in aging: One-Time Pads
- Password is valid for only one use
- May work from list, or new password may be generated from
old by a function
- Example: S/Key
- Challenge-response systems
- Computer issues challenge, user presents response to verify
secret information known/item possessed
- Example operations: f(x) = x+1, random,
string (for users without computers), time of day, computer
sends E(x), you answer
- Note: password never sent on wire or network
- Attack: monkey-in-the-middle
- Defense: mutual authentication (will discuss more
sophisticated network-based protocols later)
- Depend on physical characteristics
- Examples: pattern of typing (remarkably effective),
retinal scans, etc.
- Bind user to some location detection device (human, GPS)
- Authenticate by location of the device
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