Key exchange problem

1. Hoang Nguyen Van
Mail: hoangnvvnua@gmail.com
Department of Computer Science – FITA – HUA
Information Security Course --------------------------------------------- Fall 2013
Dept. of Computer Science – FITA – HUA

2. Information Security ------------- Fall 2013
Hoang Nguyen Van
How I can share with my boyfriend, a secret key.

3. Information Security ------------- Fall 2013
Hoang Nguyen Van
How to manage mutual keys

4. Information Security ------------- Fall 2013
Hoang Nguyen Van
I hate my keys

5. Information Security ------------- Fall 2013
Hoang Nguyen Van

6. Information Security ------------- Fall 2013
Hoang Nguyen Van
Online Trusted 3rd Party (TTP)
O(n) keys per user

7. Information Security ------------- Fall 2013
Hoang Nguyen Van
Online Trusted 3rd Party (TTP)
O(1) one key per user
kAB

8. Information Security ------------- Fall 2013
Hoang Nguyen Van
Online Trusted 3rd Party (TTP)
Generating keys: a toy protocol
“Alice wants key with Bob”
(kA)
choose
random kABE(kA,”AB”||kAB)
ticket = E(kA,”AB”||kAB)
(kB)
ticket
kAB kAB
(Eavesdropping security only)

9. Information Security ------------- Fall 2013
Hoang Nguyen Van
Can we generate shared keys without
an online trusted 3rd party?

10. Information Security ------------- Fall 2013
Hoang Nguyen Van
Ralph Merkle (1952)

11. Information Security ------------- Fall 2013
Hoang Nguyen Van
Merkle Puzzles (1974)

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Hoang Nguyen Van
Merkle Puzzles (1974)
“Puzzle # xi” ll ki

13. Information Security ------------- Fall 2013
Hoang Nguyen Van
Merkle Puzzles (1974)
BobAlice
puzzle1 , … , puzzlen
xj
kj kj
O(n)
O(n)
O( n2 )
But Infeasible

14. Information Security ------------- Fall 2013
Hoang Nguyen Van
The Diffie-Hellman protocol

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Hoang Nguyen Van
2
5
Very easy
Very hard
One-way function

16. Information Security ------------- Fall 2013
Hoang Nguyen Van
10 10
510 310
10 5
3
10 5
3
310 510
KEY
Alice Bob
The Diffie-Hellman protocol

17. Information Security ------------- Fall 2013
Hoang Nguyen Van
The Diffie-Hellman protocol
Alice Bob
choose random a in {1,…,p-1} choose random b in {1,…,p-1}
kAB = gab (mod p) = (ga)
b
= Ab (mod p)Ba (mod p) = (gb)
a
=

18. Information Security ------------- Fall 2013
Hoang Nguyen Van

19. Information Security ------------- Fall 2013
Hoang Nguyen Van