Diffie – Hellman key exchange

1. Diffie–Hellman key exchange -RamyaDeepaPalle CS-555

2. Introduction • Discovered by Whitfield Diffie and Martin Hellman • “New Directions in Cryptography”

3. Need ????? • Diffie–Hellman key exchange (D–H)is a specific method of exchangingCryptographic key.

4. Concept used: • Its easy to mix 2 colors to make a third color. • Given a mixed color its hard to reverse it in order to find the exact original colors.

5. http://www.youtube.com/watch?v=YEBfamv-_do Reference:

6. Alice & Bob • Agree on 2 numbers n and g • g is primitive relative mod (n) • For each x < n, there is an a such that ga = x mod (n) • These do not have to kept secret

7. Alice and Bob separately Alice: • Chooses a large random number x • Calculates X = gxmod (n) • Sends X, g, and n to Bob. Bob: • Chooses a large random number y • Calculates Y = gymod (n) • Sends Y toAlice.

8. Calculation • Alice:Calculates k = Yxmod (n) • Bob:Calculates k’ = Xymod (n)

9. Final Key • k’ = k is the shared key k = Yxmod (n) = (gy )xmod (n) = gyxmod (n) k’ = Xymod (n) = (gx )ymod (n) = gxymod (n) • Nobody can calculate k given n, g, X, and Y

10. References: • http://www.youtube.com/watch?v=YEBfamv-_do • http://en.wikipedia.org/wiki/Diffie–Hellman_key_exchange