Diffie-Hellman

Secure Key Exchange

1976

Whitfield Diffie Martin Hellman

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

Alice

• Chooses a large random number x

• CalculatesX = gx mod (n)

• Sends X, g, and n to Bob.

Bob

• Chooses a large random number y

• CalculatesY = gy mod (n)

• Sends Y to Alice.

Alice

• Calculates

k = Yx mod (n)

Bob

• Calculates

k’ = Xy mod (n)

The Key

• k’ = k is the shared key

k = Yx mod (n) = (gy )x mod (n) = gyx mod (n)

k’ = Xy mod (n) = (gx )y mod (n) = gxy mod (n)

• Nobody can calculate k givenn, g, X, and Y

The Key

• Only Alice and Bob know k

• Good for only one session

• Can’t be sure connected to the same person

• Used if you only want a symmetric key

• No authentication