A clever means by which two parties may agree on a

shared secret key purely using an

insecure transport mechanism.

Example taken from Simon Singh's The Code Book

The scheme relies on the one way function Y^x mod P. Y and P may be agreed by insecure means. In this example, Y=7 and P=11. In real life, I imagine
much bigger numbers would be chosen.

Alice Bob
Stage 1 Alice chooses a number, Bob chooses a number,
say 3, and keeps it say 6, and keeps it
secret. secret.
We label her number A We label his number B
Stage 2 Alice puts 3 into the Bob puts 6 into the
one way function and one way function and
works out the result works out the result of
of 7^A mod 11: 7^B mod 11:
7^3 mod 11 7^6 mod 11
= 343 mod 11 = 117,649 mod 11
= 2 = 4
Stage 3 Alice calls the result Bob calls the result
of her calculation of his calculation beta,
alpha, and she sends and he sends his result
her result, 2, to Bob. 4, to Alice.
The Ordinarily, this would be a crucial moment:
swap Alice and Bob are exchanging information over a
public transmission medium, and this is an
opportunity for an eavesdropper to snatch some
information.
However, it turns out that the two numbers alpha
and beta are useless to an eavesdropper without
knowledge of either A or B.
Stage 4 Alice takes Bob's Bob takes Alice's result
result and works out and works out the result of
the result of alpha^B mod 11:
beta^A mod 11:
4^3 mod 11 2^6 mod 11
= 64 mod 11 = 64 mod 11
= 9 = 9
The Miraculously, Alice and Bob have ended up with the
key same number, 9. This is the key!