The Diffie-Hellman protocol is a method for two computer users to generate a shared private key with which they can then exchange information across an insecure channel.
Let the users be named Alice and Bob. First, they agree on two prime numbers 
and 
,
where 
is large (typically at least 512 bits) and 
is a primitive root modulo
.
(In practice, it is a good idea to choose 
such that 
is also prime.) The numbers 
and 
need not be kept secret from other users. Now Alice chooses
a large random number 
as her private key and Bob similarly chooses a large number
.
Alice then computes 
, which she sends to Bob, and Bob computes 
,
which he sends to Alice.
Now both Alice and Bob compute their shared key 
, which Alice computes as
 |
and Bob computes as
 |
Alice and Bob can now use their shared key 
to exchange information without worrying about other users
obtaining this information. In order for a potential eavesdropper (Eve) to do so,
she would first need to obtain 
knowing only 
, 
, 
and 
.
This can be done by computing 
from 
or 
from 
. This is the discrete
logarithm problem, which is computationally infeasible for large 
. Computing the discrete logarithm of a number modulo 
takes roughly the same amount of time as factoring the product of two primes the
same size as 
,
which is what the security of the RSA cryptosystem relies on. Thus, the Diffie-Hellman
protocol is roughly as secure as RSA.
