I'm not certain I understand your questions, but here are some answers (I
In the DH protocol you have what we call public parameters, p and g.
p is a large prime integer, which defines a group Z*p, g is a generator
defines a subgroup in Z*p.
You can use fix values for p an g.
Now, participants will choose private and public keys.  The private key
is simply chosen as a random number x, whose value is between 1 and
p-1.   The public key associated to x will be y = g^x mod p.
Participants keep x secret and y is public.
You can say that (y, g, p) is the public key, or simply say that y is the
key if g and p (the public parameters) are implicitly known.
Participants can choose a different x and associated y on each execution
of the protocol, or have long term private public key pairs.


>The Check Point Firewall-1 Docs insist, that the public keys be used
>for p and g for the Oakley key exchange. I ask you: is this
>  - which of the two pubkeys will be p, which g?
>  - are they both always primes?
>  - are they both always suitable generators mod p?
>It just seems to me that Check Point isn't entirely sure themselves
>here. I'd appreciate a short cleanup...
>To my knowledge, g and p are globally defined, either in DH Groups
>(which are nothing but pre-defined g's and p's, right?), or
>otherwise set constant. Am I wrong about this?


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