Dear Henri Ruotsalainen,

possibly can help you:

• IKE (Internet Key Exchange) - used in the protocol IPsec - or
• MIKEY (Multimedia Internet KEYing), see RFC 3830

Much success and best regards

Anatol Badach

I think that your question needs further criteria to be answerable.

Let me code it:

-Common random source generates random variable X

-observer a gets to see random variable Xa =f(X)

-observer b gets to see random variable Xb=g(X)

-there is a non-linear function h such that g=hof

This is fairly general to allow for your requested protocol to be built...

Look at three examples of h: x**2, x**3, 1/(1+|x|), with one example of X being the equidistributed random variable - 1, 1 each with probability 1/2.

Assume f and g to be the identity function.

Then look at E(Xa) =0 and E(Xb) is either 1,0 or 1/2.

Therefore if you constrain h to be one among the three possibilities given above, then E(Xb) determines uniquely which h is selected from the set of three possibilities.

This is a trivial example where the question can be answered if b communicates to a an estimate of E(Xb). This becomes a coding/decoding issue, but a heavy condition has been added.

Maybe you could explain the semantic context of your question, to move from the above example (trivial) to richer responses...

Thank you Anatol Badach and Renaud Di Francesco for your kind responses! I agree that the original question is rather general and further details

should be delivered.

So let me elaborate a bit:

The research area in question is the wireless secret key agreement. In its classical setting two transceivers collect random wireless channel measurements from bidirectional communication (common source for randomness) and distill secret keys out of them. This works as long as the channel exhibits random variations due to movement of the transceivers or changes in the environment between the transceivers.

Some recent works on this topic have introduced concepts, where one of the two transceivers is able to control the wireless channel by e.g. steerable antennas. Hence the key agreement shall still work even if the channel between the antennas does not change. Now lets assume that these conditions apply for Alice and Bob. As far as I understand, Alice sees the random variable X which she uses to control her antenna(s). Therefore Bob sees correlated random variably Y, which is displaced version of X by the physical communication channel (antenna properties on both sides, wireless propagation, trasceiver impairments etc.).

The more detailed question thus becomes: How can Bob inform Alice (or vice-versa) about the displacement(s) so that no information is leaked to a 3rd party?

After some googling I came across with the paper "Common Randomness in Information Theory and Cryptography-Part I: Secret Sharing", where in the Chapter III the "Model CW (Channel type model with Wiretapper)" seems to apply to the above scenario(?)

Regards,

Henri

there are different ways to do this, one of them is reconciliation which could be achieved by using some error detection and correction codes, its not whether they share 100% alike information

Basically, there are three main steps for secure key generation based physical layer properties . These are 1) randomness extraction 2) reconciliation 3) privacy amplification .

We usually refer to key agreement by the reconciliation where some correction techniques can be used such as LDPC , cascaded , .... .

Due to the leak of the information in the reconciliation step , the privcy amplification can be utilized by the mean of some functions like universal hashing function