There is a paper: U. M. Maurer, Secret key agreement by public discussion from common information, IEEE Trans. Inf. Theory, 39(3) 733-742 of 1993, with an IMHO fairly impressive title but having apparently for some unknown reasons been hithertofore ignored in the common textbooks on modern cryptography. The material there is way above my humble knowledge, hence my request: Could some experts kindly give a sketch of the main idea of the paper such that one could get at least a certain rough comprehension of it? Are there good open-source implementations of that key agreement scheme?
Maurer is likely making unrealistic assumptions about noise. The following excerpt is from the paper's conclusion:
The paper suggests the following conclusion for the implementation of cryptographic systems on given noisy communication channels. Such channels should not be converted into error-free channels by means of error-correcting codes, followed by a cryptographic protocol based on error-free channels because this design strategy would imply that Shannon's pessimistic inequality (2) applies and therefore perfect secrecy cannot be achieved unless an impractically large amount of shared secret key is available. Instead, cryptographic coding and error-control coding should be combined, resulting in a system achieving virtually perfect secrecy, with a (short) secret key being required only for authentication.
The author hopes that this paper and a subsequent paper on practical implementations will help to move perfect secrecy closer to being practical.
I'm not an expert either, but have an interest in new and unconventional cryptography. With research papers I find it helpful as a first pass to read the abstract and conclusion. Whatever claims made in the conclusion can then be referenced by going back in the paper. In this paper, the reliance on noise and error coding seemed both its strength and weakness.
What happens if an attacker can manipulate the noise/signal of the system? If they were able to reduce the noise of a channel, wouldn't an attacker be able to derive too much information about the cryptography from the coding? Here's a hypothetical attack: attacker Eve deliberately injects noise into a system, making system seem much noisier than it actually is, which the two communicating parties Alice and Bob then derive their probabilistic models from, but when Alice and Bob start exchanging data, Eve removes the noise.
By comparison Diffie-Hellman is a simpler overall scheme that makes no assumption about the underlying communications channel.
The gist of it is, Alice is sharing a password with Bob over walkie-talkie with terrible static. Sometimes Bob has to ask Alice to repeat the last character. But Alice will never comply with Eve's requests for repeats. So Bob gets to learn the entire password while Eve does not.
This is because occasionally Eve will be unsure of the last character, while Bob will have heard it perfectly.