In plain words: Two neural networks trained on each other's output bits lock into identical weights that keep changing together over time. That shared, ever-changing weight state can act as a secret key, letting them agree on one over a public channel.
Abstract · Neural Cryptography
Two neural networks which are trained on their mutual output bits show a novel phenomenon: The networks synchronize to a state with identical time dependent weights. It is shown how synchronization by mutual learning can be applied to cryptography: secret key exchange over a public channel.
Wolfgang Kinzel, Ido Kanter
arXiv:cond-mat/0208453 · cond-mat.dis-nn, cond-mat.stat-mech · submitted Aug 23, 2002
abstract · pdf · html · 9th International Conference on Neural Information Processing, Singapore, Nov. 2002
> Why does this work at all? What is the difference between the partner B and the attacker E, who both have the same information? The reason is that B can influence the network A whereas E can only listen.
In other words, the scheme works only as long as there's no MITM ("man in the middle") attack.