I find it interesting that Stefan Brands [1] solved the zero-knowledge authentication problem a couple of decades ago and his tools are still not widely applied. Given my bias against imaginary property, I believe that's because his patents on them are still valid -- and apparently owned by Microsoft at the moment [2].
> Stefan Brands [1] solved the zero-knowledge authentication problem a couple of decades ago
Reference? If you want people to take you seriously when you claim that someone's solution to a problem has been overlooked you have to provide a link to the (alleged) solution, not just to the author's biography.
Chapter 1 explains the usage of the protocols. Quoting from the book, on page 33:
"The authentication mechanism is such that the receiver not only authenticates the message, but also demonstrates a property of the attributes encoded into its certified key pair. The receiver has full control over which property is demonstrated: it can be any satisfiable proposition from proposition logic, where the atomic propositions are relations that are linear in the encoded attributes. Any other information about the attributes remains unconditionally hidden." (Emphasis mine.)
I will admit that the math was not something I studied in depth (and I definitely didn't check the proofs!), since crypto is at best a hobby for me and not my main job.
We are actually evaluating more recent advances in zero-knowledge systems. Stay tuned on more news soon in that front :)