Some here may be interested in a new cryptosystem I've been working on which efficiently and privately proves the knowledge of secrets according to an policy defined by an AND/OR network:https://github.com/Blockstream/borromean_paper/raw/master/borromean_draft_0.01_34241bb.pdf
This new ring-signature is asymptotically 2x more efficient than the one used in Monero/Bytecoin: It needs n_pubkeys+1 field elements in the signature instead of 2 * n_pubkeys. In particular, it retains this 2x efficiency gain when doing an AND of many smaller rings, because the +1 term is amortized across all of them.
The paper also describes a new way to think about ring signatures; which might
be helpful to anyone who has looked at them before and found them confusing. (If we were successful, you'll think the new construction was so simple that it was completely obvious; I can assure you it was not... fortunately Andrew Poelstra came up with an especially good way to explain it.)
While the connection to Bitcoin may not be immediately obvious, I've used this as a building block in a much larger and more applicable cryptosystem which I'll be publishing, complete with implementation, shortly (I'm trying to not flood people with too many new ideas built on new ideas all at once, and I'm still working on the description of the other constructions). I think this construction is interesting in its own right, and I'd be happy to learn if someone knows of this being previously published (though I was unable to find anything prior).