Do you want to know what the results are, or how it works?
The results are essentially that a central party can pool together an arbitrary number of bitcoins, then issue a derivative instrument against that pool. Those derivative instruments can be constantly recreated, so they're not maintaining any history or linkability. Once you receive one, you can also redeem it, destroying it, and claim an equivalent value of bitcoin, which is removed from the pool.
Except there is no "central party", except at the initiation of the system; you can build it so the central party creates parameters but doesn't save anything, so he's just a normal participant after that, and can disappear. So it's almost as decentralized as Bitcoin/Satoshi.
How it works is a bit more complex; it involves zero knowledge proofs about the derivative instruments. This is sufficiently advanced crypto that it will be a burden to anyone trying to understand it.
There isn't anything in ZeroCash that I would describe as a derivative instrument.
The super-simplified explanation I would give is that it lets you encrypt the content of your transactions and prove just enough properties about the encrypted data so that the network can tell that the the transactions as valid without actually revealing any of the private specifics.
The math and crypto are fairly straight-forward, dunno why you're telling people they can't understand it.
I'm curious about implementation, though. Most derivatives have a cost of carry built-in and this doesn't. It also doesn't work unless you convert your bitcoin immediately; the blockchain doesn't forget.
Would you mind explaining the q-power knoweldge of exponent assumption and how someone verifying the recursively constructed proof can be confident that the prover actually knows a _specific_ satisfaction of the circuit themselves given that the proof is much smaller possible state of different inputs? :P
The results are essentially that a central party can pool together an arbitrary number of bitcoins, then issue a derivative instrument against that pool. Those derivative instruments can be constantly recreated, so they're not maintaining any history or linkability. Once you receive one, you can also redeem it, destroying it, and claim an equivalent value of bitcoin, which is removed from the pool.
Except there is no "central party", except at the initiation of the system; you can build it so the central party creates parameters but doesn't save anything, so he's just a normal participant after that, and can disappear. So it's almost as decentralized as Bitcoin/Satoshi.
How it works is a bit more complex; it involves zero knowledge proofs about the derivative instruments. This is sufficiently advanced crypto that it will be a burden to anyone trying to understand it.