...Zeroknowledge coins require a "trusted set up". We need to be absolutely sure we can trust whoever set it up...
From the first paragraph of the Zcoin section:
Since monetary inflation of any kind would be detected immediately this also mitigates any trust issues during initial setup.
Exactly!
Also see this (
http://zerocoin.org/q_and_a)
Q.Could you put a backdoor in it?
A.Not covertly. The paper has a provably secure protocol in it which is anonymous (technical note: anonymity holds even if the trusted set up is screwed with, so no thats not a backdoor), so absent modifications there is no way to track users. The software will be open source and so any attempt to modify the protocol by inserting a backdoor would be rather obvious.
Trusted setup is absolutely necessary in case of Zero
Cash implementation, buy
not in ZeroCoin. In this aspect ZCoin is superior to ZCash.