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-The math and cryptography backing it isn't peer reviewed yet and in an infancy stage.
Fair, but I doubt that's going to matter all that much to people, assuming it gets even just a few months of successful operation under its belt.
I think it will matter at some point if indeed there is any bugs or exploits in its protocol. Why risk using technology that has not had years of review and testing done than something completely brand new?
I see more risk using something new that has just been developed and released and is not based on old cryptography.
If a DNM starts using Zerocoin, and it works fine for a few months, you really think people are gonna care all that much? It can gain a good deal of adoption without demonstrating rigorous academic robustness or decades of unbroken use.
I mean, yeah, people are not gonna dump their life savings into it, but a crypto-break, even for something with newish crypto, is probably a few notches down on the list of reasons why it'd be unwise to drop tons of wealth into the coin.
Yes I think people investing into such a system that had a flaw/exploit would care.
Your presumption is that after a few months that ZC will be considered "safe". It wouldn't be the first time we heard of a new technology (usage) that people thought was "safe" then found out to be very exploitable. (example brain wallets).
Yes anything new can have massive adoption, I mean look at adoption of windows 10. Looks like it is doing pretty good even though it is full of privacy issues.
http://www.forbes.com/sites/gordonkelly/2015/11/02/microsoft-confirms-unstoppable-windows-10-tracking/Not so sure everyone who uses windows 10 wants all of their key strokes logged or actions logged and sent back to Microsoft and then to the government agencies. But of course they would need to know this is going on in order for it to be an issue. Some people may not care but I bet you it isn't 100% of them that dont care.
Dr. Adam Back also discusses the draw backs of such a zerocash/ zerocoin implementation:
https://www.youtube.com/watch?v=3dAdI3Gzodo&feature=youtu.be&t=33m10s