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I have started a separate thread over here because I don’t really know what this means for the price, but I can help answer some of your other questions. Please feel free to ask more questions here or start a thread and I will do my best to answer you.
This makes me smile. Think zk think zcash. - you should, check the details at the end of the post for a whos who and the people involved.
It says zkSNARK, then yep it is very likely either work done by the zcash community, whether a project recognises that is different, clones of clones of clones can forget what they have cloned. - It does not mean privacy though.
I am not sure if rollups are part of the zcash network, from what I read it would be more useful on networks that have smart contracts that want to do off chain work. it seems to be a bunch of t transactions wrapped into one big z transaction. I am not sure of the privacy implications, because im not really an Ethereum or smart contracts kind of person - but I dont think they are being used in a privacy context here. I could be wrong though.
I haven’t really looked into zk rollup, so others will probably have a more informed opinion. but they say they use zkSNARKS, so they very likely to be using zcash technology in some form, if not certainly the maths done buy the people i outline below.
Maybe someone else can answer more definitely as to what function they perform in regards to Eth. do they offer any form of privacy? or is it just for correctness.
Ethereum and zcash are friends.
Here is a brief who’s who and what zk-snarks are.
Sorry if I am over simplifying things, I am trying to be thorough.
Hopefully this will show you how intertwined zk-snarks and zcash are. whilst they dont own the concept of zk or snarks, they are mathematical concepts, these are the people responsible for bringing them to crypto currencies.
the “ZK” used in ZK-SNARKS, and in cryptography in general references to the cryptographic concept of “Zero Knowledge Proofs”. Something the zcash team (and its predecessors) have successfully managed to integrate with blockchain technology
These have been around for quite a long time. - here is a reasonably good article on them.
the “SNARK” is much more interesting for us and refers to “Succinct Non-interactive Argument of Knowledge”
Which are a form NIZK’s:
 - “Bitansky, Nir; Canetti, Ran; Chiesa, Alessandro”
SNARKs to the best of my knowledge were first implemented in crypto currencies in the zerocash protocol by “Eli Ben-Sasson, Alessandro Chiesa, Christina Garman, Matthew Green, Ian Miers, Eran Tromer, and Madars Virza”
I honestly dont know of Madars involvement with the ECC or zcash beyond zerocoin.
The others are zcash founding scientists. Ian Miers and Matthew Green are on the Zcash Foundation board of directors and Eran is a zcash foundation Alumni member. (You can find Ian and Eran posting on the forums, along with many ecc, zfnd and other key community members.)
Which gets its SNARKiness from work by
There are more people involved so sorry for not mentioning you (I know Aviel Rubin had involvement in zerocash but I cannot find reference to him for that or zcash. I am probably not looking hard enough.)