Why did you pick a modp group instead of an EC group?
Why doesn't Bob send y? Y is derivable from what Bob sends. (Your zero knowledge claim is at least a bit wrong, since Bob is sending correlated numbers and, in fact, y can be derived from them.)
Bob's sent values can be rewritten as y2^b, y2^c, and y^-1 * f_1 * f_2, which makes me wonder why f_3 is sent.
Why does Bob prove knowledge of x+b+c? Can you clarify the spoofing attack?
What prevents double spending if the tracker is malicious?
modp groups are easier to implement, I was look into EC but I may come back to it later.
Bob doesn't want to send y directly because then another man in the middle could, before the transaction times out, forward y, spoof his own b and c, forward the verification of x and then verify his own b and c. Then he cannot spend the coin but he can make it unspendable.
If one tracker is malicious, he'll be out of sync with all the other trackers to which the transaction is also broadcast to. Every single known tracker would need to be compromised (they are all public).
I have no idea if I'm doing this right because I am new to HN. But here is a very early WIP of a zero-knowledge cryptocurrency. I try to keep code terse to avoid bugs. Have at it!
However, if the tracker is centralized, doesn't protection against double spends basically come for free?
Or, maybe not because of the other things?
Oh, wait, ok so in this situation does the tracker have any privileged information?
It doesn't look like it, So, another party could take the place of the tracker if the tracker went down?
I don't understand the proof of stake bit in the readme. I don't see anything about staking the coin, and I generally don't understand how proof of stake applies to something like this?
The proof of stake is essentially for free; as described above, by verifying you know the current secret key of the coin, you verify you own that coin. There is no transaction history; the coin is secret and updated randomly on every transaction.
It needs a central tracker, and it needs a secure offline channel to transmit keys. The reason zerocoin uses zero-knowledge proofs is to make it impossible to trace the history of a coin. This is another property that this project does not have.
This (as far as I know) does make it impossible to trace the history of a coin, because there is no recorded transaction history, assuming you don't send the transaction details directly from your ip (and valid coin transfers are mathematically impossible to spoof from e.g. an exit node). You also don't need a centralized tracker, you just need a public record of all known coins which is kept in sync across several mirrors. I should clarify that in the readme; the only reason why I mention assuming a centralized tracker is for the performance estimate, because syncing trackers would induce overhead. Unless you see something I am missing...
The reason why this uses zero-knowledge proofs is twofold; first, to allow anonymization of individual transaction ids by ensuring it is impossible to spoof transactions without knowing the secret key of the corresponding coin, and second to avoid the use of a blockchain which further degrades anonymity. Again, it may be that you have discovered a reason why this does not hold, in which case I would be interested to hear it!
Regarding the matter of coin transfer, this was a design decision because of the project scope. I could have spent many days implementing a transaction system which did not depend on the secrecy of keys, but I have other commitments. That being said, there are a subset of transactions (involving money, but also authentication of physical goods in transit, for example) which can potentially be treated this way. For instance, I can use it to verify the user is in possession of a particular hardware (a physical "coin") which stores the secret key in encrypted form. Which could be useful in e.g. shipping applications, who knows.
http://www.8-bitcentral.com/images/nintendo/promo/virtualBoy...
Real 3d graphics, that's why!
For all the fancy cryptography this uses, I don't see how it provides any more security properties than a central actor having a databases of balances and requiring a cryptographic signature (like RSA, ECDSA etc) to authorize transactions. I don't see an extension path either.
Since the zero-knowledge proof is interactive, I am unsure how the central tracker could even be audited not to spoof transactions.
In theory, yes, a tracker could be malicious. It could even simply delete its record of all the coins and then refuse all transactions. Or change every coin so it cannot be spent. Actually the one thing it couldn't do is spoof transactions, because it doesn't know the secret key of a single coin it tracks. So it would have to make up a new coin, which would be easily detectable by other trackers because there must be a public consensus on how new coins are created (i.e., their public keys must be prime). So you would, once again, have to compromise every single tracker to spoof a transaction. Then you are right that there is no way to audit, but then you have bigger problems anyway (like people stealing money from exchanges) even before you get there.
Which brings me to the /real/ problem with my implementation, the coins are not worth nearly as much as bitcoin or zerocoin yet :P.
Suspicious Simon now wonders if Alice actually had they key. Maybe she didn't and Tom gave her easy challenges? How can Simon be sure Alice has the key?
