CoinJoin

Any transaction privacy system that hopes to hide user's addresses should start with some kind of anonymity network. This is no different. Fortunately networks like Tor, I2P, Bitmessage, and Freenet all already exist and could all be used for this. (Freenet would result in rather slow transactions, however)

However, gumming up "taint analysis" and reducing transaction sizes doesn't even require that the users be private from each other. So even without things like tor this would be no worse than regular transactions.

In the simplest possible implementation where users meet up on IRC over tor or the like, yes they do. The next simplest implementation is where the users send their input and output information to some meeting point server, and the server creates the transaction and asks people to sign it. The server learns the mapping, but no one else does, and the server still can't steal the coins.

More complicated implementations are possible where even the server doesn't learn the mapping.

E.g. Using chaum blind signatures: The users connect and provide inputs (and change addresses) and a cryptographically-blinded version of the address they want their private coins to go to; the server signs the tokens and returns them. The users anonymously reconnect, unblind their output addresses, and return them to the server. The server can see that all the outputs were signed by it and so all the outputs had to come from valid participants. Later people reconnect and sign.

Similar things can be accomplished with various zero-knowledge proof systems.

No. The same privacy can be achieved in a decentralized manner where all users act as blind-signing servers. This ends up needing n^2 signatures, and distributed systems are generally a lot harder to create. I don't know if there is, or ever would be, a reason to bother with a fully distributed version with full privacy, but it's certainly possible.

Yes, this can be DOS attacked in two different ways: someone can refuse to sign a valid joint transaction, or someone can spend their input out from under the joint transaction before it completes.

However, if all the signatures don't come in within some time limit, or a conflicting transaction is created, you can simply leave the bad parties and try again. With an automated process any retries would be invisible to the user. So the only real risk is a persistent DOS attacker.

In the non-decentralized (or decentralized but non-private to participants) case, gaining some immunity to DOS attackers is easy: if someone fails to sign for an input, you blacklist that input from further rounds. They are then naturally rate-limited by their ability to create more confirmed Bitcoin transactions.

Gaining DOS immunity in a decentralized system is considerably harder, because it's hard to tell which user actually broke the rules. One solution is to have users perform their activity under a zero-knowledge proof system, so you could be confident which user is the cheater and then agree to ignore them.

In all cases you could supplement anti-DOS mechanisms with proof of work, a fidelity bond, or other scarce resource usage. But I suspect that it's better to adapt to actual attacks as they arise, as we don't have to commit to a single security mechanism in advance and for all users. I also believe that bad input exclusion provides enough protection to get started.

Not quite. The anonymity set size of a single transaction is limited by the number of parties in it, obviously. And transaction size limits as well as failure (retry) risk mean that really huge joint transactions would not be wise. But because these transactions are cheap, there is no limit to the number of transactions you can cascade.

In particular, if you can build transactions with m participants per transaction you can create a sequence of m*3 transactions which form a three-stage switching network that permits any of m^2 final outputs to have come from any of m^2 original inputs (e.g. using three stages of 32 transactions with 32 inputs each 1024 users can be joined with a total of 96 transactions). This allows the anonymity set to be any size, limited only by participation.

In practice I expect most users only want to prevent nosy friends (and thieves) from prying into their financial lives, and to recover some of the privacy they lost due to bad practices like address reuse. These users will likely be happy with only a single pass; other people will just operate opportunistically, while others may work to achieve many passes and big anonymity sets. All can coexist.

As a crypto and computer science geek I'm super excited by Zerocoin: the technology behind it is fascinating and important. But as a Bitcoin user and developer the promotion of it as the solution to improved privacy disappoints me.

Zerocoin has a number of serious limitations:

• It uses cutting-edge cryptography which may turn out to be insecure, and which is understood by relatively few people (compared to ECDSA, for example).
• It produces large (20kbyte) signatures that would bloat the blockchain (or create risk if stuffed in external storage).
• It requires a trusted party to initiate its accumulator. If that party cheats, they can steal coin. (Perhaps fixable with more cutting-edge crypto.)
• Validation is very slow (can process about 2tx per second on a fast CPU), which is a major barrier to deployment in Bitcoin as each full node must validate every transaction.
• The large transactions and slow validation also means costly transactions, which will reduce the anonymity set size and potentially make ZC usage unavailable to random members of the public who are merely casually concerned about their privacy.
• Uses an accumulator which grows forever and has no pruning. In practice this means we'd need to switch accumulators periodically to reduce the working set size, reducing the anonymity set size. And potentially creating big UTXO bloat problems if the horizon on an accumulator isn't set in advance.

Some of these things may improve significantly with better math and software engineering over time.

But above all: Zerocoin requires a soft-forking change to the Bitcoin protocol, which all full nodes must adopt, which would commit Bitcoin to a particular version of the Zerocoin protocol. This cannot happen fast—probably not within years, especially considering that there is so much potential for further refinement to the algorithm to lower costs. It would be politically contentious, as some developers and Bitcoin businesses are very concerned about being overly associated with "anonymity". Network-wide rule changes are something of a suicide pact: we shouldn't, and don't, take them lightly.

CoinJoin transactions work today, and they've worked since the first day of Bitcoin. They are indistinguishable from normal transactions and thus cannot be blocked or inhibited except to the extent that any other Bitcoin transaction could be blocked.

(As an aside: ZC could potentially be used externally to Bitcoin in a decentralized CoinJoin as a method of mutually blinding the users in a DOS attack resistant way. This would allow ZC to mature under live fire without taking its costs or committing to a specific protocol network-wide.)

The primary argument I can make for ZC over CoinJoin, beyond it stoking my crypto-geek desires, is that it may potentially offer a larger anonymity set. But with the performance and scaling limits of ZC, and the possibility to construct sorting network transactions with CJ, or just the ability to use hundreds of CJ transactions with the storage and processing required for one ZC transactions, I don't know which would actually produce bigger anonymity sets in practice. E.g. To join 1024 users, just the ZC redemptions would involve 20k * 1024 bytes of data compared to less than 3% of that for a complete three-stage cascade of 32 32-way joint transactions. Though the ZC anonymity set could more easily cross larger spans of time.

The anonymity sets of CoinJoin transactions could easily be big enough for common users to regain some of their casual privacy and that's what I think is most interesting.

CoinWitness is even rocket-sciency than Zerocoin, it also shares many of the weaknesses as a privacy-improver: Novel crypto, computational cost, and the huge point of requiring a soft fork and not being available today. It may have some scaling advantages if it is used as more than just a privacy tool. But it really is overkill for this problem, and won't be available anytime real soon.

The two main ready-to-use software CoinJoin implementations are Wasabi Wallet (https://wasabiwallet.io/) and JoinMarket (https://github.com/Joinmarket-Org/joinmarket-clientserver).

Wasabi works thanks to a CoinJoin coordinator (run by zkSNACKs Ltd., the company that is sponsoring the development of Wasabi) who cannot steal from, nor breach the privacy of the participants. The company makes its income by taking a fee (0.003% * anonymity set) from each CoinJoin transaction.

JoinMarket, instead, works by creating a new kind of market consisting of one group of participants (called market makers) that will always be available to take part in CoinJoins at any time and another group participants (called market takers) that can create a CoinJoin at any time. The takers pay a fee which incentivizes the makers.