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Most cryptocurrencies are anonymous where the origin of coins is not known and transactions are also anonymous (this may not be 100% true but lets assume perfect anonymity). The society prevents criminalization (using the coin to commit or pay for crime) of cryptocurrencies by forcing the exchanges that trade crypto for fiat to adhere to Anti Money Laundering (AML) rules.

However this assumes that the criminal wants to convert to fiat currency. But what if there is sufficiently big economy for the currency (sufficiently big market, businesses accepting the cryptocurrency etc.), and the criminal can live without the need of fiat money? Can the society prevent this behavior somehow other than outlaw cryptocurrencies?

The only solution I can see is to request the use of governmentally issued electronic signatures to sign all transactions which would allow pseudonymity in a way that one would be identifiable to the government but not to the ordinary public crowd.

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    Every crypto is unencrypted if you have a sufficiently big wrench: imgs.xkcd.com/comics/security.png – user4012 Dec 21 '17 at 18:20
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    Sellers currently have to report large cash purchases. I fail to see why they wouldn't also have to report large cryptocurrency purchases as well. Try buying anything over $10k in the US with cash (i.e. actual, physical cash). – Harrison Paine Dec 21 '17 at 19:28
  • For this purpose you can treat them exactly as cash, I think. – Federico Poloni Dec 22 '17 at 11:15
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Blockchain-based cryptocurrencies like Bitcoin aren't actually that untraceable, because the transfer history of every wallet is public. When cryptocurrencies ever become economically relevant, you can expect law enforcement to put all those currently hyped big data analysis and machine learning technologies to use and data-mine the blockchains for suspicious transactions. If you can then link a person to their wallet, you have proof that they initiated or received those transactions.

And making that link might not actually be that hard. First, we got usual instruments of police procedure like ip traffic surveillance, seizing the devices of suspects, etc.. And then it might be hard in a cryptocurrency-based economy to do many kinds of business without ever revealing your identity to the receiver of a payment. Order something online? Pay your rent? Your physical address is now linked to your wallet. Pay for something which requires a permit or age verification? Your name and face biometry is now linked to your wallet. Have a job with social security benefits? Pay your taxes? You just handed the link to the government without them even having to issue a warrant.

There are of course ways to "launder" cryptocurrencies, for example by sending them through a cryptocurrency tumbler service. But these are equivalent to the money laundering schemes we already have with traditional currency and we can expect that they will be suppressed the same way. So if the wallet you use to receive your salary and pay your taxes has transactions with known cryptocurrency laundering services, then you will likely get into trouble. Just like you will get into trouble in the present world if you regularly show up with a plastic bag full of banknotes at your local bank and try to deposit them without having a good explanation how you obtained them.

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    @Lope That would be one of those cryptocurrency tumbler services I talked about in the 3rd paragraph. They will likely be made illegal or heavily regulated in a cryptocurrency-based economy. – Philipp Dec 21 '17 at 18:03
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    Monero should be pretty anonymous with ringCT and Kovri, right? – janh Dec 21 '17 at 19:14
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    @notstoreboughtdirt Yes, and the "how could they do that?" was the question, basically. This answer does assume that cryptocurrencies are pseudonymous at best. – janh Dec 21 '17 at 20:26
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    One quibble, I have never had a bank question me when I showed up with even thousands of USD in cash to deposit. Although I guess if I did that regularly instead of once every decade, they might... – Jared Smith Dec 21 '17 at 20:53
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    @JaredSmith banks are required to file a form if you have a transaction involving $10,000 or more in cash, and in some other situations. I don't think banks always tell you when they do this. – Justin Lardinois Dec 21 '17 at 22:08
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I imagine the future to be filled with government backed cryptocurrencies, where trade in one country is only with their own government-backed flavor. In this future hypothetical situation, the government would know when, where, how much was transferred and spent at all times.

Blockchain currencies like Ethereum already support and encourage new currencies to build on top of their blockchain 'api'

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I think that Philipp's answer is not accurate enough. Even in cryptocurrencies that are pseudonymous and provide the least anonymity (like bitcoin) you can use your wallet's address only once in a transaction. This tears the link between multiple transactions. If you delete the private keys for your spend transactions no one can prove that you actually spent that money (in transactions that are historically linked to your current unspent money).

The situation then looks like this: your employer pays you salary from their address A to your newly created address B. You then buy something with B and pay to newly created address C and return your change to your new address D. This procedure repeats over and over again. If you are careful and spend your change in a given branch completely without merging it with your other branch (as a transaction input for bigger payment) then the money from that branch basically disappears and no one is able to connect it to the money in your other branches.

By branching I mean to ask for your income to be split right at the beginning - your employer pays your monthly salary to your 10 newly created addresses. Things get a bit more complicated like this.

For further reading regarding bitcoin address reuse you can see following:

Cryptos whose goal is anonymity bring you then to a whole new level. With Monero the transactions are completely unlinkable for a blockchain observer and the ammounts are hidden too. See here for details.

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