random Monero out of the system?
That project really have nothing to with Monero. The mixers just pool together funds. A very good one will pool tons of transactions together, identical amounts and disburse them to make sure everyone gets the same amount (in most cases) in a new addresses to obfuscate the origin of funds. Dirty money get mixed in with clean money, those with the dirty money would now have a degree of plausible deniability as their funds were washed. Essentially, breaks the link between the original source and the destination. If a government tries to search the origin of the funds that are in the new address, it'd be pretty damn hard because almost every deposit and withdraw into the mixer was identical. If the US or EU tried banning/sanctioning Monero, most they can do is forbid their citizens from utilizing the coin. Of course, nothing would actually be stopping those citizens from being able to interact with whatever service, just risking heavy consequences. Can't freeze nor seize XMR without the private key, nor can they see senders/receivers and amount being transferred, which would make their job harder if you aren't doing anything that would link to your true identity, e.g., sending XMR to a CeFi exchange.
Sanctions work only at the check points. (1) They can prevent CEXes from listing monero. (2) They can blacklist traceable coins that came from DEXes where you might have swapped it for XMR. Basically they can set choke points at the on-ramp and off-ramp services. Also the chainalysis can check if you have swapped the coins somewhere in a DEX.
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