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For instance, Semaphore could be used by a service provider to offer anonymous logins to privacy-oriented customers, such that when a customer logs in, the provider can only know that they are a registered customer, but not which customer they are.
Zero-knowledge proofs allow a user to demonstrate that they have performed a predefined set of operations on some data, without revealing parts or all of said data.
If my government was stable for fifty years and then a bunch of morons get elected who do stupid shit, that trust is now worth shit, as is their backing.