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What makes cashu private?

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From my understanding:
You get a “token” when depositing, this token is a cryptographic signature, created by the system.
When you then later on withdraw, you provide this signature in a way that they can verify that it is valid, but they can never know exactly which deposit it correlates to.

Pretty much like normal bank notes? Correct me if I am wrong, if someone has a better understanding

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It's a bearer's instrument right?

I'm confused how you can give the token to someone else with out involving the mint. (Couldn't you reveal the token to someone as payment and then double spend it?)

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Yes you can, and I think they are only meant to be used by yourself or that the recipient redeems them instantly

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