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encrypt with the private key, and decrypt with the public key
That statement, and the very name privateEncrypt, is incompatible with standard terminology: "public" means known to all and opposes to "private"; and "encrypt" implies transforming some information $X$ into $Y$ in a way such that if $Y$ becomes public, $X$ does not.
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Perhaps an extensible version of the Twitter blue checkmark scheme?
A trusted central authority (Jack) sets up a parameterised system that allows signing keys to be produced whose verification keys match identifiers. A Twitter service user (Lil Nas) sets up an account with Jack. Jack carefully verifies that Lil Nas is whom they claim (or simply allows them ...
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