Does XChaCha20 (built from ChaCha20 just like XSalsa20 is built from Salsa20) exist and have XSalsa20's desirable properties?
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Unfortunately, there is no specification for XChaCha20. But several implementations provide a HChaCha20 function, built the same way as HSalsa20.
XChaCha20 can be built with HChaCha20 + ChaCha20, and the security proof is similar to the one for XSalsa20.
The Libsodium documentation has a section on HChaCha20, which includes a code snippet to build XChaCha20 out of it.
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