In connection to a commitment scheme, how are witness and commitment different? Are 'Binding' and 'Hiding' properties defined w.r.t. witness and commitment or both?
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The commitment is the receiver's output from the protocol's initial phase,
and the opening value is a witness that the commitment is to whatever it's to.
The 'Binding' and 'Hiding' properties are defined w.r.t. the commitment scheme.