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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    $\begingroup$ What research have you done? Have you read standard textbooks on commitment schemes? This is a very basic level question, and should be settled by reading standard references. I expect you to do a significant amount of research/self-study on your own before asking; this site is not a replacement for that. $\endgroup$ – D.W. Oct 4 '14 at 5:28
  • $\begingroup$ @D.W. Suggest me a good one. $\endgroup$ – Holmes.Sherlock Oct 4 '14 at 8:10
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    $\begingroup$ This site is not a book recommendation service, but Lindell & Katz is good for much intro level material, and Goldreich's book is worth reading too. $\endgroup$ – D.W. Oct 4 '14 at 15:23

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.

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    $\begingroup$ So, a witness is committed. Right? $\endgroup$ – Holmes.Sherlock Oct 1 '14 at 19:57
  • $\begingroup$ Not necessarily. $\:$ A bit or string is committed to. $\:$ That bit or string might $\hspace{1.8 in}$ happen to be a witness to something else. $\;\;\;\;$ $\endgroup$ – user991 Oct 1 '14 at 20:09
  • $\begingroup$ Even in Groth-Sahai scheme, they have introduced something called 'prof'. I am getting confused to distinguish among proof, witness and commitment. According to their construction, it is clear. The difficulty is to port the same idea to other commitment schemes.I'm going through another polynomial commitment scheme where 'prover' shares the witness with the 'verifier' along with the commitment to the polynomial. I was under the impression that only commitment is enough to convince the verfier. But, my idea is getting jumbled up. $\endgroup$ – Holmes.Sherlock Oct 1 '14 at 20:29

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