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It is well-known that, in the setup phase of Pedersen commitment, it is necessary to generate $g,h\in G$. Then a user can compute $c = g^vh^r$ to commit the value $v$.

Is a trusted center needed to generate $g$ and $h$?

In other words, can $g$ and $h$ be publicly generated?

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  • $\begingroup$ I'm not sure if I'm right. If the commitment scheme is realized in ECC setting, then there are many well studied curves, such as BabyJubJub, in which parameters are fixed, such as the generator. Consequently, with the curve, the committor or trusted thrid party can randomly pick a element $s\in Z^*_n$, compute $h=g^s$ and publish the public value $h$ and BabyJubJub curve's parameters. $\endgroup$
    – ming alex
    Oct 12, 2023 at 6:47
  • $\begingroup$ I'm not sure this is duplicate, however, see What is a Pedersen commitment? $\endgroup$
    – kelalaka
    Oct 12, 2023 at 15:14

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