Update groups.md

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ying tong 2023-01-18 10:49:29 -05:00 committed by GitHub
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@ -12,7 +12,7 @@ base $G$, i.e. finding $x$ such that $P = [x] G$, is hard in general.
## Pedersen commitment
The Pedersen commitment [[P99]] is a way to commit to a secret message in a verifiable
way. It uses two random public generators $G, H \in \mathbb{G},$ where $\mathbb{G}$ is a
cryptographic group of order $p$. A random secret $r$ is chosen in $\mathbb{Z}_q$, and the
cryptographic group of order $q$. A random secret $r$ is chosen in $\mathbb{Z}_q$, and the
message to commit to $m$ is from any subset of $\mathbb{Z}_q$. The commitment is
$$c = \text{Commit}(m,r)=[m]G + [r]H.$$