# How to use OR Proof of sigma protocol to prove a commitment C is a commitment to 0 or a commitment to 2

Such as the following relation: $$\mathcal{R} = \{(C,g;r): C = g^r \vee C = g^r h^2 \}$$

• Do you know the protocol(s) to prove the following relation $\mathcal R'=\{(C,g;r):C=g^r\}$ and $\mathcal R''=\{(C,g;r):C=g^rh^2\}$? Do you know how the sigma protocol OR composition works in general?
– SEJPM
Jul 4 at 9:42