Commitment scheme: hiding property Given two commitment schemes $Com_1, Com_2$ (both have the hiding property), I'd like to prove $Com_1(m) || Com_2(m)$ is also hiding.

I built these hybrids and want to show $H_0 =_c H_1 =_c H_2$.

\begin{align}
H_0 &amp;= Com_1(m) || Com_2(m) \\
H_1 &amp;= R_1 || Com_2(m) \\
H_2 &amp;= R_1 || R_2
\end{align}

For $H_1 =_c H_2$: If some $D$ tells apart $H_1$ from $H_2$ then we can distinguish $Com_2(m)$ and $R_2$ by prepending some random $R_1$ and then call $D$.

But how could we prove $H_0 =_c H_1$?
I hope this is not homework. It should be almost the same as proving $H_1=_cH_2$. Just let the distinguisher (that distinguishes $Com_1(m)$ and $R_1$) generate and append $Com_2(m)$ in both worlds. This can perfectly simulate the view of the distinguisher that distinguishes $H_0$ and $H_1$.